Details

Time bar (total: 5.9s)

sample15.0ms

Algorithm
intervals
Results
8.0ms256×body80valid

simplify3.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
068
178
done78

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.5b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* re re) (* im im))
28.5b
(sqrt (+ (* re re) (* im im)))

rewrite7.0ms

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:
3.0ms
(+ (* re re) (* im im))
4.0ms
(sqrt (+ (* re re) (* im im)))

series66.0ms

Counts
2 → 6
Calls
2 calls:
31.0ms
(+ (* re re) (* im im))
35.0ms
(sqrt (+ (* re re) (* im im)))

simplify1.1s

Counts
32 → 32
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
048379
1125347
2438295
31621295
done5000295

prune78.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 8.1b

localize9.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (sqrt (+ (* re re) (* im im))))
28.5b
(sqrt (+ (* re re) (* im im)))
28.5b
(sqrt (+ (* re re) (* im im)))
28.5b
(sqrt (+ (* re re) (* im im)))

rewrite15.0ms

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:
3.0ms
(cbrt (sqrt (+ (* re re) (* im im))))
4.0ms
(sqrt (+ (* re re) (* im im)))
3.0ms
(sqrt (+ (* re re) (* im im)))
4.0ms
(sqrt (+ (* re re) (* im im)))

series197.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(cbrt (sqrt (+ (* re re) (* im im))))
34.0ms
(sqrt (+ (* re re) (* im im)))
34.0ms
(sqrt (+ (* re re) (* im im)))
38.0ms
(sqrt (+ (* re re) (* im im)))

simplify1.7s

Counts
73 → 73
Iterations

Useful iterations: 3 (348.0ms)

IterNodesCost
070952
1149853
2366761
3944750
43187750
done5000750

prune194.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 8.1b

localize15.0ms

Local error

Found 4 expressions with local error:

28.5b
(sqrt (+ (* re re) (* im im)))
28.5b
(sqrt (+ (* re re) (* im im)))
28.5b
(sqrt (+ (* re re) (* im im)))
28.5b
(sqrt (+ (* re re) (* im im)))

rewrite16.0ms

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:
4.0ms
(sqrt (+ (* re re) (* im im)))
3.0ms
(sqrt (+ (* re re) (* im im)))
3.0ms
(sqrt (+ (* re re) (* im im)))
4.0ms
(sqrt (+ (* re re) (* im im)))

series144.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(sqrt (+ (* re re) (* im im)))
37.0ms
(sqrt (+ (* re re) (* im im)))
35.0ms
(sqrt (+ (* re re) (* im im)))
37.0ms
(sqrt (+ (* re re) (* im im)))

simplify1.6s

Counts
72 → 72
Iterations

Useful iterations: 3 (72.0ms)

IterNodesCost
038852
191744
2207680
3459656
41009656
52577656
done5000656

prune241.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 8.1b

localize1.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify1.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000
done00

prune0.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 8.1b

regimes204.0ms

Accuracy

58.8% (9.8b remaining)

Error of 17.4b against oracle of 7.6b and baseline of 31.5b

bsearch40.0ms

Steps
ItersRangePoint
7
1.8684288122828866e+141
1.487546070235645e+143
1.1032025771158766e+142
8
-7.694350151096703e+119
-2.0669682865938928e+117
-4.109494051147195e+119

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01319
11419
done1419

end0.0ms

sample289.0ms

Algorithm
intervals
Results
167.0ms8000×body80valid