Details

Time bar (total: 3.4s)

sample21.0ms

Algorithm
intervals
Results
9.0ms276×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: 29.7b

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

rewrite48.0ms

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:
8.0ms
(+ (* y.re y.re) (* y.im y.im))
8.0ms
(+ (* x.re y.re) (* x.im y.im))
31.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series131.0ms

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

simplify130.0ms

Algorithm
egg-herbie
Counts
62 → 62
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0272527
11164479
24451477
35003477

prune172.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 28.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.9b
(+ (* x.re y.re) (* x.im y.im))
19.1b
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
30.0b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.0b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite241.0ms

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:
8.0ms
(+ (* x.re y.re) (* x.im y.im))
32.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
190.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
8.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series193.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(+ (* x.re y.re) (* x.im y.im))
98.0ms
(/ (+ (* 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)))
35.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify99.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (22.0ms)

IterNodesCost
0273893
1868840
22693828
35001828

prune313.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 25.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.7b
(/ 1 (+ (* y.re y.re) (* y.im y.im)))
0.9b
(+ (* x.re y.re) (* x.im y.im))
28.6b
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

rewrite83.0ms

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:
8.0ms
(+ (* y.re y.re) (* y.im y.im))
14.0ms
(/ 1 (+ (* y.re y.re) (* y.im y.im)))
10.0ms
(+ (* x.re y.re) (* x.im y.im))
48.0ms
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

series167.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(+ (* y.re y.re) (* y.im y.im))
37.0ms
(/ 1 (+ (* y.re y.re) (* y.im y.im)))
29.0ms
(+ (* x.re y.re) (* x.im y.im))
76.0ms
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

simplify53.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
0393853
12037749
25003720

prune224.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 25.5b

localize21.0ms

Local error

Found 4 expressions with local error:

19.8b
(cbrt (+ (* x.re y.re) (* x.im y.im)))
30.0b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.0b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.0b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×sqrt-prod
8×add-cube-cbrt *-un-lft-identity
7×pow1
6×sqrt-div
4×add-exp-log flip3-+ add-cbrt-cube flip-+ add-log-exp
3×cbrt-prod rem-sqrt-square sqrt-pow1 pow1/2
2×cbrt-div
1×pow1/3
Counts
4 → 58
Calls
4 calls:
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)))
8.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series199.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(cbrt (+ (* x.re y.re) (* x.im y.im)))
32.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
34.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
32.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify122.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 4 (116.0ms)

IterNodesCost
0254440
1655422
21709416
34133412
45001411

prune282.0ms

Pruning

13 alts after pruning (9 fresh and 4 done)

Merged error: 25.5b

regimes259.0ms

Accuracy

37.9% (1.9b remaining)

Error of 25.3b against oracle of 23.3b and baseline of 26.4b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03038
13138
23138

end0.0ms

sample561.0ms

Algorithm
intervals
Results
276.0ms8493×body80valid