Details

Time bar (total: 3.5s)

sample24.0ms

Algorithm
intervals
Results
13.0ms267×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: 25.8b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.6b
(+ (* x.re y.re) (* x.im y.im))
25.4b
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite16.0ms

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:
4.0ms
(+ (* y.re y.re) (* y.im y.im))
3.0ms
(+ (* x.re y.re) (* x.im y.im))
8.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series137.0ms

Counts
3 → 9
Calls
3 calls:
26.0ms
(+ (* y.re y.re) (* y.im y.im))
29.0ms
(+ (* x.re y.re) (* x.im y.im))
81.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify136.0ms

Algorithm
egg-herbie
Counts
62 → 62
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0272527
11164479
24451477
35003477

prune171.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 25.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b
(+ (* x.re y.re) (* x.im y.im))
13.3b
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
29.0b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.0b
(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)))

series212.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(+ (* x.re y.re) (* x.im y.im))
105.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
35.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
39.0ms
(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

prune267.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 23.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b
(+ (* x.re y.re) (* x.im y.im))
13.3b
(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.im y.im)))
29.0b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.0b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite21.0ms

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
5×flip3-+ flip-+
3×associate-/r*
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))
8.0ms
(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.im y.im)))
3.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
3.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series184.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(+ (* x.re y.re) (* x.im y.im))
81.0ms
(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.im y.im)))
35.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
38.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify74.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (23.0ms)

IterNodesCost
0263885
1831838
22301833
35001833

prune288.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 23.2b

localize18.0ms

Local error

Found 4 expressions with local error:

6.9b
(/ (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))))
29.0b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.0b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.0b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
585×sqrt-prod
567×times-frac
302×add-sqr-sqrt
299×add-cube-cbrt *-un-lft-identity
50×sqrt-div
33×associate-/l*
22×associate-/r/
14×flip3-+ flip-+
11×div-inv
9×add-exp-log associate-/r* add-cbrt-cube
7×pow1
4×add-log-exp
3×cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 div-exp
1×frac-2neg clear-num associate-/l/
Counts
4 → 401
Calls
4 calls:
22.0ms
(/ (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))))
3.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
3.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
3.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series208.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(/ (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))))
38.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
33.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
34.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify122.0ms

Algorithm
egg-herbie
Counts
413 → 413
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
098211182
1359810142
250019999

prune698.0ms

Pruning

9 alts after pruning (5 fresh and 4 done)

Merged error: 23.2b

regimes184.0ms

Accuracy

0% (3.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01713
11713

end0.0ms

sample509.0ms

Algorithm
intervals
Results
298.0ms8449×body80valid