Details

Time bar (total: 3.6s)

sample31.0ms

Algorithm
intervals
Results
20.0ms275×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: 26.9b

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))
26.5b
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite19.0ms

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))
5.0ms
(+ (* 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)))

series142.0ms

Counts
3 → 9
Calls
3 calls:
36.0ms
(+ (* y.re y.re) (* y.im y.im))
31.0ms
(+ (* 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)))

simplify131.0ms

Algorithm
egg-herbie
Counts
62 → 62
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0272527
11164479
24451477
35003477

prune174.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 26.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(+ (* x.re y.re) (* x.im y.im))
17.5b
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.7b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.7b
(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))
12.0ms
(/ (+ (* 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)))
4.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series206.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(+ (* 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))))
37.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
34.0ms
(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

prune275.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 23.8b

localize10.0ms

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))
0.7b
(/ 1 (+ (* y.re y.re) (* y.im y.im)))
26.0b
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
21×*-un-lft-identity
20×add-cube-cbrt times-frac
17×add-exp-log
15×associate-*r*
11×add-cbrt-cube
8×add-log-exp
7×pow1
6×flip3-+ flip-+
4×div-exp prod-exp associate-/r/
3×associate-*l* associate-/r* associate-/l* unswap-sqr
2×cbrt-undiv +-commutative frac-times rec-exp 1-exp associate-*l/ sum-log cbrt-unprod div-inv
1×pow-flip frac-2neg associate-*r/ pow-prod-down clear-num un-div-inv *-commutative inv-pow
Counts
4 → 97
Calls
4 calls:
2.0ms
(+ (* y.re y.re) (* y.im y.im))
2.0ms
(+ (* x.re y.re) (* x.im y.im))
5.0ms
(/ 1 (+ (* y.re y.re) (* y.im y.im)))
21.0ms
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

series195.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(+ (* y.re y.re) (* y.im y.im))
44.0ms
(+ (* x.re y.re) (* x.im y.im))
35.0ms
(/ 1 (+ (* y.re y.re) (* y.im y.im)))
76.0ms
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

simplify66.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
0393853
12037749
25003720

prune269.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 23.8b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
17.5b
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.7b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.7b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
95×add-sqr-sqrt
76×times-frac
53×*-un-lft-identity
47×add-cube-cbrt sqrt-prod
28×add-exp-log
24×associate-*r* associate-*l*
18×add-cbrt-cube
15×unswap-sqr
10×sqrt-div
9×div-exp
8×pow1 prod-exp
6×flip3-+ associate-/r* associate-/r/ flip-+
5×cbrt-undiv
4×cbrt-unprod add-log-exp
3×div-inv associate-/l*
2×rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp associate-/l/
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num un-div-inv *-commutative
Counts
4 → 161
Calls
4 calls:
50.0ms
(* (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
21.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
6.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series277.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(* (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
111.0ms
(/ (+ (* 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)))
34.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify72.0ms

Algorithm
egg-herbie
Counts
173 → 173
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
05782493
127602257
250012142

prune412.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 23.8b

regimes148.0ms

Accuracy

0% (2.9b remaining)

Error of 26.0b against oracle of 23.1b and baseline of 26.0b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01713
11713

end0.0ms

sample872.0ms

Algorithm
intervals
Results
652.0ms8450×body80valid