Details

Time bar (total: 3.0s)

sample20.0ms

Algorithm
intervals
Results
9.0ms278×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: 25.1b

localize12.0ms

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))
24.6b
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite17.0ms

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:
2.0ms
(+ (* y.re y.re) (* y.im y.im))
3.0ms
(+ (* x.re y.re) (* x.im y.im))
11.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series157.0ms

Counts
3 → 9
Calls
3 calls:
35.0ms
(+ (* y.re y.re) (* y.im y.im))
43.0ms
(+ (* x.re y.re) (* x.im y.im))
79.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify139.0ms

Algorithm
egg-herbie
Counts
62 → 62
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0272527
11164479
24451477
35003477

prune168.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 24.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.7b
(+ (* x.re y.re) (* x.im y.im))
14.7b
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.8b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.8b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite24.0ms

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))
12.0ms
(/ (+ (* 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)))
4.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series213.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(+ (* x.re y.re) (* x.im y.im))
108.0ms
(/ (+ (* 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)))
36.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify85.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
0273895
1868840
22693828
35001828

prune262.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 22.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.6b
(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
0.7b
(+ (* x.re y.re) (* x.im y.im))
24.4b
(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
56×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×associate-/r*
17×add-exp-log
11×associate-/r/ add-cbrt-cube
8×flip3-+ div-exp flip-+ add-log-exp
6×div-inv associate-/l*
5×pow1
4×cbrt-undiv
2×+-commutative rec-exp frac-2neg 1-exp clear-num sum-log associate-/l/
1×pow-flip inv-pow
Counts
4 → 137
Calls
4 calls:
3.0ms
(+ (* y.re y.re) (* y.im y.im))
11.0ms
(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
2.0ms
(+ (* x.re y.re) (* x.im y.im))
11.0ms
(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

series247.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(+ (* y.re y.re) (* y.im y.im))
135.0ms
(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
30.0ms
(+ (* x.re y.re) (* x.im y.im))
56.0ms
(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

simplify70.0ms

Algorithm
egg-herbie
Counts
149 → 149
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
05181821
126321656
250011569

prune289.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 22.1b

localize16.0ms

Local error

Found 4 expressions with local error:

14.7b
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.8b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.8b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
40.6b
(cbrt (pow (sqrt (+ (* y.re y.re) (* y.im y.im))) 3))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
26×add-cube-cbrt *-un-lft-identity
24×sqrt-prod
18×cbrt-prod times-frac
8×sqrt-div
6×pow1 add-exp-log unpow-prod-down cube-prod associate-/r* add-cbrt-cube
5×flip3-+ flip-+
4×add-log-exp
3×associate-/l*
2×cube-div rem-sqrt-square cbrt-div sqrt-pow1 pow1/2 associate-/r/ associate-/l/
1×cbrt-undiv cube-mult frac-2neg pow1/3 unpow3 div-exp clear-num rem-cbrt-cube div-inv sqr-pow
Counts
4 → 102
Calls
4 calls:
11.0ms
(/ (+ (* 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)))
3.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
5.0ms
(cbrt (pow (sqrt (+ (* y.re y.re) (* y.im y.im))) 3))

series205.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(/ (+ (* 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)))
36.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
35.0ms
(cbrt (pow (sqrt (+ (* y.re y.re) (* y.im y.im))) 3))

simplify45.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
03401014
11338937
25001934

prune309.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 22.1b

regimes128.0ms

Accuracy

0% (2.9b remaining)

Error of 26.3b against oracle of 23.3b and baseline of 26.3b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01713
11713

end0.0ms

sample509.0ms

Algorithm
intervals
Results
297.0ms8472×body80valid