Details

Time bar (total: 18.9s)

sample109.0ms

Algorithm
intervals
Results
29.0ms121×body160valid
27.0ms225×body80nan
16.0ms135×body80valid

simplify3.1s

Counts
1 → 1
Iterations

Useful iterations: 2 (17.0ms)

IterNodesCost
01619
12919
25118
310818
427918
583518
6311618
done500018

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.7b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ t l) 2.0)
0.4b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))
0.8b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
10.3b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

rewrite240.0ms

Algorithm
rewrite-expression-head
Rules
96×add-sqr-sqrt
65×times-frac
51×*-un-lft-identity
37×add-cube-cbrt
28×sqrt-prod 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 log1p-expm1-u add-log-exp
3×pow-unpow associate-/r* div-inv
2×rem-sqrt-square div-exp pow-exp 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 → 134
Calls
4 calls:
12.0ms
(pow (/ t l) 2.0)
133.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))
1.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
84.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

series797.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(pow (/ t l) 2.0)
273.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))
24.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
402.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

simplify2.1s

Counts
146 → 146
Iterations

Useful iterations: done (2.1s)

IterNodesCost
02853461
15273355
211263196
332323196
done50013193

prune925.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 11.6b

localize35.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))
0.5b
(expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))
0.8b
(asin (sqrt (log1p (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))))
10.3b
(sqrt (log1p (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))))

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
28×times-frac
26×*-un-lft-identity
18×add-cube-cbrt
16×difference-of-squares
8×unpow-prod-down associate-/l*
6×add-exp-log add-cbrt-cube
5×pow1 log1p-expm1-u
4×expm1-log1p-u distribute-lft-out-- add-log-exp sqr-pow
3×associate-/r* sqrt-prod
2×associate-/l/
1×cbrt-undiv rem-sqrt-square asin-acos expm1-log1p flip3-- frac-2neg sqrt-pow1 pow1/2 div-sub div-exp clear-num flip-- div-inv expm1-udef
Counts
4 → 88
Calls
4 calls:
108.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))
0.0ms
(expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))
1.0ms
(asin (sqrt (log1p (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))))
2.0ms
(sqrt (log1p (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))))

series903.0ms

Counts
4 → 12
Calls
4 calls:
257.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))
271.0ms
(expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))
26.0ms
(asin (sqrt (log1p (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))))
349.0ms
(sqrt (log1p (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))))

simplify1.8s

Counts
100 → 100
Iterations

Useful iterations: 2 (182.0ms)

IterNodesCost
01702462
13292320
27522162
322432162
done50012162

prune655.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 11.6b

localize47.0ms

Local error

Found 4 expressions with local error:

0.8b
(asin (sqrt (log1p (* (sqrt (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))) (sqrt (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))))))
10.3b
(sqrt (log1p (* (sqrt (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))) (sqrt (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))))))
10.3b
(sqrt (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
10.3b
(sqrt (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
1×asin-acos
Counts
4 → 55
Calls
4 calls:
1.0ms
(asin (sqrt (log1p (* (sqrt (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))) (sqrt (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))))))
3.0ms
(sqrt (log1p (* (sqrt (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))) (sqrt (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))))))
3.0ms
(sqrt (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
3.0ms
(sqrt (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))

series1.3s

Counts
4 → 12
Calls
4 calls:
29.0ms
(asin (sqrt (log1p (* (sqrt (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))) (sqrt (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))))))
352.0ms
(sqrt (log1p (* (sqrt (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))) (sqrt (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))))))
475.0ms
(sqrt (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
409.0ms
(sqrt (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))

simplify1.8s

Counts
67 → 67
Iterations

Useful iterations: 2 (73.0ms)

IterNodesCost
0742059
11121293
21611143
32831143
45911143
514921143
done50001143

prune424.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 11.6b

localize42.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ -1 l) (/ -1 t))
0.4b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0) 1.0))
0.8b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0) 1.0))))
10.3b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0) 1.0)))

rewrite269.0ms

Algorithm
rewrite-expression-head
Rules
477×times-frac
284×add-sqr-sqrt
239×*-un-lft-identity
225×add-cube-cbrt
31×div-inv
28×sqrt-prod difference-of-squares
21×associate-/l*
18×add-exp-log add-cbrt-cube
16×associate-/r*
14×unpow-prod-down
9×cbrt-undiv div-exp
7×distribute-lft-out-- sqr-pow
5×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/l/
2×rem-sqrt-square frac-2neg clear-num
1×asin-acos flip3-- sqrt-pow1 pow1/2 sqrt-div div-sub associate-/r/ flip--
Counts
4 → 321
Calls
4 calls:
36.0ms
(/ (/ -1 l) (/ -1 t))
138.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0) 1.0))
1.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0) 1.0))))
51.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0) 1.0)))

series761.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(/ (/ -1 l) (/ -1 t))
273.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0) 1.0))
16.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0) 1.0))))
454.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0) 1.0)))

simplify1.1s

Counts
333 → 333
Iterations

Useful iterations: done (1.1s)

IterNodesCost
06207860
115237394
done50006521

prune2.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 11.6b

regimes4.0ms