Details

Time bar (total: 34.5s)

sample102.0ms

Algorithm
intervals
Results
27.0ms128×body160valid
25.0ms128×body80valid
21.0ms215×body80nan

simplify3.6s

Counts
1 → 1
Iterations

Useful iterations: 2 (10.0ms)

IterNodesCost
01619
12919
25118
310818
427918
583518
6311618
done500018

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.6b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ Om Omc) 2.0)
0.3b
(pow (/ t l) 2.0)
0.8b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
8.6b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

rewrite70.0ms

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:
6.0ms
(pow (/ Om Omc) 2.0)
12.0ms
(pow (/ t l) 2.0)
1.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
45.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

series685.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(pow (/ Om Omc) 2.0)
92.0ms
(pow (/ t l) 2.0)
15.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
464.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

simplify1.7s

Counts
124 → 124
Iterations

Useful iterations: done (1.7s)

IterNodesCost
03192298
15822196
211152088
326512082
done50012076

prune768.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 9.5b

localize38.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (/ (/ -1 l) (/ -1 t)) 2.0)
0.3b
(/ (/ -1 l) (/ -1 t))
0.8b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0) 1.0))))
8.6b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0) 1.0)))

rewrite222.0ms

Algorithm
rewrite-expression-head
Rules
852×times-frac
423×add-sqr-sqrt
402×*-un-lft-identity
396×add-cube-cbrt
180×unpow-prod-down
57×div-inv
29×add-exp-log
28×sqrt-prod
16×div-exp add-cbrt-cube
13×associate-/r* associate-/l*
12×difference-of-squares
8×cbrt-undiv
6×pow1
5×pow-exp
4×expm1-log1p-u log1p-expm1-u add-log-exp sqr-pow
3×pow-unpow distribute-lft-out--
2×rem-sqrt-square associate-/r/
1×pow-to-exp asin-acos pow-pow frac-2neg sqrt-pow1 pow1/2 sqrt-div clear-num associate-/l/
Counts
4 → 463
Calls
4 calls:
56.0ms
(pow (/ (/ -1 l) (/ -1 t)) 2.0)
21.0ms
(/ (/ -1 l) (/ -1 t))
1.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0) 1.0))))
88.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0) 1.0)))

series553.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(pow (/ (/ -1 l) (/ -1 t)) 2.0)
16.0ms
(/ (/ -1 l) (/ -1 t))
13.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0) 1.0))))
410.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0) 1.0)))

simplify1.9s

Counts
475 → 475
Iterations

Useful iterations: done (1.8s)

IterNodesCost
093110656
123819843
done50008904

prune2.9s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 9.5b

localize35.0ms

Local error

Found 4 expressions with local error:

8.6b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (* (* (cbrt (pow (/ (- t) (- l)) 2.0)) (cbrt (pow (/ (- t) (- l)) 2.0))) (cbrt (pow (/ (- t) (- l)) 2.0))) 1.0)))
26.9b
(cbrt (pow (/ (- t) (- l)) 2.0))
26.9b
(cbrt (pow (/ (- t) (- l)) 2.0))
26.9b
(cbrt (pow (/ (- t) (- l)) 2.0))

rewrite223.0ms

Algorithm
rewrite-expression-head
Rules
328×times-frac
324×cbrt-prod
318×unpow-prod-down
229×add-sqr-sqrt
208×*-un-lft-identity
202×add-cube-cbrt
180×distribute-lft-neg-in distribute-rgt-neg-in
60×neg-mul-1
28×sqrt-prod
12×difference-of-squares
6×sqr-pow
5×pow1
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u div-inv add-log-exp
3×pow1/3 distribute-lft-out--
2×rem-sqrt-square
1×sqrt-pow1 pow1/2 sqrt-div
Counts
4 → 396
Calls
4 calls:
61.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (* (* (cbrt (pow (/ (- t) (- l)) 2.0)) (cbrt (pow (/ (- t) (- l)) 2.0))) (cbrt (pow (/ (- t) (- l)) 2.0))) 1.0)))
46.0ms
(cbrt (pow (/ (- t) (- l)) 2.0))
58.0ms
(cbrt (pow (/ (- t) (- l)) 2.0))
23.0ms
(cbrt (pow (/ (- t) (- l)) 2.0))

series1.7s

Counts
4 → 12
Calls
4 calls:
515.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (* (* (cbrt (pow (/ (- t) (- l)) 2.0)) (cbrt (pow (/ (- t) (- l)) 2.0))) (cbrt (pow (/ (- t) (- l)) 2.0))) 1.0)))
399.0ms
(cbrt (pow (/ (- t) (- l)) 2.0))
430.0ms
(cbrt (pow (/ (- t) (- l)) 2.0))
400.0ms
(cbrt (pow (/ (- t) (- l)) 2.0))

simplify2.4s

Counts
408 → 408
Iterations

Useful iterations: 3 (1.4s)

