Details

Time bar (total: 3.3s)

sample21.0ms

Algorithm
intervals
Results
9.0ms270×body80valid

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0197
1367
2487
3667
4727
5727

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.5b

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))
22.2b
(/ (- (* 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)))

series166.0ms

Counts
3 → 9
Calls
3 calls:
28.0ms
(+ (* y.re y.re) (* y.im y.im))
43.0ms
(- (* x.im y.re) (* x.re y.im))
95.0ms
(/ (- (* 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 (31.0ms)

IterNodesCost
0292541
11273493
25002491

prune170.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 21.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b
(- (* x.im y.re) (* x.re y.im))
13.5b
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
26.3b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.3b
(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))))
8.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
10.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series237.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(- (* x.im y.re) (* x.re y.im))
118.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
36.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
39.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify96.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
0304910
1990857
23354845
35001845

prune280.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 20.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b
(- (* x.im y.re) (* x.re y.im))
13.6b
(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im)))
26.3b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.3b
(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)))
7.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
8.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series226.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(- (* x.im y.re) (* x.re y.im))
95.0ms
(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im)))
52.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
37.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify66.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
0264889
1808842
22357837
35001837

prune294.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 20.2b

localize15.0ms

Local error

Found 4 expressions with local error:

7.1b
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))))
26.3b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.3b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.3b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
45×sqrt-prod
32×add-sqr-sqrt
29×add-cube-cbrt *-un-lft-identity
27×times-frac
10×sqrt-div
9×associate-/r*
7×pow1
6×add-exp-log add-cbrt-cube
4×flip3-+ flip-+ add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2 associate-/l*
2×associate-/r/ associate-/l/
1×cbrt-undiv flip3-- frac-2neg div-sub div-exp clear-num flip-- div-inv
Counts
4 → 101
Calls
4 calls:
27.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))))
8.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
10.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
8.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series324.0ms

Counts
4 → 12
Calls
4 calls:
209.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))))
37.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
37.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
41.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify84.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
03291241
110311186
231121158
350011158

prune339.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 20.2b

regimes158.0ms

Accuracy

0% (3.0b remaining)

Error of 25.5b against oracle of 22.5b and baseline of 25.5b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01613
11613

end0.0ms

sample557.0ms

Algorithm
intervals
Results
278.0ms8503×body80valid