Details

Time bar (total: 2.1s)

sample25.0ms

Algorithm
intervals
Results
11.0ms266×body80valid

simplify3.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01515
11515

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 26.7b

Counts
2 → 1

localize9.0ms

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))
26.2b
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
times-frac
add-log-exp
add-exp-log add-cbrt-cube
flip3-+ flip-+
pow1 associate-/r* associate-/l*
+-commutative sum-log associate-/r/ associate-/l/
cbrt-undiv frac-2neg div-exp clear-num div-inv
Counts
3 → 53
Calls
3 calls:
3.0ms
(+ (* y.re y.re) (* y.im y.im))
4.0ms
(+ (* 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)))

series43.0ms

Counts
3 → 9
Calls
3 calls:
5.0ms
(+ (* y.re y.re) (* y.im y.im))
9.0ms
(+ (* x.re y.re) (* x.im y.im))
29.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify27.0ms

Algorithm
egg-herbie
Counts
62 → 62
Iterations

Useful iterations: 0 (21.0ms)

IterNodesCost
05430951

prune84.0ms

Filtered
48 candidates to 62 candidates (-29.2%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New58462
Fresh000
Picked011
Done000
Total58563

Merged error: 25.9b

Counts
63 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.7b
(+ (* x.re y.re) (* x.im y.im))
17.3b
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
30.1b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.1b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity
18×times-frac sqrt-prod
pow1 add-exp-log sqrt-div associate-/r* add-cbrt-cube add-log-exp
flip3-+ flip-+
associate-/l*
rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/ associate-/l/
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))
8.0ms
(/ (+ (* 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)))

series53.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(+ (* x.re y.re) (* x.im y.im))
32.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
6.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify40.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 0 (29.0ms)

IterNodesCost
050701525

prune106.0ms

Filtered
76 candidates to 96 candidates (-26.3%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New93396
Fresh033
Picked011
Done011
Total938101

Merged error: 24.2b

Counts
101 → 8

localize13.0ms

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)) (+ (* x.re y.re) (* x.im y.im))))
0.7b
(+ (* x.re y.re) (* x.im y.im))
25.9b
(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

rewrite28.0ms

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
flip3-+ div-exp flip-+ add-log-exp
div-inv associate-/l*
pow1
cbrt-undiv
+-commutative rec-exp frac-2neg 1-exp clear-num sum-log associate-/l/
pow-flip inv-pow
Counts
4 → 137
Calls
4 calls:
3.0ms
(+ (* y.re y.re) (* y.im y.im))
8.0ms
(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
3.0ms
(+ (* x.re y.re) (* x.im y.im))
8.0ms
(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

series59.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(+ (* y.re y.re) (* y.im y.im))
25.0ms
(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
9.0ms
(+ (* x.re y.re) (* x.im y.im))
17.0ms
(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

simplify61.0ms

Algorithm
egg-herbie
Counts
149 → 149
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
049573201
149573201

prune142.0ms

Filtered
103 candidates to 149 candidates (-44.7%)
Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New1481149
Fresh055
Picked011
Done022
Total1489157

Merged error: 24.2b

Counts
157 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

17.9b
(cbrt (+ (* x.re y.re) (* x.im y.im)))
17.9b
(cbrt (+ (* x.re y.re) (* x.im y.im)))
30.1b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.1b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
add-cube-cbrt *-un-lft-identity
pow1 cbrt-prod sqrt-prod
add-exp-log cbrt-div flip3-+ sqrt-div add-cbrt-cube flip-+ add-log-exp
rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 56
Calls
4 calls:
3.0ms
(cbrt (+ (* x.re y.re) (* x.im y.im)))
3.0ms
(cbrt (+ (* x.re y.re) (* x.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)))

series85.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(cbrt (+ (* x.re y.re) (* x.im y.im)))
36.0ms
(cbrt (+ (* x.re y.re) (* x.im y.im)))
6.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
8.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify48.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
05860730

prune74.0ms

Filtered
60 candidates to 68 candidates (-13.3%)
Pruning

9 alts after pruning (5 fresh and 4 done)

PrunedKeptTotal
New68068
Fresh055
Picked011
Done033
Total68977

Merged error: 24.2b

Counts
77 → 9

regimes413.0ms

Accuracy

31.4% (2.2b remaining)

Error of 25.6b against oracle of 23.4b and baseline of 26.6b

bsearch1.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02253
12253

end0.0ms

sample704.0ms

Algorithm
intervals
Results
356.0ms8509×body80valid

Profiling

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