Details

Time bar (total: 12.3s)

sample17.0ms

Algorithm
intervals
Results
7.0ms256×body80valid

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
178
done78

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.2b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* re re) (* im im))
27.4b
(sqrt (+ (* re re) (* im im)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt add-log-exp
3×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
2×add-exp-log flip3-+ sqrt-div add-cbrt-cube flip-+
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 sum-log
Counts
2 → 26
Calls
2 calls:
15.0ms
(+ (* re re) (* im im))
15.0ms
(sqrt (+ (* re re) (* im im)))

series114.0ms

Counts
2 → 6
Calls
2 calls:
46.0ms
(+ (* re re) (* im im))
68.0ms
(sqrt (+ (* re re) (* im im)))

simplify2.2s

Counts
32 → 32
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
048379
1124347
2343295
3968295
42668295
done5000295

prune95.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 10.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (sqrt (+ (* re re) (* im im))))
27.4b
(sqrt (+ (* re re) (* im im)))
27.4b
(sqrt (+ (* re re) (* im im)))
27.4b
(sqrt (+ (* re re) (* im im)))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
9×add-cube-cbrt *-un-lft-identity
8×sqrt-div
7×pow1
6×cbrt-prod
4×add-exp-log flip3-+ add-cbrt-cube flip-+ add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×cbrt-div
1×pow1/3
Counts
4 → 61
Calls
4 calls:
11.0ms
(cbrt (sqrt (+ (* re re) (* im im))))
16.0ms
(sqrt (+ (* re re) (* im im)))
15.0ms
(sqrt (+ (* re re) (* im im)))
14.0ms
(sqrt (+ (* re re) (* im im)))

series337.0ms

Counts
4 → 12
Calls
4 calls:
171.0ms
(cbrt (sqrt (+ (* re re) (* im im))))
61.0ms
(sqrt (+ (* re re) (* im im)))
48.0ms
(sqrt (+ (* re re) (* im im)))
56.0ms
(sqrt (+ (* re re) (* im im)))

simplify1.8s

Counts
73 → 73
Iterations

Useful iterations: 3 (193.0ms)

IterNodesCost
070952
1149853
2323761
3693750
41884750
done5000750

prune321.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 10.3b

localize45.0ms

Local error

Found 4 expressions with local error:

4.3b
(exp (log (cbrt (sqrt (+ (* re re) (* im im))))))
27.4b
(sqrt (+ (* re re) (* im im)))
27.4b
(sqrt (+ (* re re) (* im im)))
27.4b
(sqrt (+ (* re re) (* im im)))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×sqrt-prod
11×add-cube-cbrt *-un-lft-identity
9×log-prod exp-sum
8×pow1 sqrt-div
6×cbrt-prod
5×exp-prod
4×add-exp-log flip3-+ add-cbrt-cube flip-+ add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×log-div cbrt-div exp-diff log-pow
1×pow1/3 rem-exp-log
Counts
4 → 69
Calls
4 calls:
21.0ms
(exp (log (cbrt (sqrt (+ (* re re) (* im im))))))
19.0ms
(sqrt (+ (* re re) (* im im)))
18.0ms
(sqrt (+ (* re re) (* im im)))
16.0ms
(sqrt (+ (* re re) (* im im)))

series284.0ms

Counts
4 → 12
Calls
4 calls:
151.0ms
(exp (log (cbrt (sqrt (+ (* re re) (* im im))))))
38.0ms
(sqrt (+ (* re re) (* im im)))
38.0ms
(sqrt (+ (* re re) (* im im)))
57.0ms
(sqrt (+ (* re re) (* im im)))

simplify1.8s

Counts
81 → 81
Iterations

Useful iterations: 4 (665.0ms)

IterNodesCost
01111119
1196954
2378824
3754813
41957801
done5000801

prune390.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 10.3b

localize32.0ms

Local error

Found 4 expressions with local error:

27.4b
(sqrt (+ (* re re) (* im im)))
27.4b
(sqrt (+ (* re re) (* im im)))
27.4b
(sqrt (+ (* re re) (* im im)))
27.4b
(sqrt (+ (* re re) (* im im)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 add-cube-cbrt *-un-lft-identity sqrt-div
4×add-exp-log rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 add-cbrt-cube flip-+ add-log-exp
Counts
4 → 60
Calls
4 calls:
8.0ms
(sqrt (+ (* re re) (* im im)))
8.0ms
(sqrt (+ (* re re) (* im im)))
8.0ms
(sqrt (+ (* re re) (* im im)))
8.0ms
(sqrt (+ (* re re) (* im im)))

series261.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(sqrt (+ (* re re) (* im im)))
65.0ms
(sqrt (+ (* re re) (* im im)))
65.0ms
(sqrt (+ (* re re) (* im im)))
63.0ms
(sqrt (+ (* re re) (* im im)))

simplify2.9s

Counts
72 → 72
Iterations

Useful iterations: 3 (134.0ms)

IterNodesCost
038852
191744
2205680
3444656
41114656
53182656
done5001656

prune367.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 10.3b

regimes365.0ms

Accuracy

57.5% (10.1b remaining)

Error of 17.9b against oracle of 7.8b and baseline of 31.5b

bsearch95.0ms

Steps
ItersRangePoint
8
9.007393288790337e+101
4.198803265377596e+104
1.921239608950814e+104
5
1.804245684862004e-220
4.755976263225887e-220
1.914133431995725e-220
9
-2.18846814877946e-261
-3.2700529469739983e-270
-3.6872979313797757e-267
7
-3.9404683775550396e+127
-1.0954634436734111e+126
-5.292452664608309e+126

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01936
12036
done2036

end0.0ms

sample595.0ms

Algorithm
intervals
Results
356.0ms8000×body80valid