Details

Time bar (total: 3.2s)

sample20.0ms

Algorithm
intervals
Results
9.0ms268×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: 23.4b

localize10.0ms

Local error

Found 2 expressions with local error:

0.2b
(+ (* x.re y.re) (* x.im y.im))
23.0b
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
4×add-exp-log add-cbrt-cube add-log-exp
3×flip3-+ associate-/r* flip-+ associate-/l*
2×pow1 associate-/r/ associate-/l/
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv
Counts
2 → 42
Calls
2 calls:
3.0ms
(+ (* x.re y.re) (* x.im y.im))
8.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series108.0ms

Counts
2 → 6
Calls
2 calls:
29.0ms
(+ (* x.re y.re) (* x.im y.im))
78.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify83.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 2 (22.0ms)

IterNodesCost
0231450
1847413
22851412
35003412

prune150.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 22.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(+ (* x.re y.re) (* x.im y.im))
13.6b
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
29.2b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.2b
(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:
4.0ms
(+ (* x.re y.re) (* x.im y.im))
9.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
4.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series210.0ms

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))))
35.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
40.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify80.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (22.0ms)

IterNodesCost
0273893
1868840
22693828
35001828

prune444.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 21.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(+ (* x.re y.re) (* x.im y.im))
13.7b
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
29.2b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.2b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite31.0ms

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:
3.0ms
(+ (* x.re y.re) (* x.im y.im))
15.0ms
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
4.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series199.0ms

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)))))
33.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
34.0ms
(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

prune290.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 21.1b

localize18.0ms

Local error

Found 4 expressions with local error:

7.5b
(* (* (+ (* x.re y.re) (* x.im y.im)) (sqrt (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))) (sqrt (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im))))))
29.2b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.2b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.2b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
42×sqrt-prod
27×associate-*r*
24×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity
20×sqrt-div
18×times-frac
12×pow1
9×add-exp-log frac-times associate-*l/ add-cbrt-cube
8×flip3-+ flip-+
4×add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ pow-prod-down prod-exp cbrt-unprod
2×associate-/r/
1×associate-*l* *-commutative div-inv
Counts
4 → 98
Calls
4 calls:
24.0ms
(* (* (+ (* x.re y.re) (* x.im y.im)) (sqrt (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))) (sqrt (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im))))))
4.0ms
(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)))

series214.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(* (* (+ (* x.re y.re) (* x.im y.im)) (sqrt (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))) (sqrt (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im))))))
34.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
39.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
34.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify59.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
04361281
117291148
250021106

prune353.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 21.1b

regimes191.0ms

Accuracy

0% (3.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01713
11713

end0.0ms

sample560.0ms

Algorithm
intervals
Results
323.0ms8456×body80valid