Details

Time bar (total: 3.3s)

sample19.0ms

Algorithm
intervals
Results
9.0ms278×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: 22.5b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.2b
(+ (* x.re y.re) (* x.im y.im))
22.1b
(/ (+ (* 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)))

series133.0ms

Counts
3 → 9
Calls
3 calls:
25.0ms
(+ (* y.re y.re) (* y.im y.im))
31.0ms
(+ (* x.re y.re) (* x.im y.im))
77.0ms
(/ (+ (* 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 (27.0ms)

IterNodesCost
0272527
11164479
24451477
35003477

prune171.0ms

Filtered
62 candidates to 49 candidates (79.0%)
Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 21.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(+ (* x.re y.re) (* x.im y.im))
12.9b
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
29.2b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.2b
(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))))
4.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series234.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(+ (* x.re y.re) (* x.im y.im))
134.0ms
(/ (+ (* 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)))
33.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify78.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (22.0ms)

IterNodesCost
0273893
1868840
22693828
35001828

prune280.0ms

Filtered
96 candidates to 74 candidates (77.1%)
Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 20.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.2b
(+ (* x.re y.re) (* x.im y.im))
0.9b
(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
21.3b
(/ (+ (* 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:
2.0ms
(+ (* y.re y.re) (* y.im y.im))
2.0ms
(+ (* x.re y.re) (* x.im y.im))
11.0ms
(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* 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)))

series242.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(+ (* y.re y.re) (* y.im y.im))
32.0ms
(+ (* x.re y.re) (* x.im y.im))
130.0ms
(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
55.0ms
(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

simplify63.0ms

Algorithm
egg-herbie
Counts
149 → 149
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
05181821
126321656
250011569

prune299.0ms

Filtered
149 candidates to 86 candidates (57.7%)
Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 20.6b

localize14.0ms

Local error

Found 4 expressions with local error:

6.5b
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))))
29.2b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.2b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.2b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
45×sqrt-prod
32×add-sqr-sqrt
29×add-cube-cbrt *-un-lft-identity
27×times-frac
10×sqrt-div
9×associate-/r*
7×pow1
6×add-exp-log add-cbrt-cube
5×flip3-+ flip-+
4×add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2 associate-/l*
2×associate-/r/ associate-/l/
1×cbrt-undiv frac-2neg div-exp clear-num div-inv
Counts
4 → 100
Calls
4 calls:
13.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (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)))

series309.0ms

Counts
4 → 12
Calls
4 calls:
201.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))))
34.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
34.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
39.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify94.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
02941227
18711172
225451144
350011144

prune342.0ms

Filtered
112 candidates to 82 candidates (73.2%)
Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 20.6b

regimes236.0ms

Accuracy

0% (3.0b remaining)

Error of 26.6b against oracle of 23.5b and baseline of 26.6b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01713
11713

end0.0ms

sample483.0ms

Algorithm
intervals
Results
280.0ms8480×body80valid