Details

Time bar (total: 21.4s)

sample35.0ms

Algorithm
intervals
Results
24.0ms256×body80valid

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
010343
111343
done11343

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.4b

localize20.0ms

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))
31.7b
(sqrt (+ (* re re) (* im im)))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
22×log-pow
21×pow1
17×add-sqr-sqrt
16×*-un-lft-identity add-cube-cbrt
6×sqrt-pow1 pow1/2 associate-/l*
5×add-cbrt-cube add-exp-log add-log-exp
4×associate-/r* sqrt-div
3×flip3-+ sqrt-prod flip-+
2×log-div div-sub
1×cbrt-undiv +-commutative rem-sqrt-square clear-num sum-log frac-2neg div-exp div-inv
Counts
3 → 74
Calls
3 calls:
23.0ms
(+ (* re re) (* im im))
44.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
14.0ms
(sqrt (+ (* re re) (* im im)))

series311.0ms

Counts
3 → 9
Calls
3 calls:
41.0ms
(+ (* re re) (* im im))
203.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
67.0ms
(sqrt (+ (* re re) (* im im)))

simplify2.3s

Counts
83 → 83
Iterations

Useful iterations: 3 (872.0ms)

IterNodesCost
012533837
126230955
268330755
3228530675
done500230675

prune487.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.7b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* re re) (* im im))
0.2b
(* (/ 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)))
33.1b
(log (+ (* re re) (* im im)))

rewrite118.0ms

Algorithm
rewrite-expression-head
Rules
89×times-frac
83×add-sqr-sqrt
54×sqrt-prod
53×*-un-lft-identity add-cube-cbrt
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×frac-times +-commutative clear-num sum-log frac-2neg rem-log-exp pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 164
Calls
4 calls:
6.0ms
(+ (* re re) (* im im))
60.0ms
(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
34.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
11.0ms
(log (+ (* re re) (* im im)))

series651.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(+ (* re re) (* im im))
201.0ms
(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
319.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
82.0ms
(log (+ (* re re) (* im im)))

simplify2.8s

Counts
176 → 176
Iterations

Useful iterations: done (2.8s)

IterNodesCost
021487486
158681815
2196479726
done500179486

prune932.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.6b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* re re) (* im im))
0.2b
(* (* (/ 1/2 (sqrt (log 10.0))) (log (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10.0))))
0.3b
(* (/ 1/2 (sqrt (log 10.0))) (log (+ (* re re) (* im im))))
33.1b
(log (+ (* re re) (* im im)))

rewrite123.0ms

Algorithm
rewrite-expression-head
Rules
49×add-exp-log
44×add-sqr-sqrt times-frac
36×*-un-lft-identity add-cube-cbrt
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×frac-times +-commutative sum-log rem-log-exp associate-*r/ un-div-inv
Counts
4 → 135
Calls
4 calls:
13.0ms
(+ (* re re) (* im im))
60.0ms
(* (* (/ 1/2 (sqrt (log 10.0))) (log (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10.0))))
34.0ms
(* (/ 1/2 (sqrt (log 10.0))) (log (+ (* re re) (* im im))))
9.0ms
(log (+ (* re re) (* im im)))

series646.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(+ (* re re) (* im im))
226.0ms
(* (* (/ 1/2 (sqrt (log 10.0))) (log (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10.0))))
321.0ms
(* (/ 1/2 (sqrt (log 10.0))) (log (+ (* re re) (* im im))))
66.0ms
(log (+ (* re re) (* im im)))

simplify3.6s

Counts
147 → 147
Iterations

Useful iterations: done (3.5s)

IterNodesCost
022770539
164063140
2199861004
done500060522

prune712.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.6b

localize41.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt (/ 1/2 (sqrt (log 10.0)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
0.4b
(* (sqrt (/ 1/2 (sqrt (log 10.0)))) (* (sqrt (/ 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)))
33.1b
(log (+ (* re re) (* im im)))

rewrite243.0ms

Algorithm
rewrite-expression-head
Rules
126×sqrt-prod
112×times-frac
107×add-sqr-sqrt
69×*-un-lft-identity add-cube-cbrt
56×associate-*l*
42×pow1
33×associate-*r*
31×log-pow
21×add-exp-log
20×add-cbrt-cube
12×unswap-sqr
10×sqrt-div
7×associate-/r* prod-exp cbrt-unprod
6×frac-times associate-*r/
4×log-div pow-prod-down associate-*l/ div-inv associate-/l* add-log-exp
3×cbrt-undiv log-prod div-exp
2×flip3-+ div-sub *-commutative flip-+
1×clear-num frac-2neg rem-log-exp
Counts
4 → 207
Calls
4 calls:
72.0ms
(* (sqrt (/ 1/2 (sqrt (log 10.0)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
103.0ms
(* (sqrt (/ 1/2 (sqrt (log 10.0)))) (* (sqrt (/ 1/2 (sqrt (log 10.0)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))))
40.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
10.0ms
(log (+ (* re re) (* im im)))

series1.4s

Counts
4 → 12
Calls
4 calls:
731.0ms
(* (sqrt (/ 1/2 (sqrt (log 10.0)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
371.0ms
(* (sqrt (/ 1/2 (sqrt (log 10.0)))) (* (sqrt (/ 1/2 (sqrt (log 10.0)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))))
276.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
63.0ms
(log (+ (* re re) (* im im)))

simplify3.3s

Counts
219 → 219
Iterations

Useful iterations: done (3.2s)

IterNodesCost
0269123496
1680118035
22316115423
done5000115101

prune1.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 8.5b

regimes1.0s

Accuracy

57.5% (10.4b remaining)

Error of 17.7b against oracle of 7.3b and baseline of 31.7b

bsearch165.0ms

Steps
ItersRangePoint
9
0.1909160003853501
166131308.15705827
85920091.53009516
7
-1.4132096724829227e+117
-8.348201730236839e+114
-1.9687011839458517e+116

simplify26.0ms

Iterations

Useful iterations: 0 (10.0ms)

IterNodesCost
0471920
1601920
done601920

end0.0ms

sample1.0s

Algorithm
intervals
Results
803.0ms8000×body80valid