Details

Time bar (total: 23.9s)

sample113.0ms

Algorithm
intervals
Results
31.0ms125×body160valid
25.0ms221×body80nan
15.0ms131×body80valid

simplify1.4s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01619
12919
24919
310119
427719
5156119
done500119

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.2b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ Om Omc) 2.0)
0.2b
(pow (/ t l) 2.0)
0.4b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
9.7b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
59×add-sqr-sqrt
46×times-frac
38×*-un-lft-identity
32×add-cube-cbrt unpow-prod-down
30×sqrt-prod
12×difference-of-squares
10×add-exp-log
7×pow1
6×pow-unpow
5×sqr-pow
4×pow-exp add-cbrt-cube add-log-exp
3×div-inv distribute-lft-out--
2×pow-to-exp rem-sqrt-square pow-pow div-exp associate-/r/
1×asin-acos sqrt-pow1 flip3-+ pow1/2 sqrt-div flip-+
Counts
4 → 106
Calls
4 calls:
14.0ms
(pow (/ Om Omc) 2.0)
14.0ms
(pow (/ t l) 2.0)
1.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
64.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series817.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(pow (/ Om Omc) 2.0)
119.0ms
(pow (/ t l) 2.0)
40.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
561.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify1.4s

Counts
118 → 118
Iterations

Useful iterations: 2 (612.0ms)

IterNodesCost
03522388
18582272
223692160
done50012160

prune729.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 10.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
1.8b
(sqrt (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
15.0b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
15.0b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite222.0ms

Algorithm
rewrite-expression-head
Rules
192×add-sqr-sqrt
183×cbrt-prod
149×times-frac
105×*-un-lft-identity
79×add-cube-cbrt
72×sqrt-prod
52×difference-of-squares
26×unpow-prod-down
13×distribute-lft-out-- sqr-pow
11×associate-/l*
10×cbrt-div
6×add-exp-log associate-/r*
5×pow1 rem-sqrt-square
4×flip3-+ associate-/r/ add-cbrt-cube flip-+ add-log-exp
2×pow1/3 div-inv associate-/l/
1×cbrt-undiv flip3-- frac-2neg sqrt-pow1 pow1/2 sqrt-div div-exp clear-num flip--
Counts
4 → 212
Calls
4 calls:
86.0ms
(/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
101.0ms
(sqrt (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
6.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
6.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.8s

Counts
4 → 12
Calls
4 calls:
594.0ms
(/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
493.0ms
(sqrt (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
374.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
329.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify1.0s

Counts
224 → 224
Iterations

Useful iterations: done (1.0s)

IterNodesCost
03547722
15637481
214477317
done50007302

prune2.0s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 10.1b

localize44.0ms

Local error

Found 4 expressions with local error:

0.4b
(asin (* (fabs (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
1.8b
(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
15.4b
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
15.4b
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite173.0ms

Algorithm
rewrite-expression-head
Rules
117×add-sqr-sqrt
92×cbrt-prod
82×times-frac
59×*-un-lft-identity
41×add-cube-cbrt
36×difference-of-squares
33×sqrt-prod
18×unpow-prod-down
9×distribute-lft-out-- sqr-pow
6×associate-/r/
5×pow1
4×add-exp-log add-cbrt-cube add-log-exp
3×rem-sqrt-square cbrt-div flip3-+ pow1/3 flip-+ div-inv
2×sqrt-pow1
1×asin-acos pow1/2 sqrt-div
Counts
4 → 133
Calls
4 calls:
2.0ms
(asin (* (fabs (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
79.0ms
(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
41.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
37.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series1.7s

Counts
4 → 12
Calls
4 calls:
73.0ms
(asin (* (fabs (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
575.0ms
(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
466.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
548.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify2.1s

Counts
145 → 145
Iterations

Useful iterations: done (2.1s)

IterNodesCost
02965194
15395053
212574860
341424799
done50004784

prune1.3s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 10.1b

localize67.0ms

Local error

Found 4 expressions with local error:

15.0b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
15.0b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
15.0b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
15.0b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
8×add-sqr-sqrt add-cube-cbrt cbrt-div *-un-lft-identity
4×pow1 add-exp-log flip3-+ pow1/3 add-cbrt-cube flip-+ add-log-exp
Counts
4 → 52
Calls
4 calls:
6.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
6.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
6.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
6.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.5s

Counts
4 → 12
Calls
4 calls:
324.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
359.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
410.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
421.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify1.3s

Counts
64 → 64
Iterations

Useful iterations: 3 (418.0ms)

IterNodesCost
0601256
11461196
24631096
323301076
done50011076

prune636.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 10.1b

regimes1.2s

Accuracy

0% (0.0b remaining)

Error of 10.6b against oracle of 10.6b and baseline of 10.6b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01619
11819
done1819

end0.0ms

sample4.2s

Algorithm
intervals
Results
1.4s3713×body160valid
1.2s7869×body80nan
645.0ms4287×body80valid