Details

Time bar (total: 3.2s)

sample20.0ms

Algorithm
intervals
Results
9.0ms266×body80valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0157
1157

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.1b

localize14.0ms

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))
26.7b
(/ (+ (* 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)))

series136.0ms

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))
80.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify132.0ms

Algorithm
egg-herbie
Counts
62 → 62
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0272527
11164479
24451477
35003477

prune178.0ms

Filtered
62 candidates to 49 candidates (79.0%)
Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 26.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.9b
(+ (* x.re y.re) (* x.im y.im))
16.2b
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
31.4b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.4b
(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))))
4.0ms
(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:
30.0ms
(+ (* x.re y.re) (* x.im y.im))
110.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
39.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
35.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify90.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
0273893
1868840
22693828
35001828

prune293.0ms

Filtered
96 candidates to 74 candidates (77.1%)
Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 24.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.5b
(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
0.9b
(+ (* x.re y.re) (* x.im y.im))
26.3b
(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
56×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×associate-/r*
17×add-exp-log
11×associate-/r/ add-cbrt-cube
8×flip3-+ div-exp flip-+ add-log-exp
6×div-inv associate-/l*
5×pow1
4×cbrt-undiv
2×+-commutative rec-exp frac-2neg 1-exp clear-num sum-log associate-/l/
1×pow-flip inv-pow
Counts
4 → 137
Calls
4 calls:
3.0ms
(+ (* y.re y.re) (* y.im y.im))
11.0ms
(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
2.0ms
(+ (* x.re y.re) (* x.im y.im))
11.0ms
(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

series257.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(+ (* y.re y.re) (* y.im y.im))
144.0ms
(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
30.0ms
(+ (* x.re y.re) (* x.im y.im))
56.0ms
(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

simplify70.0ms

Algorithm
egg-herbie
Counts
149 → 149
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
05181821
126321656
250011569

prune289.0ms

Filtered
149 candidates to 85 candidates (57.0%)
Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 24.6b

localize20.0ms

Local error

Found 4 expressions with local error:

16.8b
(cbrt (+ (* x.re y.re) (* x.im y.im)))
16.8b
(cbrt (+ (* x.re y.re) (* x.im y.im)))
31.4b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.4b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite12.0ms

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:
2.0ms
(cbrt (+ (* x.re y.re) (* x.im y.im)))
2.0ms
(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)))

series284.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(cbrt (+ (* x.re y.re) (* x.im y.im)))
104.0ms
(cbrt (+ (* x.re y.re) (* x.im y.im)))
42.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
36.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify123.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 4 (116.0ms)

IterNodesCost
0254480
1655456
21709444
34133440
45001438

prune261.0ms

Filtered
68 candidates to 60 candidates (88.2%)
Pruning

9 alts after pruning (5 fresh and 4 done)

Merged error: 24.6b

regimes195.0ms

Accuracy

4.5% (3.0b remaining)

Error of 26.3b against oracle of 23.4b and baseline of 26.5b

bsearch2.0ms

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02921
13321
23621
33821
43821

end0.0ms

sample522.0ms

Algorithm
intervals
Results
304.0ms8455×body80valid