Details

Time bar (total: 20.6s)

sample126.0ms

Algorithm
intervals
Results
44.0ms117×body160valid
27.0ms257×body80nan
15.0ms139×body80valid

simplify1.3s

Counts
1 → 1
Iterations

Useful iterations: 2 (9.0ms)

IterNodesCost
01619
12919
25118
310818
429218
5158518
done500018

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.6b

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (/ t l) 2.0)
0.6b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
1.0b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))
9.7b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

rewrite199.0ms

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:
9.0ms
(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))))
143.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))
39.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

series787.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(pow (/ t l) 2.0)
14.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
256.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))
428.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

simplify1.1s

Counts
146 → 146
Iterations

Useful iterations: done (1.1s)

IterNodesCost
02853461
16283355
217993198
done50003196

prune1.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 11.5b

localize48.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (/ t l) 2.0)
0.6b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (pow (/ t l) 2.0) 1) 1.0))))
1.0b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (pow (/ t l) 2.0) 1) 1.0))
9.7b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (pow (/ t l) 2.0) 1) 1.0)))

rewrite205.0ms

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:
16.0ms
(pow (/ t l) 2.0)
1.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (pow (/ t l) 2.0) 1) 1.0))))
103.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (pow (/ t l) 2.0) 1) 1.0))
72.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (pow (/ t l) 2.0) 1) 1.0)))

series868.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(pow (/ t l) 2.0)
17.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (pow (/ t l) 2.0) 1) 1.0))))
268.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (pow (/ t l) 2.0) 1) 1.0))
489.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (pow (/ t l) 2.0) 1) 1.0)))

simplify1.0s

Counts
146 → 146
Iterations

Useful iterations: done (1.0s)

IterNodesCost
02873787
16413355
218933198
done50003196

prune886.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 11.5b

localize28.0ms

Local error

Found 4 expressions with local error:

0.6b
(asin (sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))) (sqrt (fma 2.0 (pow (pow (/ t l) 2.0) 1) 1.0)))))
9.7b
(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))) (sqrt (fma 2.0 (pow (pow (/ t l) 2.0) 1) 1.0))))
10.6b
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
10.6b
(sqrt (fma 2.0 (pow (pow (/ t l) 2.0) 1) 1.0))

rewrite183.0ms

Algorithm
rewrite-expression-head
Rules
646×times-frac
627×sqrt-prod
556×add-sqr-sqrt
321×*-un-lft-identity
249×add-cube-cbrt
144×difference-of-squares
72×unpow-prod-down
36×distribute-lft-out-- sqr-pow
9×rem-sqrt-square
7×pow1 div-inv
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×sqrt-pow1 pow1/2
1×asin-acos sqrt-div
Counts
4 → 375
Calls
4 calls:
1.0ms
(asin (sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))) (sqrt (fma 2.0 (pow (pow (/ t l) 2.0) 1) 1.0)))))
101.0ms
(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))) (sqrt (fma 2.0 (pow (pow (/ t l) 2.0) 1) 1.0))))
2.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
2.0ms
(sqrt (fma 2.0 (pow (pow (/ t l) 2.0) 1) 1.0))

series682.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(asin (sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))) (sqrt (fma 2.0 (pow (pow (/ t l) 2.0) 1) 1.0)))))
406.0ms
(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))) (sqrt (fma 2.0 (pow (pow (/ t l) 2.0) 1) 1.0))))
116.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
146.0ms
(sqrt (fma 2.0 (pow (pow (/ t l) 2.0) 1) 1.0))

simplify1.0s

Counts
387 → 387
Iterations

Useful iterations: done (996.0ms)

IterNodesCost
083422438
1166819029
done500117689

prune1.5s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 11.5b

localize53.0ms

Local error

Found 4 expressions with local error:

8.7b
(sqrt (/ (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))))
10.6b
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
10.6b
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
10.6b
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

rewrite213.0ms

Algorithm
rewrite-expression-head
Rules
976×sqrt-prod
666×times-frac
574×add-sqr-sqrt
334×*-un-lft-identity
262×add-cube-cbrt
144×difference-of-squares
72×unpow-prod-down
36×distribute-lft-out-- sqr-pow
12×rem-sqrt-square
8×pow1
7×div-inv
4×add-exp-log expm1-log1p-u sqrt-pow1 pow1/2 add-cbrt-cube log1p-expm1-u add-log-exp
1×sqrt-div
Counts
4 → 400
Calls
4 calls:
128.0ms
(sqrt (/ (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))))
3.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
3.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
3.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

series1.1s

Counts
4 → 12
Calls
4 calls:
698.0ms
(sqrt (/ (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))))
154.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
132.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
163.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

simplify1.3s

Counts
412 → 412
Iterations

Useful iterations: done (1.3s)

IterNodesCost
089422672
1115220818
2247120461
done500020459

prune2.3s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 11.5b

regimes492.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
01720
11918
done1918

end0.0ms

sample4.0s

Algorithm
intervals
Results
1.2s3760×body160valid
1.2s8004×body80nan
621.0ms4240×body80valid