Details

Time bar (total: 8.6s)

sample16.0ms

Algorithm
intervals
Results
9.0ms256×body80valid

simplify3.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
079
189
done89

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.5b

localize8.0ms

Local error

Found 3 expressions with local error:

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

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt
6×pow1 add-cube-cbrt log-prod *-un-lft-identity sqrt-prod
5×add-log-exp
4×add-exp-log sqrt-div
3×flip3-+ log-pow add-cbrt-cube flip-+
2×log-div sqrt-pow1 pow1/2
1×+-commutative rem-sqrt-square rem-log-exp sum-log
Counts
3 → 45
Calls
3 calls:
2.0ms
(+ (* re re) (* im im))
3.0ms
(log (sqrt (+ (* re re) (* im im))))
3.0ms
(sqrt (+ (* re re) (* im im)))

series144.0ms

Counts
3 → 9
Calls
3 calls:
35.0ms
(+ (* re re) (* im im))
56.0ms
(log (sqrt (+ (* re re) (* im im))))
53.0ms
(sqrt (+ (* re re) (* im im)))

simplify1.1s

Counts
54 → 54
Iterations

Useful iterations: 3 (275.0ms)

IterNodesCost
073702
1157651
2474561
31662555
done5001555

prune136.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.6b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(log (sqrt (exp (log (+ (* re re) (* im im))))))
3.0b
(exp (log (+ (* re re) (* im im))))
28.5b
(sqrt (exp (log (+ (* re re) (* im im)))))
29.6b
(log (+ (* re re) (* im im)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
22×log-prod
16×add-sqr-sqrt
14×add-cube-cbrt *-un-lft-identity
12×exp-prod sqrt-prod
11×pow1 log-pow
10×log-div sqrt-pow1 exp-sum
6×add-exp-log exp-diff
4×flip3-+ sqrt-div add-cbrt-cube flip-+ add-log-exp
2×rem-sqrt-square pow1/2 rem-log-exp
1×rem-exp-log
Counts
4 → 80
Calls
4 calls:
6.0ms
(log (sqrt (exp (log (+ (* re re) (* im im))))))
4.0ms
(exp (log (+ (* re re) (* im im))))
7.0ms
(sqrt (exp (log (+ (* re re) (* im im)))))
5.0ms
(log (+ (* re re) (* im im)))

series173.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(log (sqrt (exp (log (+ (* re re) (* im im))))))
32.0ms
(exp (log (+ (* re re) (* im im))))
35.0ms
(sqrt (exp (log (+ (* re re) (* im im)))))
51.0ms
(log (+ (* re re) (* im im)))

simplify965.0ms

Counts
92 → 92
Iterations

Useful iterations: 3 (221.0ms)

IterNodesCost
01181365
12011112
2474972
31382966
done5000966

prune208.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 7.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(log (sqrt (+ (* re re) (* im im))))
0.5b
(cbrt (pow (log (sqrt (+ (* re re) (* im im)))) 3))
0.7b
(pow (log (sqrt (+ (* re re) (* im im)))) 3)
28.5b
(sqrt (+ (* re re) (* im im)))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-prod
16×pow1
15×log-pow
14×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
12×unpow-prod-down cube-prod
6×add-exp-log log-prod sqrt-pow1 pow1/2 sqrt-prod
5×add-cbrt-cube
4×sqrt-div add-log-exp
3×pow-unpow
2×cube-mult log-div flip3-+ unpow3 flip-+ sqr-pow
1×pow-to-exp rem-sqrt-square pow-pow pow1/3 rem-log-exp pow-exp rem-cbrt-cube rem-cube-cbrt
Counts
4 → 90
Calls
4 calls:
3.0ms
(log (sqrt (+ (* re re) (* im im))))
2.0ms
(cbrt (pow (log (sqrt (+ (* re re) (* im im)))) 3))
2.0ms
(pow (log (sqrt (+ (* re re) (* im im)))) 3)
4.0ms
(sqrt (+ (* re re) (* im im)))

series254.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(log (sqrt (+ (* re re) (* im im))))
57.0ms
(cbrt (pow (log (sqrt (+ (* re re) (* im im)))) 3))
96.0ms
(pow (log (sqrt (+ (* re re) (* im im)))) 3)
40.0ms
(sqrt (+ (* re re) (* im im)))

simplify1.8s

Counts
102 → 102
Iterations

Useful iterations: 3 (421.0ms)

IterNodesCost
01131598
12491320
26051176
326541162
done50011162

prune219.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 7.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (pow (log (sqrt (+ (* re re) (* im im)))) 3))
0.7b
(pow (cbrt (pow (log (sqrt (+ (* re re) (* im im)))) 3)) 3)
0.7b
(pow (log (sqrt (+ (* re re) (* im im)))) 3)
28.5b
(sqrt (+ (* re re) (* im im)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
54×cbrt-prod
45×unpow-prod-down cube-prod
24×log-pow
23×pow1
21×add-sqr-sqrt
20×add-cube-cbrt *-un-lft-identity
9×sqrt-pow1 pow1/2
6×add-exp-log pow-unpow
5×cube-mult unpow3 add-cbrt-cube sqr-pow
4×add-log-exp
3×pow-pow sqrt-prod
2×pow-to-exp pow1/3 sqrt-div pow-exp rem-cube-cbrt
1×rem-sqrt-square flip3-+ rem-cbrt-cube flip-+
Counts
4 → 131
Calls
4 calls:
2.0ms
(cbrt (pow (log (sqrt (+ (* re re) (* im im)))) 3))
7.0ms
(pow (cbrt (pow (log (sqrt (+ (* re re) (* im im)))) 3)) 3)
2.0ms
(pow (log (sqrt (+ (* re re) (* im im)))) 3)
4.0ms
(sqrt (+ (* re re) (* im im)))

series289.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(cbrt (pow (log (sqrt (+ (* re re) (* im im)))) 3))
94.0ms
(pow (cbrt (pow (log (sqrt (+ (* re re) (* im im)))) 3)) 3)
94.0ms
(pow (log (sqrt (+ (* re re) (* im im)))) 3)
37.0ms
(sqrt (+ (* re re) (* im im)))

simplify2.2s

Counts
143 → 143
Iterations

Useful iterations: 3 (723.0ms)

IterNodesCost
01302778
13182079
26961831
331311801
done50001801

prune255.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 7.6b

regimes300.0ms

Accuracy

58.9% (10.1b remaining)

Error of 17.1b against oracle of 7.0b and baseline of 31.6b

bsearch53.0ms

Steps
ItersRangePoint
7
1.8684288122828866e+141
1.487546070235645e+143
6.23122095692667e+141
8
-7.694350151096703e+119
-2.0669682865938928e+117
-2.0142287793804751e+118

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02026
12126
done2126

end0.0ms

sample429.0ms

Algorithm
intervals
Results
280.0ms8000×body80valid