Details

Time bar (total: 2.8s)

analyze325.0ms

Algorithm
search

sample33.0ms

Algorithm
intervals
Results
9.0ms204×body80valid
5.0ms18×body2560valid
3.0ms256×pre80true
3.0ms8×body5120valid
2.0ms9×body1280valid
1.0ms8×body640valid
1.0ms7×body320valid
0.0ms2×body160valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0178
1248
2308
3358
4358

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 36.7b

Counts
2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* re re) (* im im))
0.7b
(- (sqrt (+ (* re re) (* im im))) re)
28.9b
(sqrt (+ (* re re) (* im im)))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
7×add-log-exp
6×*-un-lft-identity
4×pow1 add-cube-cbrt sqrt-prod
3×add-exp-log add-cbrt-cube
2×flip3-+ sqrt-div flip-+ difference-of-squares
1×+-commutative sub-neg rem-sqrt-square flip3-- sqrt-pow1 pow1/2 diff-log sum-log flip-- distribute-lft-out--
Counts
3 → 41
Calls
3 calls:
4.0ms
(+ (* re re) (* im im))
7.0ms
(- (sqrt (+ (* re re) (* im im))) re)
4.0ms
(sqrt (+ (* re re) (* im im)))

series19.0ms

Counts
3 → 9
Calls
3 calls:
5.0ms
(+ (* re re) (* im im))
7.0ms
(- (sqrt (+ (* re re) (* im im))) re)
7.0ms
(sqrt (+ (* re re) (* im im)))

simplify60.0ms

Algorithm
egg-herbie
Counts
50 → 50
Iterations

Useful iterations: 3 (55.0ms)

IterNodesCost
0172305
1661282
21936278
35002276

prune96.0ms

Filtered
38 candidates to 50 candidates (-31.6%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New44650
Fresh000
Picked101
Done000
Total45651

Merged error: 7.3b

Counts
51 → 6

localize6.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify2.0ms

Algorithm
egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000

prune15.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New000
Fresh055
Picked011
Done000
Total066

Merged error: 7.3b

Counts
6 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
6.8b
(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
28.9b
(sqrt (+ (* re re) (* im im)))
28.9b
(sqrt (+ (* re re) (* im im)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
72×sqrt-prod
51×add-sqr-sqrt
34×sqrt-pow1
29×pow1
28×sqrt-div
18×add-cube-cbrt *-un-lft-identity pow1/2
15×swap-sqr
9×associate-*r* associate-*l* pow-prod-up unswap-sqr
8×flip3-+ flip-+
6×add-exp-log add-cbrt-cube add-log-exp
5×pow-prod-down pow-sqr
4×frac-times
2×rem-sqrt-square associate-*r/ associate-*l/
1×pow2 sub-neg flip3-- pow-plus sqrt-unprod diff-log prod-exp rem-square-sqrt *-commutative flip-- cbrt-unprod difference-of-squares
Counts
4 → 126
Calls
4 calls:
17.0ms
(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
14.0ms
(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
4.0ms
(sqrt (+ (* re re) (* im im)))
4.0ms
(sqrt (+ (* re re) (* im im)))

series25.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
7.0ms
(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
6.0ms
(sqrt (+ (* re re) (* im im)))
6.0ms
(sqrt (+ (* re re) (* im im)))

simplify47.0ms

Algorithm
egg-herbie
Counts
138 → 138
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
02611112
1935975
25001951

prune130.0ms

Filtered
73 candidates to 138 candidates (-89.0%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1371138
Fresh134
Picked011
Done011
Total1386144

Merged error: 7.3b

Counts
144 → 6

localize24.0ms

Local error

Found 4 expressions with local error:

28.9b
(sqrt (+ (* re re) (* im im)))
29.9b
(cbrt (+ (* re re) (* im im)))
29.9b
(cbrt (+ (* re re) (* im im)))
29.9b
(cbrt (+ (* re re) (* im im)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×cbrt-div
5×pow1
4×add-exp-log flip3-+ add-cbrt-cube flip-+ add-log-exp
3×pow1/3 sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 54
Calls
4 calls:
4.0ms
(sqrt (+ (* re re) (* im im)))
4.0ms
(cbrt (+ (* re re) (* im im)))
4.0ms
(cbrt (+ (* re re) (* im im)))
4.0ms
(cbrt (+ (* re re) (* im im)))

series73.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(sqrt (+ (* re re) (* im im)))
21.0ms
(cbrt (+ (* re re) (* im im)))
22.0ms
(cbrt (+ (* re re) (* im im)))
24.0ms
(cbrt (+ (* re re) (* im im)))

simplify47.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 3 (40.0ms)

IterNodesCost
0169520
1455490
21289472
35001447

prune122.0ms

Filtered
57 candidates to 66 candidates (-15.8%)
Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New65166
Fresh033
Picked011
Done022
Total65772

Merged error: 7.3b

Counts
72 → 7

regimes250.0ms

Accuracy

38.7% (11.7b remaining)

Error of 22.2b against oracle of 10.5b and baseline of 29.5b

bsearch91.0ms

Steps
ItersRangePoint
11
2.4166428348319508e-98
4.56117083092322e-76
2.4430739350760497e-98
11
-3.2590171789530054e-32
-4.7611513332258787e-60
-2.593246184514998e-37

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03918
13918

end0.0ms

analyze321.0ms

Algorithm
search

sample1.0s

Algorithm
intervals
Results
276.0ms5966×body80valid
185.0ms684×body2560valid
120.0ms534×body1280valid
107.0ms307×body5120valid
91.0ms8000×pre80true
46.0ms266×body640valid
20.0ms158×body320valid
7.0ms85×body160valid

Profiling

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