Details

Time bar (total: 4.2s)

sample39.0ms

Algorithm
intervals
Results
28.0ms274×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: 22.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.5b
(+ (* x.re y.re) (* x.im y.im))
21.6b
(/ (+ (* 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:
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)))

series142.0ms

Counts
3 → 9
Calls
3 calls:
31.0ms
(+ (* y.re y.re) (* y.im y.im))
30.0ms
(+ (* x.re y.re) (* x.im y.im))
80.0ms
(/ (+ (* 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 (28.0ms)

IterNodesCost
0272527
11164479
24451477
35003477

prune181.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 21.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b
(+ (* x.re y.re) (* x.im y.im))
14.0b
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
25.2b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
25.2b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite24.0ms

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)))

series215.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(+ (* x.re y.re) (* x.im y.im))
106.0ms
(/ (+ (* 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)))

simplify79.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (22.0ms)

IterNodesCost
0273893
1868840
22693828
35001828

prune289.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 19.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b
(+ (* x.re y.re) (* x.im y.im))
14.0b
(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.im y.im)))
25.2b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
25.2b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite195.0ms

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:
2.0ms
(+ (* x.re y.re) (* x.im y.im))
10.0ms
(/ (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)))
4.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series184.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(+ (* x.re y.re) (* x.im y.im))
80.0ms
(/ (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)))
35.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify70.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
0263883
1831838
22301833
35001833

prune286.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 19.1b

localize16.0ms

Local error

Found 4 expressions with local error:

14.0b
(/ (+ (* x.re y.re) (* x.im y.im)) (* (fabs (cbrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (cbrt (+ (* y.re y.re) (* y.im y.im))))))
25.2b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.1b
(cbrt (+ (* y.re y.re) (* y.im y.im)))
26.1b
(cbrt (+ (* y.re y.re) (* y.im y.im)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×cbrt-prod cbrt-div
5×pow1 flip3-+ flip-+
4×sqrt-div add-log-exp
3×times-frac sqrt-prod associate-/l*
2×cbrt-undiv pow1/3 associate-*r/ div-exp associate-/r/ associate-/l/
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 66
Calls
4 calls:
12.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (* (fabs (cbrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (cbrt (+ (* y.re y.re) (* y.im y.im))))))
3.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
2.0ms
(cbrt (+ (* y.re y.re) (* y.im y.im)))
2.0ms
(cbrt (+ (* y.re y.re) (* y.im y.im)))

series558.0ms

Counts
4 → 12
Calls
4 calls:
328.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (* (fabs (cbrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (cbrt (+ (* y.re y.re) (* y.im y.im))))))
36.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
101.0ms
(cbrt (+ (* y.re y.re) (* y.im y.im)))
93.0ms
(cbrt (+ (* y.re y.re) (* y.im y.im)))

simplify42.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0399908
11522808
25002804

prune335.0ms

Pruning

11 alts after pruning (7 fresh and 4 done)

Merged error: 19.1b

regimes234.0ms

Accuracy

28.9% (2.1b remaining)

Error of 24.9b against oracle of 22.9b and baseline of 25.7b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02626
12826
22826

end0.0ms

sample1.1s

Algorithm
intervals
Results
888.0ms8483×body80valid