Details

sample23.0ms

Algorithm

intervals

Results

11.0ms

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: 28.1b

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))
27.5b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite71.0ms

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:

9.0ms	(+ (* y.re y.re) (* y.im y.im))
8.0ms	(- (* 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)))

series135.0ms

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))
75.0ms	(/ (- (* 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

prune178.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 27.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (* x.im y.re) (* x.re y.im))
16.8b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
29.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite53.0ms

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))
26.0ms	(/ (- (* 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)))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series203.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* x.im y.re) (* x.re y.im))
102.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
31.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
33.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify96.0ms

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

10 alts after pruning (10 fresh and 0 done)

Merged error: 24.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (* x.im y.re) (* x.re y.im))
16.8b	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im)))
29.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite51.0ms

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:

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

series174.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* x.im y.re) (* x.re y.im))
69.0ms	(/ (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)))
33.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify67.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	264	889
1	808	842
2	2357	837
3	5001	837

prune278.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 24.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (* x.im y.re) (* x.re y.im))
16.8b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
29.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite53.0ms

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))
25.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
11.0ms	(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))
103.0ms	(/ (- (* 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)))
36.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify99.0ms

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

prune267.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 24.1b

regimes150.0ms

Accuracy

3.3% (2.8b remaining)

Error of 26.4b against oracle of 23.5b and baseline of 26.4b

bsearch43.0ms

Steps

Iters	Range		Point
9	1.4444100680103096e+82	2.0449168201690372e+88	2.0132411455167335e+88

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	20
1	30	20
2	30	20

end0.0ms

sample568.0ms

Algorithm

intervals

Results

289.0ms

8506×

body

valid