Details

Time bar (total: 3.7s)

sample24.0ms

Algorithm
intervals
Results
11.0ms270×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: 26.1b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* x.re y.re) (* x.im y.im))
25.7b
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
4×add-exp-log add-cbrt-cube add-log-exp
3×flip3-+ associate-/r* flip-+ associate-/l*
2×pow1 associate-/r/ associate-/l/
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv
Counts
2 → 42
Calls
2 calls:
10.0ms
(+ (* x.re y.re) (* x.im y.im))
30.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series106.0ms

Counts
2 → 6
Calls
2 calls:
32.0ms
(+ (* x.re y.re) (* x.im y.im))
74.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify82.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 2 (22.0ms)

IterNodesCost
0231450
1847413
22851412
35003412

prune136.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 25.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
15.9b
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
29.5b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.5b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
288×times-frac
164×add-sqr-sqrt
162×add-cube-cbrt *-un-lft-identity
156×sqrt-prod
27×associate-/l*
22×sqrt-div
18×associate-/r/
12×flip3-+ associate-/r* flip-+
11×add-exp-log add-cbrt-cube
9×div-inv
6×pow1
4×cbrt-undiv div-exp add-log-exp
3×associate-/l/
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
Counts
4 → 264
Calls
4 calls:
53.0ms
(/ (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
30.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
7.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
10.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series270.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(/ (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
129.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
32.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
36.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify82.0ms

Algorithm
egg-herbie
Counts
276 → 276
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
07145680
125165201
250015144

prune518.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 23.3b

localize19.0ms

Local error

Found 4 expressions with local error:

8.2b
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))))
29.5b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.5b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.5b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite62.0ms

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:
36.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))))
8.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
7.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
8.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series291.0ms

Counts
4 → 12
Calls
4 calls:
187.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (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)))
34.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify76.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (22.0ms)

IterNodesCost
02941227
18711172
225451144
350011144

prune356.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 23.3b

localize16.0ms

Local error

Found 4 expressions with local error:

16.5b
(cbrt (+ (* x.re y.re) (* x.im y.im)))
16.5b
(cbrt (+ (* x.re y.re) (* x.im y.im)))
29.5b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.5b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite29.0ms

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:
4.0ms
(cbrt (+ (* x.re y.re) (* x.im y.im)))
5.0ms
(cbrt (+ (* x.re y.re) (* x.im y.im)))
8.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
8.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series271.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(cbrt (+ (* x.re y.re) (* x.im y.im)))
101.0ms
(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)))

simplify116.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 4 (110.0ms)

IterNodesCost
0254480
1655456
21709444
34133440
45001438

prune246.0ms

Pruning

10 alts after pruning (6 fresh and 4 done)

Merged error: 23.3b

regimes222.0ms

Accuracy

25.6% (2.2b remaining)

Error of 25.4b against oracle of 23.2b and baseline of 26.1b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02626
12826
22826

end0.0ms

sample590.0ms

Algorithm
intervals
Results
287.0ms8488×body80valid