Details

Time bar (total: 3.5s)

sample34.0ms

Algorithm
intervals
Results
23.0ms272×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: 25.7b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.8b
(+ (* 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)))

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:
5.0ms
(+ (* 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)))

series140.0ms

Counts
3 → 9
Calls
3 calls:
29.0ms
(+ (* y.re y.re) (* y.im y.im))
35.0ms
(+ (* x.re y.re) (* x.im y.im))
76.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify133.0ms

Algorithm
egg-herbie
Counts
62 → 62
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0272527
11164479
24451477
35003477

prune173.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 25.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.8b
(+ (* x.re y.re) (* x.im y.im))
16.0b
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
31.2b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.2b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite22.0ms

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)))

series215.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(+ (* x.re y.re) (* x.im y.im))
109.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
39.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
35.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify83.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
0273893
1868840
22693828
35001828

prune290.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 22.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.8b
(+ (* x.re y.re) (* x.im y.im))
16.2b
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
31.2b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.2b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite36.0ms

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))
24.0ms
(* (+ (* 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)))

series217.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(+ (* x.re y.re) (* x.im y.im))
110.0ms
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
36.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
40.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify54.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0385911
11913826
25002802

prune293.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 22.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.5b
(/ 1 (+ (* y.re y.re) (* y.im y.im)))
0.8b
(+ (* x.re y.re) (* x.im y.im))
24.9b
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

rewrite32.0ms

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))
5.0ms
(/ 1 (+ (* y.re y.re) (* y.im y.im)))
2.0ms
(+ (* x.re y.re) (* x.im y.im))
20.0ms
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

series183.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(+ (* y.re y.re) (* y.im y.im))
39.0ms
(/ 1 (+ (* y.re y.re) (* y.im y.im)))
35.0ms
(+ (* x.re y.re) (* x.im y.im))
82.0ms
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

simplify54.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
0393853
12037749
25003720

prune239.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 22.5b

regimes201.0ms

Accuracy

26.3% (2.3b remaining)

Error of 25.8b against oracle of 23.5b and baseline of 26.6b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02626
12826
22826

end0.0ms

sample970.0ms

Algorithm
intervals
Results
733.0ms8457×body80valid