Details

Time bar (total: 6.7s)

sample23.0ms

Algorithm
intervals
Results
13.0ms256×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: 32.1b

localize10.0ms

Local error

Found 2 expressions with local error:

0.6b
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
29.6b
(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)))

series171.0ms

Counts
2 → 6
Calls
2 calls:
131.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
40.0ms
(sqrt (+ (* re re) (* im im)))

simplify124.0ms

Counts
69 → 69
Iterations

Useful iterations: 4 (118.0ms)

IterNodesCost
0221664
1556631
21309628
34047628
45001627
done5001627

prune201.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.3b

localize14.0ms

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))))
0.5b
(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
29.6b
(sqrt (+ (* re re) (* im im)))

rewrite103.0ms

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)))

series388.0ms

Counts
3 → 9
Calls
3 calls:
143.0ms
(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
208.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
37.0ms
(sqrt (+ (* re re) (* im im)))

simplify65.0ms

Counts
203 → 203
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
06132721
124602427
250012325
done50012325

prune425.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 7.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
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))))
29.6b
(sqrt (+ (* re re) (* im im)))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
58×add-sqr-sqrt
47×*-un-lft-identity
46×times-frac
45×add-cube-cbrt
41×sqrt-prod
30×log-prod
25×pow-unpow associate-*l*
24×unpow-prod-down
16×add-exp-log
15×pow1
10×distribute-rgt-in distribute-lft-in
9×add-cbrt-cube
8×log-pow
5×unswap-sqr
4×associate-*r* prod-exp add-log-exp sqr-pow
3×pow-pow rem-log-exp
2×pow-to-exp sqrt-pow1 pow1/2 sqrt-div div-exp pow-exp cbrt-unprod div-inv
1×cbrt-undiv rem-sqrt-square rec-exp flip3-+ 1-exp pow-prod-down associate-*l/ *-commutative sqrt-pow2 flip-+
Counts
4 → 151
Calls
4 calls:
13.0ms
(log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
44.0ms
(* (/ 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)))

series1.0s

Counts
4 → 12
Calls
4 calls:
303.0ms
(log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
351.0ms
(* (/ 1 (sqrt (log 10.0))) (log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))))
338.0ms
(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
37.0ms
(sqrt (+ (* re re) (* im im)))

simplify59.0ms

Counts
163 → 163
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
05582291
123431895
250021744
done50021744

prune439.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 7.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))) 3)
3.9b
(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
29.6b
(sqrt (+ (* re re) (* im im)))
30.3b
(cbrt (pow (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))) 3))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
50×unpow-prod-down
36×add-sqr-sqrt
35×add-cube-cbrt *-un-lft-identity
30×sqrt-prod
28×pow-unpow
26×cbrt-prod
21×times-frac
20×cube-prod
10×pow1
7×add-exp-log sqr-pow
5×pow-exp add-cbrt-cube
4×pow-pow add-log-exp
3×pow-to-exp log-pow
2×cube-mult sqrt-pow1 pow1/2 sqrt-div unpow3
1×rem-sqrt-square flip3-+ pow1/3 sqrt-pow2 rem-cbrt-cube flip-+ div-inv rem-cube-cbrt
Counts
4 → 134
Calls
4 calls:
19.0ms
(pow (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))) 3)
13.0ms
(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
11.0ms
(sqrt (+ (* re re) (* im im)))
20.0ms
(cbrt (pow (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))) 3))

series1.3s

Counts
4 → 12
Calls
4 calls:
530.0ms
(pow (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))) 3)
351.0ms
(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
37.0ms
(sqrt (+ (* re re) (* im im)))
346.0ms
(cbrt (pow (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))) 3))

simplify49.0ms

Counts
146 → 146
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
04561704
116691620
250021585
done50021585

prune544.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 7.1b

regimes787.0ms

Accuracy

56.5% (10.5b remaining)

Error of 17.8b against oracle of 7.3b and baseline of 31.4b

bsearch188.0ms

Steps
ItersRangePoint
8
5.820219195236088e+119
5.264749266612397e+122
1.0492502064085514e+120
10
7.495911143049393e-219
4.3617670924590225e-206
7.357011145278624e-217
9
-2.3334929034181844e-189
-6.067510619484345e-195
-1.1358230465666132e-194
8
-3.6336066115999543e+118
-2.2779413149403165e+115
-3.9466473421826745e+116

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06275
16275
done6275

end0.0ms

sample550.0ms

Algorithm
intervals
Results
354.0ms8000×body80valid