Details

Time bar (total: 15.4s)

sample23.0ms

Algorithm
intervals
Results
12.0ms256×body80valid

simplify3.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
178
done78

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite29.0ms

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:
14.0ms
(+ (* re re) (* im im))
14.0ms
(sqrt (+ (* re re) (* im im)))

series110.0ms

Counts
2 → 6
Calls
2 calls:
51.0ms
(+ (* re re) (* im im))
59.0ms
(sqrt (+ (* re re) (* im im)))

simplify2.8s

Counts
32 → 32
Iterations

Useful iterations: 2 (97.0ms)

IterNodesCost
048379
1124347
2343295
3968295
42668295
done5000295

prune78.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 6.3b

localize11.0ms

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)))

rewrite36.0ms

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:
8.0ms
(+ (* re re) (* im im))
12.0ms
(exp (log (sqrt (+ (* re re) (* im im)))))
15.0ms
(sqrt (+ (* re re) (* im im)))

series141.0ms

Counts
3 → 9
Calls
3 calls:
52.0ms
(+ (* re re) (* im im))
49.0ms
(exp (log (sqrt (+ (* re re) (* im im)))))
40.0ms
(sqrt (+ (* re re) (* im im)))

simplify2.8s

Counts
57 → 57
Iterations

Useful iterations: 4 (1.3s)

IterNodesCost
087739
1169626
2398534
31056534
42807528
done5001528

prune150.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.3b

localize21.0ms

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)))

rewrite30.0ms

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:
9.0ms
(+ (* re re) (* im im))
13.0ms
(pow (exp 1/2) (log (+ (* re re) (* im im))))
7.0ms
(log (+ (* re re) (* im im)))

series272.0ms

Counts
3 → 9
Calls
3 calls:
32.0ms
(+ (* re re) (* im im))
151.0ms
(pow (exp 1/2) (log (+ (* re re) (* im im))))
89.0ms
(log (+ (* re re) (* im im)))

simplify3.0s

Counts
60 → 60
Iterations

Useful iterations: done (3.0s)

IterNodesCost
096872
1239822
2572714
31369714
43795714
done5001708

prune229.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.3b

localize46.0ms

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)))

rewrite44.0ms

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:
16.0ms
(pow (pow (exp 1/2) (* (cbrt (log (+ (* re re) (* im im)))) (cbrt (log (+ (* re re) (* im im)))))) (cbrt (log (+ (* re re) (* im im)))))
6.0ms
(log (+ (* re re) (* im im)))
8.0ms
(log (+ (* re re) (* im im)))
12.0ms
(log (+ (* re re) (* im im)))

series654.0ms

Counts
4 → 12
Calls
4 calls:
456.0ms
(pow (pow (exp 1/2) (* (cbrt (log (+ (* re re) (* im im)))) (cbrt (log (+ (* re re) (* im im)))))) (cbrt (log (+ (* re re) (* im im)))))
76.0ms
(log (+ (* re re) (* im im)))
63.0ms
(log (+ (* re re) (* im im)))
59.0ms
(log (+ (* re re) (* im im)))

simplify3.1s

Counts
81 → 81
Iterations

Useful iterations: 4 (1.6s)

IterNodesCost
01111966
12521846
25431603
313721562
440161561
done50001561

prune424.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.3b

regimes581.0ms

Accuracy

58.6% (9.6b remaining)

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

bsearch95.0ms

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

sample675.0ms

Algorithm
intervals
Results
402.0ms8000×body80valid