Details

Time bar (total: 2.5s)

sample19.0ms

Algorithm
intervals
Results
9.0ms269×body80valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0157
1157

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.5b

localize9.0ms

Local error

Found 2 expressions with local error:

0.5b
(+ (* x.re y.re) (* x.im y.im))
26.0b
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite12.0ms

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)))

series106.0ms

Counts
2 → 6
Calls
2 calls:
29.0ms
(+ (* x.re y.re) (* x.im y.im))
77.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify82.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 2 (22.0ms)

IterNodesCost
0231450
1847413
22851412
35003412

prune138.0ms

Filtered
48 candidates to 38 candidates (79.2%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 25.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b
(+ (* x.re y.re) (* x.im y.im))
14.9b
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
30.9b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.9b
(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:
3.0ms
(+ (* 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))))
3.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
3.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series203.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(+ (* 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))))
34.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
35.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify81.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
0273893
1868840
22693828
35001828

prune265.0ms

Filtered
96 candidates to 74 candidates (77.1%)
Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 24.2b

localize11.0ms

Local error

Found 2 expressions with local error:

0.5b
(+ (* x.re y.re) (* x.im y.im))
26.0b
(/ (pow (+ (* x.re y.re) (* x.im y.im)) 1) (+ (* y.re y.re) (* y.im y.im)))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
21×times-frac
18×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×unpow-prod-down
7×add-exp-log associate-/l*
4×add-cbrt-cube add-log-exp sqr-pow
3×div-exp associate-/r*
2×pow1 flip3-+ associate-/r/ flip-+
1×cbrt-undiv +-commutative pow-to-exp frac-2neg pow-exp clear-num sum-log div-inv
Counts
2 → 58
Calls
2 calls:
3.0ms
(+ (* x.re y.re) (* x.im y.im))
9.0ms
(/ (pow (+ (* x.re y.re) (* x.im y.im)) 1) (+ (* y.re y.re) (* y.im y.im)))

series107.0ms

Counts
2 → 6
Calls
2 calls:
31.0ms
(+ (* x.re y.re) (* x.im y.im))
76.0ms
(/ (pow (+ (* x.re y.re) (* x.im y.im)) 1) (+ (* y.re y.re) (* y.im y.im)))

simplify37.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0280718
11065662
25001661

prune151.0ms

Filtered
64 candidates to 40 candidates (62.5%)
Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 24.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b
(+ (* x.re y.re) (* x.im y.im))
14.9b
(/ (pow (+ (* x.re y.re) (* x.im y.im)) 1) (sqrt (+ (* y.re y.re) (* y.im y.im))))
30.9b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.9b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
42×times-frac
38×add-sqr-sqrt
36×add-cube-cbrt *-un-lft-identity
30×sqrt-prod
21×unpow-prod-down
9×add-exp-log
7×associate-/l* sqr-pow
6×pow1 sqrt-div associate-/r* add-cbrt-cube add-log-exp
4×flip3-+ flip-+
3×div-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/
1×cbrt-undiv +-commutative pow-to-exp frac-2neg pow-exp clear-num sum-log div-inv
Counts
4 → 112
Calls
4 calls:
3.0ms
(+ (* x.re y.re) (* x.im y.im))
10.0ms
(/ (pow (+ (* 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)))

series195.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(+ (* x.re y.re) (* x.im y.im))
99.0ms
(/ (pow (+ (* 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)))
33.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify48.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
03321447
111641315
250021313

prune286.0ms

Filtered
124 candidates to 77 candidates (62.1%)
Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 24.2b

regimes139.0ms

Accuracy

0% (2.3b remaining)

Error of 26.9b against oracle of 24.6b and baseline of 26.9b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0198
1198

end0.0ms

sample495.0ms

Algorithm
intervals
Results
283.0ms8488×body80valid