Details

Time bar (total: 17.5s)

sample32.0ms

Algorithm
intervals
Results
16.0ms256×body80valid

simplify8.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01012
11112
done1112

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.8b

localize26.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* re re) (* im im))
0.6b
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
28.4b
(sqrt (+ (* re re) (* im im)))

rewrite113.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
22×log-pow
21×pow1
17×add-sqr-sqrt
16×add-cube-cbrt *-un-lft-identity
6×sqrt-pow1 pow1/2 associate-/l*
5×add-exp-log add-cbrt-cube add-log-exp
4×sqrt-div associate-/r*
3×flip3-+ sqrt-prod flip-+
2×log-div div-sub
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg div-exp clear-num sum-log div-inv
Counts
3 → 74
Calls
3 calls:
33.0ms
(+ (* re re) (* im im))
55.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
19.0ms
(sqrt (+ (* re re) (* im im)))

series330.0ms

Counts
3 → 9
Calls
3 calls:
36.0ms
(+ (* re re) (* im im))
213.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
81.0ms
(sqrt (+ (* re re) (* im im)))

simplify3.1s

Counts
83 → 83
Iterations

Useful iterations: 3 (437.0ms)

IterNodesCost
01251357
12541281
25881165
313941163
435091163
done50011163

prune342.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 6.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* re re) (* im im))
0.3b
(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
0.5b
(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
29.6b
(log (+ (* re re) (* im im)))

rewrite124.0ms

Algorithm
rewrite-expression-head
Rules
89×times-frac
83×add-sqr-sqrt
54×sqrt-prod
53×add-cube-cbrt *-un-lft-identity
34×pow1
32×associate-*r*
28×log-pow
25×associate-*l*
19×add-exp-log
18×add-cbrt-cube
9×unswap-sqr
7×associate-/r*
6×add-log-exp
5×cbrt-undiv div-exp
4×log-div prod-exp cbrt-unprod associate-/l*
3×log-prod flip3-+ flip-+ div-inv
2×div-sub
1×+-commutative frac-times frac-2neg associate-*r/ rem-log-exp pow-prod-down associate-*l/ clear-num sum-log *-commutative
Counts
4 → 164
Calls
4 calls:
9.0ms
(+ (* re re) (* im im))
51.0ms
(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
41.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
8.0ms
(log (+ (* re re) (* im im)))

series582.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(+ (* re re) (* im im))
194.0ms
(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
262.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
83.0ms
(log (+ (* re re) (* im im)))

simplify1.7s

Counts
176 → 176
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02143631
15503423
216513032
done50002997

prune674.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 6.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* re re) (* im im))
0.3b
(* (/ 1/2 (sqrt (log 10.0))) (log (+ (* re re) (* im im))))
0.3b
(* (* (/ 1/2 (sqrt (log 10.0))) (log (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10.0))))
29.6b
(log (+ (* re re) (* im im)))

rewrite157.0ms

Algorithm
rewrite-expression-head
Rules
49×add-exp-log
44×add-sqr-sqrt times-frac
36×add-cube-cbrt *-un-lft-identity
30×add-cbrt-cube
29×associate-*r*
26×associate-*l*
25×sqrt-prod
22×prod-exp
19×pow1
12×cbrt-unprod
11×div-exp
9×log-prod
8×log-pow
6×cbrt-undiv add-log-exp
4×pow-prod-down associate-*l/
3×distribute-rgt-in rec-exp distribute-lft-in 1-exp unswap-sqr
2×log-div flip3-+ *-commutative flip-+ div-inv
1×+-commutative frac-times associate-*r/ rem-log-exp sum-log un-div-inv
Counts
4 → 135
Calls
4 calls:
18.0ms
(+ (* re re) (* im im))
40.0ms
(* (/ 1/2 (sqrt (log 10.0))) (log (+ (* re re) (* im im))))
80.0ms
(* (* (/ 1/2 (sqrt (log 10.0))) (log (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10.0))))
7.0ms
(log (+ (* re re) (* im im)))

series738.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(+ (* re re) (* im im))
383.0ms
(* (/ 1/2 (sqrt (log 10.0))) (log (+ (* re re) (* im im))))
200.0ms
(* (* (/ 1/2 (sqrt (log 10.0))) (log (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10.0))))
102.0ms
(log (+ (* re re) (* im im)))

simplify2.7s

Counts
147 → 147
Iterations

Useful iterations: 2 (855.0ms)

