Details

Time bar (total: 3.1s)

sample24.0ms

Algorithm
intervals
Results
12.0ms272×body80valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0157
1157

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 26.9b

Counts
2 → 1

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.9b
(+ (* x.re y.re) (* x.im y.im))
26.4b
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite28.0ms

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:
6.0ms
(+ (* y.re y.re) (* y.im y.im))
6.0ms
(+ (* x.re y.re) (* x.im y.im))
14.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series194.0ms

Counts
3 → 9
Calls
3 calls:
29.0ms
(+ (* y.re y.re) (* y.im y.im))
45.0ms
(+ (* x.re y.re) (* x.im y.im))
120.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify130.0ms

Algorithm
egg-herbie
Counts
62 → 62
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0272527
11164479
24437477
35002477

prune147.0ms

Filtered
62 candidates to 49 candidates (79.0%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New57562
Fresh000
Picked011
Done000
Total57663

Merged error: 26.2b

Counts
63 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.9b
(+ (* x.re y.re) (* x.im y.im))
16.8b
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
26.2b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.2b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite22.0ms

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:
3.0ms
(+ (* x.re y.re) (* x.im y.im))
9.0ms
(/ (+ (* 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)))

series204.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(+ (* x.re y.re) (* x.im y.im))
102.0ms
(/ (+ (* 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)))
34.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify81.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (23.0ms)

IterNodesCost
0273893
1868840
22679828
35002828

prune231.0ms

Filtered
96 candidates to 74 candidates (77.1%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New92496
Fresh134
Picked011
Done011
Total939102

Merged error: 23.7b

Counts
102 → 9

localize22.0ms

Local error

Found 4 expressions with local error:

26.2b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.2b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.2b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.2b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 add-cube-cbrt *-un-lft-identity sqrt-div
4×add-exp-log rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 add-cbrt-cube flip-+ add-log-exp
Counts
4 → 60
Calls
4 calls:
3.0ms
(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)))
4.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series150.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
35.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
41.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
34.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify142.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 5 (136.0ms)

IterNodesCost
089400
1215388
2503388
31265388
44227388
55002384

prune247.0ms

Filtered
72 candidates to 60 candidates (83.3%)
Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New72072
Fresh066
Picked011
Done022
Total72981

Merged error: 23.7b

Counts
81 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

17.5b
(cbrt (+ (* x.re y.re) (* x.im y.im)))
17.5b
(cbrt (+ (* x.re y.re) (* x.im y.im)))
26.2b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.2b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×pow1 cbrt-prod sqrt-prod
4×add-exp-log cbrt-div flip3-+ sqrt-div add-cbrt-cube flip-+ add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 56
Calls
4 calls:
3.0ms
(cbrt (+ (* x.re y.re) (* x.im y.im)))
3.0ms
(cbrt (+ (* x.re y.re) (* x.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)))

series269.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(cbrt (+ (* x.re y.re) (* x.im y.im)))
99.0ms
(cbrt (+ (* x.re y.re) (* x.im y.im)))
38.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
34.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify118.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 4 (112.0ms)

IterNodesCost
0254480
1655456
21709444
34253438
45003436

prune214.0ms

Filtered
68 candidates to 60 candidates (88.2%)
Pruning

9 alts after pruning (5 fresh and 4 done)

PrunedKeptTotal
New68068
Fresh055
Picked011
Done033
Total68977

Merged error: 23.7b

Counts
77 → 9

regimes190.0ms

Accuracy

25.3% (2.2b remaining)

Error of 25.5b against oracle of 23.3b and baseline of 26.3b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02921
13321
23621
33821
43821

end0.0ms

sample591.0ms

Algorithm
intervals
Results
379.0ms8469×body80valid

Profiling

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