Details

Time bar (total: 23.2s)

sample121.0ms

Algorithm
intervals
Results
37.0ms120×body160valid
23.0ms233×body80nan
15.0ms136×body80valid

simplify2.0s

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

prune27.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.8b

localize34.0ms

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

rewrite181.0ms

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:
11.0ms
(pow (/ t l) 2.0)
120.0ms
(/ (- 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))))
39.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

series796.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(pow (/ t l) 2.0)
282.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))
23.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
391.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

simplify1.7s

Counts
146 → 146
Iterations
IterNodes
done5000
21798
1628
0285

prune1.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 10.7b

localize69.0ms

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

rewrite316.0ms

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:
100.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
147.0ms
(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))) (sqrt (fma 2.0 (pow (/ 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))

series1.0s

Counts
4 → 12
Calls
4 calls:
338.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
436.0ms
(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))))
117.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
132.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

simplify1.6s

Counts
456 → 456
Iterations
IterNodes
done5001
11546
0829

prune2.6s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 10.7b

localize143.0ms

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 2.0 (pow (/ t l) 2.0) 1.0))
13.9b
(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
13.9b
(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×cbrt-prod pow1 sqrt-prod
4×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 56
Calls
4 calls:
2.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
2.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
1.0ms
(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
1.0ms
(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

series610.0ms

Counts
4 → 12
Calls
4 calls:
140.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
137.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
171.0ms
(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
162.0ms
(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

simplify1.6s

Counts
68 → 68
Iterations
IterNodes
done5000
42230
3581
2225
1119
067

prune687.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 10.7b

localize118.0ms

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 2.0 (pow (/ t l) 2.0) 1.0))
13.9b
(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
13.9b
(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×cbrt-prod pow1 sqrt-prod
4×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 56
Calls
4 calls:
1.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
1.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
1.0ms
(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
1.0ms
(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

series652.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
157.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
148.0ms
(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
205.0ms
(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

simplify1.4s

Counts
68 → 68
Iterations
IterNodes
done5000
42230
3581
2225
1119
067

prune796.0ms

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 10.7b

regimes1.1s

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
done15
015

end0.0ms

sample4.2s

Algorithm
intervals
Results
1.7s8095×body80nan
875.0ms3806×body160valid
571.0ms4194×body80valid