Details

Time bar (total: 4.5s)

sample20.0ms

Algorithm
intervals
Results
11.0ms256×body80valid

simplify3.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0117
1117
done117

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.3b

localize10.0ms

Local error

Found 2 expressions with local error:

0.6b
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
31.7b
(sqrt (+ (* re re) (* im im)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
22×log-pow
20×pow1
16×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
6×sqrt-pow1 pow1/2 associate-/l*
4×add-exp-log sqrt-div associate-/r* add-cbrt-cube
3×sqrt-prod
2×log-div flip3-+ div-sub flip-+ add-log-exp
1×cbrt-undiv rem-sqrt-square frac-2neg div-exp clear-num div-inv
Counts
2 → 63
Calls
2 calls:
26.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
8.0ms
(sqrt (+ (* re re) (* im im)))

series163.0ms

Counts
2 → 6
Calls
2 calls:
127.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
36.0ms
(sqrt (+ (* re re) (* im im)))

simplify123.0ms

Counts
69 → 69
Iterations

Useful iterations: 4 (116.0ms)

IterNodesCost
0221664
1556631
21309628
34047628
45001627
done5001627

prune183.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 8.2b

localize12.0ms

Local error

Found 3 expressions with local error:

0.3b
(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
0.4b
(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
33.0b
(log (+ (* re re) (* im im)))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
89×times-frac
82×add-sqr-sqrt
54×sqrt-prod
52×add-cube-cbrt *-un-lft-identity
33×pow1
32×associate-*r*
28×log-pow
25×associate-*l*
18×add-exp-log
17×add-cbrt-cube
9×unswap-sqr
7×associate-/r*
5×cbrt-undiv div-exp
4×log-div prod-exp cbrt-unprod associate-/l*
3×log-prod div-inv add-log-exp
2×flip3-+ div-sub flip-+
1×frac-times frac-2neg associate-*r/ rem-log-exp pow-prod-down associate-*l/ clear-num *-commutative
Counts
3 → 153
Calls
3 calls:
47.0ms
(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
23.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
7.0ms
(log (+ (* re re) (* im im)))

series359.0ms

Counts
3 → 9
Calls
3 calls:
131.0ms
(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
177.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
51.0ms
(log (+ (* re re) (* im im)))

simplify59.0ms

Counts
162 → 162
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
05282082
120651915
250011832
done50011832

prune339.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.0b

localize22.0ms

Local error

Found 3 expressions with local error:

0.3b
(* (/ 1/2 (sqrt (log 10.0))) (log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))))
15.3b
(log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0)))))
18.6b
(pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
47×add-sqr-sqrt
44×times-frac
39×add-cube-cbrt *-un-lft-identity
25×pow-unpow associate-*l* sqrt-prod
21×log-prod
12×pow1 unpow-prod-down
11×add-exp-log
8×log-pow add-cbrt-cube
7×distribute-rgt-in distribute-lft-in
4×associate-*r* sqr-pow
3×rem-log-exp add-log-exp unswap-sqr
2×pow-to-exp pow-exp prod-exp cbrt-unprod div-inv
1×cbrt-undiv pow-pow div-exp pow-prod-down associate-*l/ *-commutative
Counts
3 → 117
Calls
3 calls:
40.0ms
(* (/ 1/2 (sqrt (log 10.0))) (log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))))
11.0ms
(log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0)))))
13.0ms
(pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))

series953.0ms

Counts
3 → 9
Calls
3 calls:
377.0ms
(* (/ 1/2 (sqrt (log 10.0))) (log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))))
277.0ms
(log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0)))))
298.0ms
(pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))

simplify54.0ms

Counts
126 → 126
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
04631699
119901501
250011310
done50011310

prune310.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 8.0b

localize21.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt (* (cbrt (log 10.0)) (cbrt (log 10.0))))
1.0b
(/ (* (cbrt 1/2) (cbrt 1/2)) (sqrt (* (cbrt (log 10.0)) (cbrt (log 10.0)))))
1.6b
(* (cbrt (log 10.0)) (cbrt (log 10.0)))
33.0b
(log (+ (* re re) (* im im)))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
26×pow1
24×cbrt-prod
23×add-sqr-sqrt
17×*-un-lft-identity
15×add-cube-cbrt
12×add-exp-log pow1/3
9×sqrt-pow1 swap-sqr
7×associate-*r* associate-*l* log-pow add-cbrt-cube
4×times-frac pow-prod-down associate-/r* pow-sqr pow-prod-up add-log-exp unswap-sqr
3×log-prod sqrt-prod
2×cbrt-undiv pow2 log-div pow-plus div-exp prod-exp cbrt-unprod
1×rem-sqrt-square frac-2neg flip3-+ pow1/2 rem-log-exp clear-num *-commutative flip-+ div-inv associate-/l*
Counts
4 → 101
Calls
4 calls:
6.0ms
(sqrt (* (cbrt (log 10.0)) (cbrt (log 10.0))))
20.0ms
(/ (* (cbrt 1/2) (cbrt 1/2)) (sqrt (* (cbrt (log 10.0)) (cbrt (log 10.0)))))
13.0ms
(* (cbrt (log 10.0)) (cbrt (log 10.0)))
6.0ms
(log (+ (* re re) (* im im)))

series50.0ms

Counts
4 → 6
Calls
4 calls:
0.0ms
(sqrt (* (cbrt (log 10.0)) (cbrt (log 10.0))))
0.0ms
(/ (* (cbrt 1/2) (cbrt 1/2)) (sqrt (* (cbrt (log 10.0)) (cbrt (log 10.0)))))
0.0ms
(* (cbrt (log 10.0)) (cbrt (log 10.0)))
50.0ms
(log (+ (* re re) (* im im)))

simplify40.0ms

Counts
107 → 107
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0300840
11152751
25001675
done5001675

prune343.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 7.9b

regimes516.0ms

Accuracy

57.7% (10.5b remaining)

Error of 17.6b against oracle of 7.1b and baseline of 31.9b

bsearch165.0ms

Steps
ItersRangePoint
9
1.596161804377022e+119
4.919965018933925e+124
4.9691480257024896e+122
10
2.67271266005654e-166
4.421061065096694e-156
2.6951869124740155e-166
7
-1.1247036883386809e-263
-5.3645173288875583e-266
-9.578288750802015e-264
11
-6.794613467217019e+116
-3.315834628005633e+95
-5.543624575485825e+99

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05349
15349
done5349

end0.0ms

sample536.0ms

Algorithm
intervals
Results
339.0ms8000×body80valid