Details

Time bar (total: 26.6s)

sample144.0ms

Algorithm
intervals
Results
54.0ms126×body160valid
33.0ms270×body80nan
17.0ms130×body80valid

simplify2.8s

Counts
1 → 1
Iterations
IterNodes
done5000
62611
5774
4250
3102
251
129
016

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.9b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))
0.3b
(pow (/ Om Omc) 2.0)
0.5b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))))
8.1b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0)))

rewrite191.0ms

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:
108.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))
12.0ms
(pow (/ Om Omc) 2.0)
1.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))))
59.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0)))

series762.0ms

Counts
4 → 12
Calls
4 calls:
265.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))
69.0ms
(pow (/ Om Omc) 2.0)
17.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))))
410.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0)))

simplify2.9s

Counts
146 → 146
Iterations
IterNodes
done5010
34163
21294
1595
0276

prune1.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 8.8b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0)))
0.3b
(pow (/ Om Omc) 2.0)
0.5b
(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0)))))
8.2b
(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
108×add-sqr-sqrt
95×sqrt-prod
82×times-frac
65×*-un-lft-identity
51×add-cube-cbrt
28×difference-of-squares
27×unpow-prod-down
11×associate-/l*
9×add-exp-log
8×sqr-pow
7×distribute-lft-out--
6×pow1 associate-/r* add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow
2×sqrt-div div-exp pow-exp div-inv associate-/l/
1×pow-to-exp cbrt-undiv rem-sqrt-square asin-acos sqrt-undiv clear-num pow-pow frac-2neg sqrt-pow1 flip3-- pow1/2 flip--
Counts
4 → 155
Calls
4 calls:
58.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0)))
5.0ms
(pow (/ Om Omc) 2.0)
0.0ms
(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0)))))
1.0ms
(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))

series576.0ms

Counts
4 → 12
Calls
4 calls:
369.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0)))
82.0ms
(pow (/ Om Omc) 2.0)
13.0ms
(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0)))))
112.0ms
(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))

simplify2.4s

Counts
167 → 167
Iterations
IterNodes
done5001
32960
21168
1608
0312

prune1.4s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 8.8b

localize67.0ms

Local error

Found 4 expressions with local error:

7.8b
(sqrt (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0)))
7.8b
(sqrt (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0)))
8.2b
(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
8.2b
(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
26×sqrt-prod
16×add-sqr-sqrt
10×pow1 *-un-lft-identity sqrt-pow1 add-cube-cbrt
6×rem-sqrt-square pow1/2
4×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u add-log-exp
Counts
4 → 72
Calls
4 calls:
3.0ms
(sqrt (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0)))
3.0ms
(sqrt (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0)))
2.0ms
(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
2.0ms
(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))

series663.0ms

Counts
4 → 12
Calls
4 calls:
172.0ms
(sqrt (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0)))
187.0ms
(sqrt (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0)))
134.0ms
(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
169.0ms
(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))

simplify2.6s

Counts
84 → 84
Iterations
IterNodes
done5000
53983
41188
3488
2228
1129
075

prune655.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 8.8b

localize65.0ms

Local error

Found 4 expressions with local error:

8.1b
(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (* (cbrt (fma (pow (/ t l) 2.0) 2.0 1.0)) (cbrt (fma (pow (/ t l) 2.0) 2.0 1.0)))) (cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))))
14.1b
(cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))
14.1b
(cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))
14.1b
(cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
132×times-frac
101×add-sqr-sqrt
76×sqrt-prod
56×*-un-lft-identity
47×cbrt-prod
44×add-cube-cbrt
24×difference-of-squares
12×unpow-prod-down
7×div-inv
6×distribute-lft-out-- sqr-pow
5×pow1 rem-sqrt-square
4×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u add-log-exp
3×pow1/3
1×sqrt-pow1 pow1/2 sqrt-div
Counts
4 → 132
Calls
4 calls:
80.0ms
(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (* (cbrt (fma (pow (/ t l) 2.0) 2.0 1.0)) (cbrt (fma (pow (/ t l) 2.0) 2.0 1.0)))) (cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))))
1.0ms
(cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))
1.0ms
(cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))
1.0ms
(cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))

series990.0ms

Counts
4 → 12
Calls
4 calls:
433.0ms
(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (* (cbrt (fma (pow (/ t l) 2.0) 2.0 1.0)) (cbrt (fma (pow (/ t l) 2.0) 2.0 1.0)))) (cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))))
195.0ms
(cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))
170.0ms
(cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))
192.0ms
(cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))

simplify2.8s

Counts
144 → 144
Iterations
IterNodes
done5005
33364
21203
1568
0330

prune1.5s

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 8.8b

regimes1.2s

Accuracy

0% (0.1b remaining)

Error of 9.8b against oracle of 9.7b and baseline of 9.8b

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
done15
015

end0.0ms

sample3.7s

Algorithm
intervals
Results
1.5s7907×body80nan
888.0ms3791×body160valid
619.0ms4209×body80valid