Details

Time bar (total: 14.5s)

sample59.0ms

Algorithm
intervals
Results
14.0ms232×body80nan
14.0ms116×body160valid
11.0ms140×body80valid

simplify2.0s

Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
01619
12919
25118
310618
425218
575918
6271618
done500018

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ Om Omc) 2.0)
0.3b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
1.0b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
10.7b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
96×add-sqr-sqrt
65×times-frac
51×*-un-lft-identity
37×add-cube-cbrt
30×sqrt-prod
28×difference-of-squares
27×unpow-prod-down
9×add-exp-log
8×associate-/l* sqr-pow
7×distribute-lft-out--
6×pow1 add-cbrt-cube
4×expm1-log1p-u associate-/r/ log1p-expm1-u add-log-exp
3×pow-unpow associate-/r* div-inv
2×rem-sqrt-square flip3-+ div-exp pow-exp flip-+ associate-/l/
1×cbrt-undiv pow-to-exp asin-acos flip3-- pow-pow frac-2neg sqrt-pow1 pow1/2 sqrt-div div-sub clear-num flip--
Counts
4 → 138
Calls
4 calls:
3.0ms
(pow (/ Om Omc) 2.0)
49.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
27.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series616.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(pow (/ Om Omc) 2.0)
219.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
16.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
320.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify761.0ms

Counts
150 → 150
Iterations

Useful iterations: done (756.0ms)

IterNodesCost
03163783
16523663
215523335
done50003323

prune628.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 12.0b

localize22.0ms

Local error

Found 4 expressions with local error:

10.8b
(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
10.8b
(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
16.1b
(sqrt (pow (/ Om Omc) 2.0))
16.1b
(sqrt (pow (/ Om Omc) 2.0))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
40×sqrt-prod
32×add-sqr-sqrt
30×unpow-prod-down
22×add-cube-cbrt *-un-lft-identity
20×times-frac
10×rem-sqrt-square
6×pow1
4×add-exp-log expm1-log1p-u sqrt-pow1 pow1/2 add-cbrt-cube log1p-expm1-u add-log-exp sqr-pow
2×div-inv
Counts
4 → 94
Calls
4 calls:
1.0ms
(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
1.0ms
(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
6.0ms
(sqrt (pow (/ Om Omc) 2.0))
7.0ms
(sqrt (pow (/ Om Omc) 2.0))

series735.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
106.0ms
(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
263.0ms
(sqrt (pow (/ Om Omc) 2.0))
266.0ms
(sqrt (pow (/ Om Omc) 2.0))

simplify1.3s

Counts
106 → 106
Iterations

Useful iterations: 4 (502.0ms)

IterNodesCost
01711478
13221364
26121338
313331338
431661320
done50001320

prune578.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 12.0b

localize29.0ms

Local error

Found 4 expressions with local error:

10.8b
(sqrt (fma 2.0 (pow (* (/ (/ -1 l) -1) t) 2.0) 1.0))
10.8b
(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
16.1b
(sqrt (pow (/ Om Omc) 2.0))
16.1b
(sqrt (pow (/ Om Omc) 2.0))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
40×sqrt-prod
32×add-sqr-sqrt
30×unpow-prod-down
22×add-cube-cbrt *-un-lft-identity
20×times-frac
10×rem-sqrt-square
6×pow1
4×add-exp-log expm1-log1p-u sqrt-pow1 pow1/2 add-cbrt-cube log1p-expm1-u add-log-exp sqr-pow
2×div-inv
Counts
4 → 94
Calls
4 calls:
1.0ms
(sqrt (fma 2.0 (pow (* (/ (/ -1 l) -1) t) 2.0) 1.0))
1.0ms
(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
6.0ms
(sqrt (pow (/ Om Omc) 2.0))
6.0ms
(sqrt (pow (/ Om Omc) 2.0))

series740.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(sqrt (fma 2.0 (pow (* (/ (/ -1 l) -1) t) 2.0) 1.0))
103.0ms
(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
267.0ms
(sqrt (pow (/ Om Omc) 2.0))
267.0ms
(sqrt (pow (/ Om Omc) 2.0))

simplify1.2s

Counts
106 → 106
Iterations

Useful iterations: 4 (611.0ms)

IterNodesCost
01891550
13511428
26671368
314441360
434111312
done50001312

prune700.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 12.0b

localize27.0ms

Local error

Found 4 expressions with local error:

16.1b
(sqrt (pow (/ Om Omc) 2.0))
16.1b
(sqrt (pow (/ Om Omc) 2.0))
16.9b
(cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))
16.9b
(cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
34×sqrt-prod
30×add-sqr-sqrt unpow-prod-down
22×add-cube-cbrt *-un-lft-identity
20×times-frac
8×rem-sqrt-square
6×cbrt-prod
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp sqr-pow
2×sqrt-pow1 pow1/2 pow1/3 div-inv
Counts
4 → 90
Calls
4 calls:
9.0ms
(sqrt (pow (/ Om Omc) 2.0))
6.0ms
(sqrt (pow (/ Om Omc) 2.0))
0.0ms
(cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))
1.0ms
(cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))

series781.0ms

Counts
4 → 12
Calls
4 calls:
264.0ms
(sqrt (pow (/ Om Omc) 2.0))
267.0ms
(sqrt (pow (/ Om Omc) 2.0))
125.0ms
(cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))
124.0ms
(cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))

simplify1.1s

Counts
102 → 102
Iterations

Useful iterations: 4 (515.0ms)

IterNodesCost
01711478
13311404
26261356
313491350
431881332
done50001332

prune644.0ms

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 12.0b

regimes723.0ms

Accuracy

0% (0.1b remaining)

Error of 10.0b against oracle of 10.0b and baseline of 10.0b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01619
11819
done1819

end0.0ms

sample1.7s

Algorithm
intervals
Results
484.0ms8094×body80nan
468.0ms3849×body160valid
256.0ms4151×body80valid