Details

Time bar (total: 3.3s)

sample20.0ms

Algorithm
intervals
Results
9.0ms267×body80valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0157
1157

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.7b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.7b
(+ (* x.re y.re) (* x.im y.im))
27.2b
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite18.0ms

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
4×flip3-+ flip-+
3×pow1 associate-/r* associate-/l*
2×+-commutative sum-log associate-/r/ associate-/l/
1×cbrt-undiv frac-2neg div-exp clear-num div-inv
Counts
3 → 53
Calls
3 calls:
3.0ms
(+ (* y.re y.re) (* y.im y.im))
2.0ms
(+ (* x.re y.re) (* x.im y.im))
11.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series143.0ms

Counts
3 → 9
Calls
3 calls:
30.0ms
(+ (* y.re y.re) (* y.im y.im))
31.0ms
(+ (* x.re y.re) (* x.im y.im))
82.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify133.0ms

Algorithm
egg-herbie
Counts
62 → 62
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0272527
11164479
24451477
35003477

prune173.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 26.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.7b
(+ (* x.re y.re) (* x.im y.im))
17.5b
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
29.5b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.5b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite27.0ms

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
5×flip3-+ flip-+
3×associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/ associate-/l/
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv
Counts
4 → 84
Calls
4 calls:
2.0ms
(+ (* x.re y.re) (* x.im y.im))
15.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
4.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series218.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(+ (* x.re y.re) (* x.im y.im))
114.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
36.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
37.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify83.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
0273895
1868840
22693828
35001828

prune283.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 25.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.7b
(+ (* x.re y.re) (* x.im y.im))
17.5b
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
29.5b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.5b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite27.0ms

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
5×flip3-+ flip-+
3×associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/ associate-/l/
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv
Counts
4 → 84
Calls
4 calls:
2.0ms
(+ (* x.re y.re) (* x.im y.im))
14.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
4.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series219.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(+ (* x.re y.re) (* x.im y.im))
115.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
37.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
36.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify84.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
0273893
1868840
22693828
35001828

prune295.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 25.8b

localize15.0ms

Local error

Found 4 expressions with local error:

9.2b
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))))
29.5b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.5b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.5b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite31.0ms

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
5×flip3-+ flip-+
4×add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2 associate-/l*
2×associate-/r/ associate-/l/
1×cbrt-undiv frac-2neg div-exp clear-num div-inv
Counts
4 → 100
Calls
4 calls:
13.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (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)))
4.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series314.0ms

Counts
4 → 12
Calls
4 calls:
199.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))))
36.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
42.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
37.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify78.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (22.0ms)

IterNodesCost
02941227
18711172
225451144
350011144

prune373.0ms

Pruning

11 alts after pruning (7 fresh and 4 done)

Merged error: 25.8b

regimes236.0ms

Accuracy

0% (3.0b remaining)

Error of 26.4b against oracle of 23.4b and baseline of 26.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01713
11713

end0.0ms

sample494.0ms

Algorithm
intervals
Results
283.0ms8442×body80valid