IterNodesCost
02272987
15862699
218872139
done50002139

prune650.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.2b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* re re) (* im im))
0.0b
(log (pow (+ (* re re) (* im im)) (/ 1/2 (sqrt (log 10.0)))))
0.3b
(* (log (pow (+ (* re re) (* im im)) (/ 1/2 (sqrt (log 10.0))))) (/ 1 (sqrt (log 10.0))))
30.6b
(pow (+ (* re re) (* im im)) (/ 1/2 (sqrt (log 10.0))))

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
48×add-sqr-sqrt
46×times-frac
38×*-un-lft-identity
36×add-cube-cbrt
26×sqrt-prod
25×pow-unpow associate-*r*
16×add-exp-log
13×pow1
9×add-cbrt-cube
8×log-pow
7×log-prod
6×unpow-prod-down add-log-exp
5×unswap-sqr
4×associate-*l* prod-exp
3×rem-log-exp
2×pow-to-exp div-exp pow-exp cbrt-unprod div-inv sqr-pow
1×cbrt-undiv +-commutative rec-exp pow-pow flip3-+ 1-exp associate-*r/ pow-prod-down sum-log un-div-inv *-commutative flip-+
Counts
4 → 119
Calls
4 calls:
9.0ms
(+ (* re re) (* im im))
12.0ms
(log (pow (+ (* re re) (* im im)) (/ 1/2 (sqrt (log 10.0)))))
42.0ms
(* (log (pow (+ (* re re) (* im im)) (/ 1/2 (sqrt (log 10.0))))) (/ 1 (sqrt (log 10.0))))
30.0ms
(pow (+ (* re re) (* im im)) (/ 1/2 (sqrt (log 10.0))))

series1.7s

Counts
4 → 12
Calls
4 calls:
45.0ms
(+ (* re re) (* im im))
502.0ms
(log (pow (+ (* re re) (* im im)) (/ 1/2 (sqrt (log 10.0)))))
568.0ms
(* (log (pow (+ (* re re) (* im im)) (/ 1/2 (sqrt (log 10.0))))) (/ 1 (sqrt (log 10.0))))
560.0ms
(pow (+ (* re re) (* im im)) (/ 1/2 (sqrt (log 10.0))))

simplify1.9s

Counts
131 → 131
Iterations

Useful iterations: done (1.9s)

IterNodesCost
02032627
15152368
214541996
done50001979

prune560.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 6.2b

regimes663.0ms

Accuracy

27.8% (17.6b remaining)

Error of 24.9b against oracle of 7.3b and baseline of 31.7b

bsearch455.0ms

Steps
ItersRangePoint
6
5.648580377641702e+85
7.97203048753092e+86
1.4275530984731863e+86
7
3.1017552524573808e-170
2.9279685249567416e-168
9.430941523167469e-169
6
1.6291874015072715e-199
1.4316726427427919e-198
7.52812535531041e-199
8
1.130281079294657e-219
8.79270723422623e-217
3.867993196915089e-217
8
4.806576296215955e-236
2.5891023046651694e-233
9.677784630305516e-234
10
-1.900142676637447e-261
-8.898276766909416e-272
-4.5026408152664893e-262
8
-3.1089471099746935e+33
-1.8643414828365696e+30
-3.0545556871718285e+33
6
-6.745190138739985e+57
-6.4659780467737265e+56
-6.570997735276895e+56
5
-3.001107438090069e+136
-1.2675207568445035e+136
-2.9574832218065225e+136

simplify24.0ms

Iterations

Useful iterations: 3 (18.0ms)

IterNodesCost
079203
199201
2105201
3108200
done108200

end0.0ms

sample912.0ms

Algorithm
intervals
Results
720.0ms8000×body80valid