Details

Time bar (total: 5.5s)

sample21.0ms

Algorithm
intervals
Results
11.0ms256×body80valid

simplify3.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0117
1117
done117

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.3b

localize13.0ms

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)))

rewrite36.0ms

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)))

series172.0ms

Counts
2 → 6
Calls
2 calls:
131.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
41.0ms
(sqrt (+ (* re re) (* im im)))

simplify125.0ms

Counts
69 → 69
Iterations

Useful iterations: 4 (118.0ms)

IterNodesCost
0221664
1556631
21309628
34047628
45001627
done5001627

prune190.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 8.2b

localize17.0ms

Local error

Found 3 expressions with local error:

0.3b
(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
0.4b
(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
31.7b
(sqrt (+ (* re re) (* im im)))

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
127×times-frac
107×add-sqr-sqrt
78×sqrt-prod
66×*-un-lft-identity
61×log-pow
60×add-cube-cbrt
52×pow1
46×associate-*r*
27×add-exp-log
25×associate-*l*
17×add-cbrt-cube
16×sqrt-pow1 pow1/2
15×unswap-sqr
9×div-exp
8×prod-exp
7×associate-/r*
6×associate-/l*
5×cbrt-undiv
4×sqrt-div cbrt-unprod
3×div-inv add-log-exp
2×log-div rec-exp flip3-+ 1-exp div-sub flip-+
1×frac-times rem-sqrt-square frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative
Counts
3 → 194
Calls
3 calls:
56.0ms
(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
27.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
8.0ms
(sqrt (+ (* re re) (* im im)))

series520.0ms

Counts
3 → 9
Calls
3 calls:
137.0ms
(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
342.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
40.0ms
(sqrt (+ (* re re) (* im im)))

simplify66.0ms

Counts
203 → 203
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
06132721
124602427
250012325
done50012325

prune394.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 8.1b

localize21.0ms

Local error

Found 3 expressions with local error:

0.3b
(* (/ 1 (sqrt (log 10.0))) (log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))))
3.9b
(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
31.7b
(sqrt (+ (* re re) (* im im)))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
54×add-sqr-sqrt
46×times-frac
43×*-un-lft-identity
41×add-cube-cbrt
38×sqrt-prod
25×pow-unpow associate-*l*
20×log-prod
18×unpow-prod-down
14×pow1
13×add-exp-log
10×distribute-rgt-in distribute-lft-in
8×add-cbrt-cube
7×log-pow
5×unswap-sqr
4×associate-*r* prod-exp
3×pow-pow add-log-exp sqr-pow
2×sqrt-pow1 pow1/2 sqrt-div div-exp cbrt-unprod div-inv
1×cbrt-undiv pow-to-exp rem-sqrt-square rec-exp flip3-+ 1-exp pow-prod-down associate-*l/ pow-exp *-commutative sqrt-pow2 flip-+
Counts
3 → 130
Calls
3 calls:
43.0ms
(* (/ 1 (sqrt (log 10.0))) (log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))))
13.0ms
(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
8.0ms
(sqrt (+ (* re re) (* im im)))

series707.0ms

Counts
3 → 9
Calls
3 calls:
343.0ms
(* (/ 1 (sqrt (log 10.0))) (log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))))
328.0ms
(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
37.0ms
(sqrt (+ (* re re) (* im im)))

simplify59.0ms

Counts
139 → 139
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
05571973
123331615
250021476
done50021476

prune353.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 8.0b

localize22.0ms

Local error

Found 3 expressions with local error:

0.3b
(* (log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))) (/ 1 (sqrt (log 10.0))))
3.9b
(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
31.7b
(sqrt (+ (* re re) (* im im)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
48×add-sqr-sqrt
46×times-frac
37×*-un-lft-identity
35×add-cube-cbrt
32×sqrt-prod
25×pow-unpow associate-*r*
14×pow1
13×add-exp-log
8×add-cbrt-cube
7×log-pow
6×unpow-prod-down
5×unswap-sqr
4×associate-*l* prod-exp
3×pow-pow add-log-exp
2×sqrt-pow1 pow1/2 sqrt-div div-exp cbrt-unprod div-inv
1×cbrt-undiv pow-to-exp rem-sqrt-square rec-exp flip3-+ 1-exp associate-*r/ pow-prod-down pow-exp un-div-inv *-commutative sqrt-pow2 flip-+ sqr-pow
Counts
3 → 111
Calls
3 calls:
26.0ms
(* (log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))) (/ 1 (sqrt (log 10.0))))
13.0ms
(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
8.0ms
(sqrt (+ (* re re) (* im im)))

series711.0ms

Counts
3 → 9
Calls
3 calls:
344.0ms
(* (log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))) (/ 1 (sqrt (log 10.0))))
326.0ms
(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
40.0ms
(sqrt (+ (* re re) (* im im)))

simplify58.0ms

Counts
120 → 120
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
04671445
121301279
250011157
done50011157

prune290.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 8.0b

regimes778.0ms

Accuracy

57.9% (10.4b remaining)

Error of 17.6b against oracle of 7.2b and baseline of 31.9b

bsearch183.0ms

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
-1.0055073931540527e-263
11
-6.794613467217019e+116
-3.315834628005633e+95
-5.543624575485825e+99

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05771
15771
done5771

end0.0ms

sample537.0ms

Algorithm
intervals
Results
342.0ms8000×body80valid