Details

Time bar (total: 12.7s)

sample19.0ms

Algorithm
intervals
Results
11.0ms256×body80valid

simplify3.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01012
11112
done1112

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.9b

localize10.0ms

Local error

Found 2 expressions with local error:

0.6b
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
30.5b
(sqrt (+ (* re re) (* im im)))

rewrite17.0ms

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:
11.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
4.0ms
(sqrt (+ (* re re) (* im im)))

series174.0ms

Counts
2 → 6
Calls
2 calls:
134.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
40.0ms
(sqrt (+ (* re re) (* im im)))

simplify1.6s

Counts
69 → 69
Iterations

Useful iterations: 3 (195.0ms)

IterNodesCost
01161191
12221120
24861046
312001032
432591032
done50001032

prune204.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 8.2b

localize12.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ (/ 1 2) (/ (log 10.0) (log (+ (* re re) (* im im)))))
0.6b
(/ (log 10.0) (log (+ (* re re) (* im im))))
31.6b
(log (+ (* re re) (* im im)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
689×times-frac
287×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
126×pow1
123×log-pow
37×div-inv
28×add-exp-log
24×associate-/r*
17×div-exp add-cbrt-cube associate-/l*
9×cbrt-undiv
3×log-prod add-log-exp
2×log-div rec-exp frac-2neg 1-exp clear-num
1×flip3-+ rem-log-exp associate-/r/ flip-+ associate-/l/
Counts
3 → 367
Calls
3 calls:
14.0ms
(/ (/ 1 2) (/ (log 10.0) (log (+ (* re re) (* im im)))))
3.0ms
(/ (log 10.0) (log (+ (* re re) (* im im))))
3.0ms
(log (+ (* re re) (* im im)))

series316.0ms

Counts
3 → 9
Calls
3 calls:
137.0ms
(/ (/ 1 2) (/ (log 10.0) (log (+ (* re re) (* im im)))))
126.0ms
(/ (log 10.0) (log (+ (* re re) (* im im))))
53.0ms
(log (+ (* re re) (* im im)))

simplify1.3s

Counts
376 → 376
Iterations

Useful iterations: 2 (704.0ms)

IterNodesCost
046611021
113379369
235558971
done50018971

prune470.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ (sqrt 1/2) (sqrt (log 10.0))) (/ (sqrt 1/2) (/ (sqrt (log 10.0)) (log (+ (* re re) (* im im))))))
0.4b
(/ (sqrt 1/2) (/ (sqrt (log 10.0)) (log (+ (* re re) (* im im)))))
0.4b
(/ (sqrt (log 10.0)) (log (+ (* re re) (* im im))))
31.6b
(log (+ (* re re) (* im im)))

rewrite244.0ms

Algorithm
rewrite-expression-head
Rules
896×times-frac
537×add-sqr-sqrt
521×sqrt-prod
389×add-cube-cbrt *-un-lft-identity
197×associate-*r*
169×pow1
163×log-pow
46×associate-*l*
36×associate-/r*
35×unswap-sqr
33×add-exp-log
32×add-cbrt-cube
17×div-inv
13×cbrt-undiv div-exp associate-/l*
6×prod-exp cbrt-unprod
4×add-log-exp
3×log-prod
2×log-div frac-2neg clear-num associate-/r/
1×frac-times flip3-+ associate-*r/ rem-log-exp pow-prod-down associate-*l/ *-commutative flip-+
Counts
4 → 612
Calls
4 calls:
171.0ms
(* (/ (sqrt 1/2) (sqrt (log 10.0))) (/ (sqrt 1/2) (/ (sqrt (log 10.0)) (log (+ (* re re) (* im im))))))
12.0ms
(/ (sqrt 1/2) (/ (sqrt (log 10.0)) (log (+ (* re re) (* im im)))))
4.0ms
(/ (sqrt (log 10.0)) (log (+ (* re re) (* im im))))
5.0ms
(log (+ (* re re) (* im im)))

series678.0ms

Counts
4 → 12
Calls
4 calls:
223.0ms
(* (/ (sqrt 1/2) (sqrt (log 10.0))) (/ (sqrt 1/2) (/ (sqrt (log 10.0)) (log (+ (* re re) (* im im))))))
235.0ms
(/ (sqrt 1/2) (/ (sqrt (log 10.0)) (log (+ (* re re) (* im im)))))
170.0ms
(/ (sqrt (log 10.0)) (log (+ (* re re) (* im im))))
50.0ms
(log (+ (* re re) (* im im)))

simplify2.1s

Counts
624 → 624
Iterations

Useful iterations: 2 (871.0ms)

IterNodesCost
050217358
1145915561
2483714919
done500014919

prune1.1s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 8.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (/ (sqrt (sqrt 1/2)) (sqrt (log 10.0))) (* (sqrt (sqrt 1/2)) (log (+ (* re re) (* im im)))))
1.0b
(sqrt (sqrt 1/2))
1.0b
(sqrt (sqrt 1/2))
31.6b
(log (+ (* re re) (* im im)))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
119×sqrt-prod
67×associate-*l*
63×times-frac
57×add-sqr-sqrt
53×add-cube-cbrt *-un-lft-identity
23×pow1
17×add-exp-log
16×add-cbrt-cube
15×log-prod
12×distribute-rgt-in distribute-lft-in
10×log-pow
8×sqrt-pow1
6×prod-exp cbrt-unprod
4×rem-sqrt-square pow1/2 add-log-exp
3×pow-prod-down
2×cbrt-undiv log-div div-exp
1×flip3-+ rem-log-exp associate-*r* associate-*l/ *-commutative flip-+ div-inv
Counts
4 → 151
Calls
4 calls:
45.0ms
(* (/ (sqrt (sqrt 1/2)) (sqrt (log 10.0))) (* (sqrt (sqrt 1/2)) (log (+ (* re re) (* im im)))))
4.0ms
(sqrt (sqrt 1/2))
1.0ms
(sqrt (sqrt 1/2))
3.0ms
(log (+ (* re re) (* im im)))

series292.0ms

Counts
4 → 8
Calls
4 calls:
239.0ms
(* (/ (sqrt (sqrt 1/2)) (sqrt (log 10.0))) (* (sqrt (sqrt 1/2)) (log (+ (* re re) (* im im)))))
0.0ms
(sqrt (sqrt 1/2))
0.0ms
(sqrt (sqrt 1/2))
52.0ms
(log (+ (* re re) (* im im)))

simplify2.5s

Counts
159 → 159
Iterations

Useful iterations: 3 (1.2s)

IterNodesCost
01993073
15052624
213632410
347302376
done50002376

prune430.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 8.0b

regimes557.0ms

Accuracy

58.7% (10.4b remaining)

Error of 18.0b against oracle of 7.6b and baseline of 32.7b

bsearch141.0ms

Steps
ItersRangePoint
9
1.3371381883907536e+91
9.843787102234572e+98
8.027827998243755e+98
7
7.991847353731723e-282
1.110810473879014e-279
1.2766285812733717e-281
2
-4.9541499614204095e-275
-4.29238249318267e-275
-4.540545293771823e-275
8
-5.294872751913314e+157
-4.107841816162241e+153
-4.197550803800697e+153

simplify6.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
045110
155109
257109
done57109

end0.0ms

sample487.0ms

Algorithm
intervals
Results
347.0ms8000×body80valid