Details

Time bar (total: 3.3s)

sample20.0ms

Algorithm
intervals
Results
9.0ms269×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: 25.6b

localize10.0ms

Local error

Found 2 expressions with local error:

0.4b
(+ (* x.re y.re) (* x.im y.im))
25.2b
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite14.0ms

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:
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)))

series115.0ms

Counts
2 → 6
Calls
2 calls:
31.0ms
(+ (* x.re y.re) (* x.im y.im))
84.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify86.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
0231450
1847413
22851412
35003412

prune140.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 24.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.4b
(+ (* x.re y.re) (* x.im y.im))
14.6b
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
31.7b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.7b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite25.0ms

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))
11.0ms
(/ (+ (* 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)))
3.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series211.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(+ (* x.re y.re) (* x.im y.im))
108.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
36.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
36.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify80.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (23.0ms)

IterNodesCost
0273895
1868840
22693828
35001828

prune291.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 24.1b

localize15.0ms

Local error

Found 4 expressions with local error:

7.5b
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))))
31.7b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.7b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.7b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite29.0ms

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)))))
6.0ms
(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)))

series305.0ms

Counts
4 → 12
Calls
4 calls:
193.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (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)))
37.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify81.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (23.0ms)

IterNodesCost
02941227
18711172
225451144
350011144

prune377.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 24.1b

localize25.0ms

Local error

Found 4 expressions with local error:

31.7b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
32.8b
(cbrt (+ (* y.re y.re) (* y.im y.im)))
32.8b
(cbrt (+ (* y.re y.re) (* y.im y.im)))
32.8b
(cbrt (+ (* y.re y.re) (* y.im y.im)))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×cbrt-div
5×pow1
4×add-exp-log flip3-+ add-cbrt-cube flip-+ add-log-exp
3×pow1/3 sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 54
Calls
4 calls:
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)))
2.0ms
(cbrt (+ (* y.re y.re) (* y.im y.im)))

series322.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
96.0ms
(cbrt (+ (* y.re y.re) (* y.im y.im)))
92.0ms
(cbrt (+ (* y.re y.re) (* y.im y.im)))
94.0ms
(cbrt (+ (* y.re y.re) (* y.im y.im)))

simplify54.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 3 (48.0ms)

IterNodesCost
0141466
1440436
21471430
35001429

prune369.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 24.1b

regimes186.0ms

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

sample498.0ms

Algorithm
intervals
Results
294.0ms8463×body80valid