Details

Time bar (total: 13.6s)

sample60.0ms

Algorithm
intervals
Results
16.0ms251×body80nan
13.0ms111×body160valid
9.0ms145×body80valid

simplify2.0s

Counts
1 → 1
Iterations

Useful iterations: 2 (10.0ms)

IterNodesCost
01619
12919
25118
310618
425218
575918
6271618
done500018

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.4b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ Om Omc) 2.0)
0.3b
(pow (/ t l) 2.0)
0.7b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
8.4b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
59×add-sqr-sqrt
46×times-frac
38×*-un-lft-identity
32×add-cube-cbrt unpow-prod-down
28×sqrt-prod
12×difference-of-squares
10×add-exp-log
7×pow1
6×pow-unpow
5×sqr-pow
4×expm1-log1p-u pow-exp add-cbrt-cube log1p-expm1-u add-log-exp
3×div-inv distribute-lft-out--
2×pow-to-exp rem-sqrt-square pow-pow div-exp
1×asin-acos sqrt-pow1 pow1/2 sqrt-div
Counts
4 → 112
Calls
4 calls:
4.0ms
(pow (/ Om Omc) 2.0)
3.0ms
(pow (/ t l) 2.0)
0.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
26.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

series398.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(pow (/ Om Omc) 2.0)
62.0ms
(pow (/ t l) 2.0)
11.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
266.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

simplify1.0s

Counts
124 → 124
Iterations

Useful iterations: 3 (488.0ms)

IterNodesCost
03192298
15862196
211442088
327172082
done50012082

prune473.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 9.3b

localize20.0ms

Local error

Found 4 expressions with local error:

8.4b
(sqrt (/ (- 1.0 (* (pow (* (cbrt (/ Om Omc)) (cbrt (/ Om Omc))) 2.0) (pow (cbrt (/ Om Omc)) 2.0))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))
13.8b
(cbrt (/ Om Omc))
13.8b
(cbrt (/ Om Omc))
13.8b
(cbrt (/ Om Omc))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
39×cbrt-prod
37×times-frac
35×add-sqr-sqrt
32×add-cube-cbrt *-un-lft-identity
13×sqrt-prod
5×pow1
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u div-inv add-log-exp
3×cbrt-div pow1/3
2×rem-sqrt-square
1×sqrt-pow1 pow1/2 sqrt-div
Counts
4 → 99
Calls
4 calls:
4.0ms
(sqrt (/ (- 1.0 (* (pow (* (cbrt (/ Om Omc)) (cbrt (/ Om Omc))) 2.0) (pow (cbrt (/ Om Omc)) 2.0))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))
2.0ms
(cbrt (/ Om Omc))
1.0ms
(cbrt (/ Om Omc))
2.0ms
(cbrt (/ Om Omc))

series672.0ms

Counts
4 → 12
Calls
4 calls:
488.0ms
(sqrt (/ (- 1.0 (* (pow (* (cbrt (/ Om Omc)) (cbrt (/ Om Omc))) 2.0) (pow (cbrt (/ Om Omc)) 2.0))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))
63.0ms
(cbrt (/ Om Omc))
58.0ms
(cbrt (/ Om Omc))
62.0ms
(cbrt (/ Om Omc))

simplify758.0ms

Counts
111 → 111
Iterations

Useful iterations: 3 (204.0ms)

IterNodesCost
01631987
12661883
25561762
314301744
done50001744

prune551.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 9.3b

localize22.0ms

Local error

Found 4 expressions with local error:

8.5b
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
13.8b
(cbrt (/ Om Omc))
13.8b
(cbrt (/ Om Omc))
13.8b
(cbrt (/ Om Omc))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
39×cbrt-prod
27×add-sqr-sqrt times-frac
26×add-cube-cbrt *-un-lft-identity
5×pow1
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×cbrt-div pow1/3 sqrt-prod div-inv
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 87
Calls
4 calls:
1.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
1.0ms
(cbrt (/ Om Omc))
1.0ms
(cbrt (/ Om Omc))
2.0ms
(cbrt (/ Om Omc))

series287.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
59.0ms
(cbrt (/ Om Omc))
61.0ms
(cbrt (/ Om Omc))
61.0ms
(cbrt (/ Om Omc))

simplify2.5s

Counts
99 → 99
Iterations

Useful iterations: 5 (1.7s)

IterNodesCost
0130972
1200913
2357874
3792856
41766820
54369789
done5000789

prune479.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 9.3b

localize30.0ms

Local error

Found 4 expressions with local error:

13.8b
(cbrt (/ Om Omc))
13.8b
(cbrt (/ Om Omc))
14.8b
(cbrt (/ (- 1.0 (* (pow (* (cbrt (/ Om Omc)) (cbrt (/ Om Omc))) 2.0) (pow (cbrt (/ Om Omc)) 2.0))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))
14.8b
(cbrt (/ (- 1.0 (* (pow (* (cbrt (/ Om Omc)) (cbrt (/ Om Omc))) 2.0) (pow (cbrt (/ Om Omc)) 2.0))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
52×cbrt-prod
36×times-frac
32×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u cbrt-div pow1/3 add-cbrt-cube log1p-expm1-u div-inv add-log-exp
Counts
4 → 96
Calls
4 calls:
1.0ms
(cbrt (/ Om Omc))
1.0ms
(cbrt (/ Om Omc))
2.0ms
(cbrt (/ (- 1.0 (* (pow (* (cbrt (/ Om Omc)) (cbrt (/ Om Omc))) 2.0) (pow (cbrt (/ Om Omc)) 2.0))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))
2.0ms
(cbrt (/ (- 1.0 (* (pow (* (cbrt (/ Om Omc)) (cbrt (/ Om Omc))) 2.0) (pow (cbrt (/ Om Omc)) 2.0))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

series646.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(cbrt (/ Om Omc))
62.0ms
(cbrt (/ Om Omc))
257.0ms
(cbrt (/ (- 1.0 (* (pow (* (cbrt (/ Om Omc)) (cbrt (/ Om Omc))) 2.0) (pow (cbrt (/ Om Omc)) 2.0))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))
264.0ms
(cbrt (/ (- 1.0 (* (pow (* (cbrt (/ Om Omc)) (cbrt (/ Om Omc))) 2.0) (pow (cbrt (/ Om Omc)) 2.0))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

simplify861.0ms

Counts
108 → 108
Iterations

Useful iterations: 3 (236.0ms)

IterNodesCost
01612990
12712942
26052802
319342780
done50012780

prune668.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 9.3b

regimes444.0ms

Accuracy

0% (0.1b remaining)

Error of 10.2b against oracle of 10.2b and baseline of 10.2b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01931
12031
done2031

end0.0ms

sample1.7s

Algorithm
intervals
Results
496.0ms8170×body80nan
456.0ms3852×body160valid
250.0ms4148×body80valid