Details

Time bar (total: 3.4s)

sample21.0ms

Algorithm
intervals
Results
10.0ms272×body80valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0157
1157

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.9b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.3b
(+ (* x.re y.re) (* x.im y.im))
22.5b
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite17.0ms

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:
2.0ms
(+ (* 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)))

series145.0ms

Counts
3 → 9
Calls
3 calls:
27.0ms
(+ (* y.re y.re) (* y.im y.im))
34.0ms
(+ (* x.re y.re) (* x.im y.im))
84.0ms
(/ (+ (* 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 (28.0ms)

IterNodesCost
0272527
11164479
24451477
35003477

prune185.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 22.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(+ (* x.re y.re) (* x.im y.im))
14.7b
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
26.8b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.8b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite23.0ms

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))
12.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
3.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series220.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(+ (* x.re y.re) (* x.im y.im))
111.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (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)))

simplify83.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
0273893
1868840
22693828
35001828

prune292.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 20.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b
(+ (* x.re y.re) (* x.im y.im))
14.7b
(/ (* 1 (+ (* x.re y.re) (* x.im y.im))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
26.8b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.8b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
11×add-exp-log
10×add-cube-cbrt *-un-lft-identity
9×add-cbrt-cube
6×pow1 times-frac sqrt-div associate-/r* add-log-exp
5×flip3-+ flip-+
3×div-exp
2×cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ prod-exp associate-/r/ associate-/l/
1×+-commutative frac-2neg 1-exp clear-num sum-log cbrt-unprod div-inv associate-/l*
Counts
4 → 73
Calls
4 calls:
2.0ms
(+ (* x.re y.re) (* x.im y.im))
9.0ms
(/ (* 1 (+ (* x.re y.re) (* x.im y.im))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
3.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series213.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(+ (* x.re y.re) (* x.im y.im))
107.0ms
(/ (* 1 (+ (* x.re y.re) (* x.im y.im))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
41.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
36.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify119.0ms

Algorithm
egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 3 (112.0ms)

IterNodesCost
0312660
11314596
24715596
35001595

prune257.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 20.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b
(+ (* x.re y.re) (* x.im y.im))
14.7b
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
26.8b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.8b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite23.0ms

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))
11.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
3.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series255.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(+ (* x.re y.re) (* x.im y.im))
135.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
46.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
40.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify80.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (23.0ms)

IterNodesCost
0273893
1868840
22693828
35001828

prune481.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 20.9b

regimes240.0ms

Accuracy

0% (3.1b remaining)

Error of 26.5b against oracle of 23.4b and baseline of 26.5b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02214
12414
22414

end0.0ms

sample526.0ms

Algorithm
intervals
Results
311.0ms8448×body80valid