Details

Time bar (total: 15.0s)

sample31.0ms

Algorithm
intervals
Results
13.0ms256×body80valid

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
178
done78

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite27.0ms

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:
10.0ms
(+ (* re re) (* im im))
17.0ms
(sqrt (+ (* re re) (* im im)))

series76.0ms

Counts
2 → 6
Calls
2 calls:
29.0ms
(+ (* re re) (* im im))
47.0ms
(sqrt (+ (* re re) (* im im)))

simplify2.7s

Counts
32 → 32
Iterations

Useful iterations: 2 (99.0ms)

IterNodesCost
048379
1124347
2343295
3968295
42668295
done5000295

prune79.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 6.3b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* re re) (* im im))
5.5b
(exp (log (sqrt (+ (* re re) (* im im)))))
27.4b
(sqrt (+ (* re re) (* im im)))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×pow1 log-prod exp-prod exp-sum sqrt-prod
5×add-log-exp
4×sqrt-div
3×add-exp-log flip3-+ log-pow add-cbrt-cube flip-+
2×log-div sqrt-pow1 pow1/2 exp-diff
1×+-commutative rem-sqrt-square sum-log rem-exp-log
Counts
3 → 48
Calls
3 calls:
10.0ms
(+ (* re re) (* im im))
17.0ms
(exp (log (sqrt (+ (* re re) (* im im)))))
14.0ms
(sqrt (+ (* re re) (* im im)))

series152.0ms

Counts
3 → 9
Calls
3 calls:
36.0ms
(+ (* re re) (* im im))
65.0ms
(exp (log (sqrt (+ (* re re) (* im im)))))
51.0ms
(sqrt (+ (* re re) (* im im)))

simplify2.4s

Counts
57 → 57
Iterations

Useful iterations: 4 (1.1s)

IterNodesCost
087739
1169626
2398534
31056534
42807528
done5001528

prune205.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.3b

localize26.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* re re) (* im im))
6.3b
(pow (exp 1/2) (log (+ (* re re) (* im im))))
28.4b
(log (+ (* re re) (* im im)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×pow1 log-prod
5×add-log-exp
4×add-exp-log log-div pow-unpow pow-pow
3×unpow-prod-up unpow-prod-down exp-prod flip3-+ add-cbrt-cube flip-+
2×log-pow pow-sub
1×+-commutative pow-to-exp rem-log-exp pow-exp sum-log sqr-pow
Counts
3 → 51
Calls
3 calls:
14.0ms
(+ (* re re) (* im im))
11.0ms
(pow (exp 1/2) (log (+ (* re re) (* im im))))
7.0ms
(log (+ (* re re) (* im im)))

series241.0ms

Counts
3 → 9
Calls
3 calls:
29.0ms
(+ (* re re) (* im im))
130.0ms
(pow (exp 1/2) (log (+ (* re re) (* im im))))
82.0ms
(log (+ (* re re) (* im im)))

simplify2.9s

Counts
60 → 60
Iterations

Useful iterations: done (2.9s)

IterNodesCost
096872
1239822
2572714
31369714
43795714
done5001708

prune199.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.3b

localize58.0ms

Local error

Found 4 expressions with local error:

5.8b
(pow (pow (exp 1/2) (* (cbrt (log (+ (* re re) (* im im)))) (cbrt (log (+ (* re re) (* im im)))))) (cbrt (log (+ (* re re) (* im im)))))
28.4b
(log (+ (* re re) (* im im)))
28.4b
(log (+ (* re re) (* im im)))
28.4b
(log (+ (* re re) (* im im)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
10×unpow-prod-down
9×log-prod
8×pow1 add-exp-log
7×pow-unpow
6×log-div
4×cbrt-prod pow-exp log-pow add-cbrt-cube add-log-exp
3×flip3-+ rem-log-exp flip-+
2×pow-to-exp sqr-pow
1×pow-pow
Counts
4 → 69
Calls
4 calls:
14.0ms
(pow (pow (exp 1/2) (* (cbrt (log (+ (* re re) (* im im)))) (cbrt (log (+ (* re re) (* im im)))))) (cbrt (log (+ (* re re) (* im im)))))
7.0ms
(log (+ (* re re) (* im im)))
13.0ms
(log (+ (* re re) (* im im)))
14.0ms
(log (+ (* re re) (* im im)))

series715.0ms

Counts
4 → 12
Calls
4 calls:
482.0ms
(pow (pow (exp 1/2) (* (cbrt (log (+ (* re re) (* im im)))) (cbrt (log (+ (* re re) (* im im)))))) (cbrt (log (+ (* re re) (* im im)))))
86.0ms
(log (+ (* re re) (* im im)))
93.0ms
(log (+ (* re re) (* im im)))
53.0ms
(log (+ (* re re) (* im im)))

simplify3.3s

Counts
81 → 81
Iterations

Useful iterations: 4 (1.7s)

IterNodesCost
01111966
12521846
25431603
313721562
440161561
done50001561

prune466.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.3b

regimes489.0ms

Accuracy

58.6% (9.6b remaining)

Error of 17.5b against oracle of 7.9b and baseline of 31.2b

bsearch98.0ms

Steps
ItersRangePoint
9
3.828787491213863e+135
1.1582935083099526e+141
2.931608767883357e+138
9
-2.0350997751618612e+124
-4.455739765009825e+115
-8.953163933293596e+119

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01319
11419
done1419

end0.0ms

sample781.0ms

Algorithm
intervals
Results
462.0ms8000×body80valid