Details

Time bar (total: 23.2s)

sample85.0ms

Algorithm
intervals
Results
19.0ms233×body80nan
18.0ms120×body160valid
16.0ms136×body80valid

simplify1.3s

Counts
1 → 1
Iterations
IterNodes
done5001
51583
4292
3108
251
129
016

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.8b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ t l) 2.0)
0.4b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.4b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
9.8b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite165.0ms

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×pow-to-exp cbrt-undiv asin-acos clear-num pow-pow frac-2neg sqrt-pow1 flip3-- pow1/2 sqrt-div div-sub flip--
Counts
4 → 138
Calls
4 calls:
5.0ms
(pow (/ t l) 2.0)
100.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
1.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
53.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series1.0s

Counts
4 → 12
Calls
4 calls:
110.0ms
(pow (/ t l) 2.0)
381.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
31.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
499.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify1.7s

Counts
150 → 150
Iterations
IterNodes
done5000
22499
1771
0325

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 10.7b

localize56.0ms

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 (pow (/ t l) 2.0) 2.0 1.0))
0.4b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))))
9.8b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0)))

rewrite144.0ms

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×pow-to-exp cbrt-undiv asin-acos clear-num pow-pow frac-2neg sqrt-pow1 flip3-- pow1/2 sqrt-div div-sub flip--
Counts
4 → 134
Calls
4 calls:
14.0ms
(pow (/ t l) 2.0)
78.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))
1.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))))
42.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0)))

series737.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(pow (/ t l) 2.0)
208.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))
13.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))))
401.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0)))

simplify759.0ms

Counts
146 → 146
Iterations
IterNodes
done5001
21798
1628
0285

prune1.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 10.7b

localize75.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
9.8b
(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))))
9.9b
(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
9.9b
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

rewrite249.0ms

Algorithm
rewrite-expression-head
Rules
701×times-frac
654×sqrt-prod
637×add-sqr-sqrt
360×*-un-lft-identity
274×add-cube-cbrt
172×difference-of-squares
86×unpow-prod-down
43×distribute-lft-out-- sqr-pow
9×rem-sqrt-square
8×div-inv associate-/l*
7×pow1
6×associate-/r* add-cbrt-cube add-exp-log
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×sqrt-pow1 pow1/2
2×associate-/l/
1×cbrt-undiv clear-num frac-2neg flip3-- sqrt-div div-sub div-exp flip--
Counts
4 → 444
Calls
4 calls:
97.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
104.0ms
(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))))
1.0ms
(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
1.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

series1.1s

Counts
4 → 12
Calls
4 calls:
354.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
455.0ms
(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))))
149.0ms
(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
150.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

simplify856.0ms

Counts
456 → 456
Iterations
IterNodes
done5001
11551
0851

prune3.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 10.7b

localize115.0ms

Local error

Found 4 expressions with local error:

9.9b
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
9.9b
(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
18.7b
(sqrt (pow (/ Om Omc) 2.0))
18.7b
(sqrt (pow (/ Om Omc) 2.0))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
40×sqrt-prod
32×add-sqr-sqrt
30×unpow-prod-down
22×*-un-lft-identity add-cube-cbrt
20×times-frac
10×rem-sqrt-square
6×pow1
4×expm1-log1p-u sqrt-pow1 add-cbrt-cube pow1/2 add-exp-log log1p-expm1-u add-log-exp sqr-pow
2×div-inv
Counts
4 → 94
Calls
4 calls:
3.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
2.0ms
(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
14.0ms
(sqrt (pow (/ Om Omc) 2.0))
18.0ms
(sqrt (pow (/ Om Omc) 2.0))

series1.1s

Counts
4 → 12
Calls
4 calls:
148.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
202.0ms
(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
389.0ms
(sqrt (pow (/ Om Omc) 2.0))
381.0ms
(sqrt (pow (/ Om Omc) 2.0))

simplify840.0ms

Counts
106 → 106
Iterations
IterNodes
done5000
31771
2685
1346
0186

prune1.3s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 10.7b

regimes1.2s

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
done21
021

end0.0ms

sample4.0s

Algorithm
intervals
Results
1.6s8095×body80nan
1.1s3806×body160valid
549.0ms4194×body80valid