Details

Time bar (total: 3.7s)

sample37.0ms

Algorithm
intervals
Results
15.0ms271×body80valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0157
1157

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.4b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.7b
(+ (* x.re y.re) (* x.im y.im))
25.0b
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite47.0ms

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:
7.0ms
(+ (* y.re y.re) (* y.im y.im))
7.0ms
(+ (* x.re y.re) (* x.im y.im))
32.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series138.0ms

Counts
3 → 9
Calls
3 calls:
26.0ms
(+ (* y.re y.re) (* y.im y.im))
31.0ms
(+ (* x.re y.re) (* x.im y.im))
81.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify124.0ms

Algorithm
egg-herbie
Counts
62 → 62
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
0272527
11164479
24451477
35003477

prune164.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 24.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.7b
(+ (* x.re y.re) (* x.im y.im))
15.6b
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
26.3b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.3b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite57.0ms

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:
7.0ms
(+ (* x.re y.re) (* x.im y.im))
33.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
7.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
7.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series221.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(+ (* x.re y.re) (* x.im y.im))
115.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
40.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
35.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify80.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
0273893
1868840
22693828
35001828

prune266.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 21.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.7b
(+ (* x.re y.re) (* x.im y.im))
15.7b
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
26.3b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.3b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite80.0ms

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:
7.0ms
(+ (* x.re y.re) (* x.im y.im))
51.0ms
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
12.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
7.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series212.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(+ (* x.re y.re) (* x.im y.im))
112.0ms
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
34.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
35.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify45.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0385911
11913826
25002802

prune302.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 21.6b

localize16.0ms

Local error

Found 4 expressions with local error:

8.7b
(* (+ (* x.re y.re) (* x.im y.im)) (sqrt (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im))))))
26.3b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.3b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.3b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
49×sqrt-prod
39×add-sqr-sqrt
27×associate-*r*
24×*-un-lft-identity
22×add-cube-cbrt times-frac
11×sqrt-div
9×pow1
6×add-exp-log flip3-+ add-cbrt-cube flip-+ unswap-sqr
4×add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l*
2×frac-times associate-*l/ associate-/r/
1×associate-*r/ pow-prod-down prod-exp *-commutative cbrt-unprod div-inv
Counts
4 → 97
Calls
4 calls:
66.0ms
(* (+ (* x.re y.re) (* x.im y.im)) (sqrt (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im))))))
15.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
14.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
12.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series512.0ms

Counts
4 → 12
Calls
4 calls:
399.0ms
(* (+ (* x.re y.re) (* x.im y.im)) (sqrt (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im))))))
36.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
41.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
37.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify47.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
03541029
11410983
25001943

prune361.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 21.6b

regimes234.0ms

Accuracy

24.7% (2.3b remaining)

Error of 25.0b against oracle of 22.7b and baseline of 25.7b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03127
13327
23327

end0.0ms

sample559.0ms

Algorithm
intervals
Results
274.0ms8473×body80valid