Details

Time bar (total: 7.5s)

sample29.0ms

Algorithm
intervals
Results
12.0ms256×body80valid

simplify23.0ms

Counts
1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

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))
16.0ms
(sqrt (+ (* re re) (* im im)))

series115.0ms

Counts
2 → 6
Calls
2 calls:
40.0ms
(+ (* re re) (* im im))
74.0ms
(sqrt (+ (* re re) (* im im)))

simplify767.0ms

Counts
32 → 32

prune123.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 6.3b

localize17.0ms

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)))

rewrite43.0ms

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:
11.0ms
(+ (* re re) (* im im))
18.0ms
(exp (log (sqrt (+ (* re re) (* im im)))))
14.0ms
(sqrt (+ (* re re) (* im im)))

series124.0ms

Counts
3 → 9
Calls
3 calls:
37.0ms
(+ (* re re) (* im im))
41.0ms
(exp (log (sqrt (+ (* re re) (* im im)))))
46.0ms
(sqrt (+ (* re re) (* im im)))

simplify866.0ms

Counts
57 → 57

prune144.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.3b

localize20.0ms

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
14×add-sqr-sqrt add-cube-cbrt pow-pow *-un-lft-identity
13×exp-prod
9×times-frac
6×pow1 log-prod
5×add-log-exp
4×add-exp-log log-div pow-unpow
3×unpow-prod-up unpow-prod-down flip3-+ add-cbrt-cube flip-+
2×log-pow pow-sub
1×+-commutative pow-to-exp exp-sqrt rem-log-exp pow-exp sum-log sqrt-pow2 div-inv sqr-pow
Counts
3 → 62
Calls
3 calls:
8.0ms
(+ (* re re) (* im im))
16.0ms
(pow (exp (/ 1 2)) (log (+ (* re re) (* im im))))
7.0ms
(log (+ (* re re) (* im im)))

series268.0ms

Counts
3 → 9
Calls
3 calls:
40.0ms
(+ (* re re) (* im im))
150.0ms
(pow (exp (/ 1 2)) (log (+ (* re re) (* im im))))
78.0ms
(log (+ (* re re) (* im im)))

simplify1.1s

Counts
71 → 71

prune234.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.3b

localize45.0ms

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)))

rewrite52.0ms

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:
12.0ms
(pow (pow (exp (/ 1 2)) (* (cbrt (log (+ (* re re) (* im im)))) (cbrt (log (+ (* re re) (* im im)))))) (cbrt (log (+ (* re re) (* im im)))))
9.0ms
(log (+ (* re re) (* im im)))
18.0ms
(log (+ (* re re) (* im im)))
11.0ms
(log (+ (* re re) (* im im)))

series751.0ms

Counts
4 → 12
Calls
4 calls:
507.0ms
(pow (pow (exp (/ 1 2)) (* (cbrt (log (+ (* re re) (* im im)))) (cbrt (log (+ (* re re) (* im im)))))) (cbrt (log (+ (* re re) (* im im)))))
74.0ms
(log (+ (* re re) (* im im)))
91.0ms
(log (+ (* re re) (* im im)))
79.0ms
(log (+ (* re re) (* im im)))

simplify1.0s

Counts
81 → 81

prune428.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.3b

regimes460.0ms

Accuracy

58.6% (9.6b remaining)

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

bsearch71.0ms

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

simplify28.0ms

end0.0ms

sample731.0ms

Algorithm
intervals
Results
430.0ms8000×body80valid