IterNodesCost
06289550
111729138
220377978
340917777
done50007777

prune3.0s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 9.5b

localize81.0ms

Local error

Found 4 expressions with local error:

8.6b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (* (* (* (cbrt (pow (/ (* (cbrt (- t)) (cbrt (- t))) (* (cbrt (- l)) (cbrt (- l)))) 2.0)) (cbrt (pow (/ (cbrt (- t)) (cbrt (- l))) 2.0))) (cbrt (pow (/ (- t) (- l)) 2.0))) (cbrt (pow (/ (- t) (- l)) 2.0))) 1.0)))
20.1b
(cbrt (pow (/ (* (cbrt (- t)) (cbrt (- t))) (* (cbrt (- l)) (cbrt (- l)))) 2.0))
26.9b
(cbrt (pow (/ (- t) (- l)) 2.0))
26.9b
(cbrt (pow (/ (- t) (- l)) 2.0))

rewrite195.0ms

Algorithm
rewrite-expression-head
Rules
229×times-frac
225×cbrt-prod
219×unpow-prod-down
169×add-sqr-sqrt
148×*-un-lft-identity
142×add-cube-cbrt
120×distribute-lft-neg-in distribute-rgt-neg-in
40×neg-mul-1
28×sqrt-prod
12×difference-of-squares
6×sqr-pow
5×pow1
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u div-inv add-log-exp
3×pow1/3 distribute-lft-out--
2×rem-sqrt-square
1×sqrt-pow1 pow1/2 sqrt-div
Counts
4 → 297
Calls
4 calls:
55.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (* (* (* (cbrt (pow (/ (* (cbrt (- t)) (cbrt (- t))) (* (cbrt (- l)) (cbrt (- l)))) 2.0)) (cbrt (pow (/ (cbrt (- t)) (cbrt (- l))) 2.0))) (cbrt (pow (/ (- t) (- l)) 2.0))) (cbrt (pow (/ (- t) (- l)) 2.0))) 1.0)))
10.0ms
(cbrt (pow (/ (* (cbrt (- t)) (cbrt (- t))) (* (cbrt (- l)) (cbrt (- l)))) 2.0))
47.0ms
(cbrt (pow (/ (- t) (- l)) 2.0))
47.0ms
(cbrt (pow (/ (- t) (- l)) 2.0))

series1.9s

Counts
4 → 12
Calls
4 calls:
602.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (* (* (* (cbrt (pow (/ (* (cbrt (- t)) (cbrt (- t))) (* (cbrt (- l)) (cbrt (- l)))) 2.0)) (cbrt (pow (/ (cbrt (- t)) (cbrt (- l))) 2.0))) (cbrt (pow (/ (- t) (- l)) 2.0))) (cbrt (pow (/ (- t) (- l)) 2.0))) 1.0)))
413.0ms
(cbrt (pow (/ (* (cbrt (- t)) (cbrt (- t))) (* (cbrt (- l)) (cbrt (- l)))) 2.0))
448.0ms
(cbrt (pow (/ (- t) (- l)) 2.0))
425.0ms
(cbrt (pow (/ (- t) (- l)) 2.0))

simplify3.1s

Counts
309 → 309
Iterations

Useful iterations: 3 (1.9s)

IterNodesCost
06849408
112949054
222778840
346878831
done50008831

prune4.0s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 9.5b

regimes744.0ms

Accuracy

0% (0.1b remaining)

Error of 10.3b against oracle of 10.2b and baseline of 10.3b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01822
done1822

end0.0ms

sample4.3s

Algorithm
intervals
Results
1.6s7919×body80nan
1.1s3788×body160valid
799.0ms4212×body80valid