Details

Time bar (total: 2.7s)

sample13.0ms

Algorithm
intervals
Results
5.0ms256×body80valid

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
074
174
done74

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize8.0ms

Local error

Found 1 expressions with local error:

29.6b
(sqrt (+ (* re re) (* im im)))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
3×add-sqr-sqrt sqrt-prod
2×pow1 add-cube-cbrt *-un-lft-identity sqrt-div
1×add-exp-log rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 add-cbrt-cube flip-+ add-log-exp
Counts
1 → 15
Calls
1 calls:
8.0ms
(sqrt (+ (* re re) (* im im)))

series37.0ms

Counts
1 → 3
Calls
1 calls:
37.0ms
(sqrt (+ (* re re) (* im im)))

simplify137.0ms

Counts
18 → 18
Iterations

Useful iterations: 5 (134.0ms)

IterNodesCost
089100
121597
250397
3126597
4422797
5500296
done500296

prune44.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 7.8b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (sqrt (+ (* re re) (* im im))))
0.5b
(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
29.6b
(sqrt (+ (* re re) (* im im)))
29.6b
(sqrt (+ (* re re) (* im im)))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
82×sqrt-prod
54×add-sqr-sqrt
38×sqrt-pow1
32×sqrt-div
31×pow1
20×add-cube-cbrt *-un-lft-identity pow1/2
15×swap-sqr
9×flip3-+ associate-*r* associate-*l* pow-prod-up flip-+ unswap-sqr
6×add-exp-log add-cbrt-cube
5×pow-prod-down pow-sqr
4×frac-times rem-sqrt-square add-log-exp
2×associate-*r/ associate-*l/
1×pow2 pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 134
Calls
4 calls:
8.0ms
(sqrt (sqrt (+ (* re re) (* im im))))
53.0ms
(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
7.0ms
(sqrt (+ (* re re) (* im im)))
8.0ms
(sqrt (+ (* re re) (* im im)))

series194.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(sqrt (sqrt (+ (* re re) (* im im))))
38.0ms
(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
35.0ms
(sqrt (+ (* re re) (* im im)))
40.0ms
(sqrt (+ (* re re) (* im im)))

simplify48.0ms

Counts
146 → 146
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
02511056
1951985
25002964
done5002964

prune229.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 7.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.9b
(pow (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) 4)
29.6b
(sqrt (+ (* re re) (* im im)))
29.6b
(sqrt (+ (* re re) (* im im)))
29.6b
(sqrt (+ (* re re) (* im im)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
18×sqrt-prod
15×add-sqr-sqrt
12×add-cube-cbrt unpow-prod-down *-un-lft-identity
9×cbrt-prod
8×pow1
6×sqrt-div
5×add-exp-log
4×add-cbrt-cube add-log-exp
3×rem-sqrt-square pow-unpow sqrt-pow1 flip3-+ pow1/2 flip-+
2×pow-pow
1×pow-to-exp pow1/3 pow-exp sqr-pow
Counts
4 → 72
Calls
4 calls:
12.0ms
(pow (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) 4)
7.0ms
(sqrt (+ (* re re) (* im im)))
7.0ms
(sqrt (+ (* re re) (* im im)))
8.0ms
(sqrt (+ (* re re) (* im im)))

series231.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(pow (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) 4)
38.0ms
(sqrt (+ (* re re) (* im im)))
36.0ms
(sqrt (+ (* re re) (* im im)))
51.0ms
(sqrt (+ (* re re) (* im im)))

simplify84.0ms

Counts
84 → 84
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
0220629
1704598
22426590
35001590
done5001590

prune253.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 7.8b

localize17.0ms

Local error

Found 4 expressions with local error:

6.1b
(pow (sqrt (sqrt (+ (* re re) (* im im)))) 4/3)
29.6b
(sqrt (+ (* re re) (* im im)))
29.6b
(sqrt (+ (* re re) (* im im)))
29.6b
(sqrt (+ (* re re) (* im im)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
18×sqrt-prod
14×add-sqr-sqrt
11×add-cube-cbrt *-un-lft-identity
10×pow1
9×unpow-prod-down
7×sqrt-pow1
6×sqrt-div
5×add-exp-log pow-pow pow1/2
4×add-cbrt-cube add-log-exp
3×rem-sqrt-square pow-unpow flip3-+ flip-+
1×pow-to-exp pow-exp sqrt-pow2 sqr-pow
Counts
4 → 73
Calls
4 calls:
14.0ms
(pow (sqrt (sqrt (+ (* re re) (* im im)))) 4/3)
7.0ms
(sqrt (+ (* re re) (* im im)))
7.0ms
(sqrt (+ (* re re) (* im im)))
8.0ms
(sqrt (+ (* re re) (* im im)))

series246.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(pow (sqrt (sqrt (+ (* re re) (* im im)))) 4/3)
38.0ms
(sqrt (+ (* re re) (* im im)))
37.0ms
(sqrt (+ (* re re) (* im im)))
37.0ms
(sqrt (+ (* re re) (* im im)))

simplify90.0ms

Counts
85 → 85
Iterations

Useful iterations: 2 (22.0ms)

IterNodesCost
0229555
1796521
22809514
35001514
done5001514

prune238.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 7.8b

regimes239.0ms

Accuracy

57.9% (9.8b remaining)

Error of 17.6b against oracle of 7.8b and baseline of 31.1b

bsearch83.0ms

Steps
ItersRangePoint
8
5.820219195236088e+119
5.264749266612397e+122
5.540206777357536e+120
10
7.495911143049393e-219
4.3617670924590225e-206
7.357011145278624e-217
8
2.604130790303375e-303
6.94733584068207e-301
3.9445916272249785e-301
9
-4.1556755132915836e+156
-7.793373352168505e+150
-4.154655280967186e+151

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0239
1239
done239

end0.0ms

sample337.0ms

Algorithm
intervals
Results
168.0ms8000×body80valid