Details

Time bar (total: 3.2s)

sample26.0ms

Algorithm
intervals
Results
16.0ms270×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: 27.9b

localize12.0ms

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))
27.3b
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite16.0ms

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

series131.0ms

Counts
3 → 9
Calls
3 calls:
25.0ms
(+ (* y.re y.re) (* y.im y.im))
28.0ms
(+ (* 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)))

simplify140.0ms

Algorithm
egg-herbie
Counts
62 → 62
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0272527
11164479
24451477
35003477

prune171.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 27.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.9b
(+ (* x.re y.re) (* x.im y.im))
17.2b
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
29.0b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.0b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite23.0ms

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)))

series213.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(+ (* x.re y.re) (* x.im y.im))
105.0ms
(/ (+ (* 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)))

simplify82.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
0273893
1868840
22693828
35001828

prune273.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 24.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.9b
(+ (* x.re y.re) (* x.im y.im))
17.2b
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
29.0b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.0b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite23.0ms

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)))

series206.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(+ (* x.re y.re) (* x.im y.im))
102.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
33.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
38.0ms
(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

prune293.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 24.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.9b
(+ (* x.re y.re) (* x.im y.im))
17.3b
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
29.0b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.0b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
24×associate-*r*
22×*-un-lft-identity times-frac
20×add-cube-cbrt
17×sqrt-prod
13×add-exp-log
9×add-cbrt-cube
8×pow1
6×flip3-+ sqrt-div flip-+ add-log-exp
5×unswap-sqr
4×prod-exp
3×associate-*l*
2×frac-times rem-sqrt-square sqrt-pow1 pow1/2 div-exp associate-*l/ associate-/r/ cbrt-unprod
1×cbrt-undiv +-commutative rec-exp 1-exp associate-*r/ pow-prod-down sum-log un-div-inv *-commutative div-inv
Counts
4 → 94
Calls
4 calls:
2.0ms
(+ (* x.re y.re) (* x.im y.im))
28.0ms
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (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)))

series209.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(+ (* x.re y.re) (* x.im y.im))
103.0ms
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
40.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
36.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify47.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0385911
11913826
25002802

prune282.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 24.1b

regimes160.0ms

Accuracy

0% (2.8b remaining)

Error of 25.8b against oracle of 23.0b and baseline of 25.8b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01713
11713

end0.0ms

sample731.0ms

Algorithm
intervals
Results
521.0ms8459×body80valid