Details

Time bar (total: 27.2s)

sample124.0ms

Algorithm
intervals
Results
48.0ms257×body80nan
24.0ms109×body160valid
16.0ms147×body80valid

simplify3.5s

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

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.9b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ t l) 2.0)
0.3b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))))
0.6b
(/ (- 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)))

rewrite152.0ms

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:
7.0ms
(pow (/ t l) 2.0)
1.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))))
79.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))
60.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0)))

series820.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(pow (/ t l) 2.0)
16.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))))
230.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))
481.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0)))

simplify3.2s

Counts
146 → 146
Iterations
IterNodes
done5006
34014
21316
1618
0285

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 10.8b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ t l) 2.0)
0.3b
(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0)))))
1.0b
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0)))
9.7b
(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))

rewrite120.0ms

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:
5.0ms
(pow (/ t l) 2.0)
1.0ms
(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0)))))
105.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0)))
3.0ms
(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))

series720.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(pow (/ t l) 2.0)
25.0ms
(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0)))))
461.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0)))
138.0ms
(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))

simplify2.6s

Counts
167 → 167
Iterations
IterNodes
done5004
32842
21112
1596
0302

prune1.5s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 10.8b

localize69.0ms

Local error

Found 4 expressions with local error:

9.8b
(sqrt (* (/ 1 (* (cbrt (fma (pow (/ t l) 2.0) 2.0 1.0)) (cbrt (fma (pow (/ t l) 2.0) 2.0 1.0)))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (fma (pow (/ t l) 2.0) 2.0 1.0)))))
17.1b
(cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))
17.1b
(cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))
17.1b
(cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt pow1 *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u add-log-exp
3×pow1/3 sqrt-div
2×sqrt-pow1
1×frac-times pow1/2 pow-prod-down associate-*l/ associate-*r/ sqrt-prod
Counts
4 → 55
Calls
4 calls:
63.0ms
(sqrt (* (/ 1 (* (cbrt (fma (pow (/ t l) 2.0) 2.0 1.0)) (cbrt (fma (pow (/ t l) 2.0) 2.0 1.0)))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (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))

series1.1s

Counts
4 → 12
Calls
4 calls:
525.0ms
(sqrt (* (/ 1 (* (cbrt (fma (pow (/ t l) 2.0) 2.0 1.0)) (cbrt (fma (pow (/ t l) 2.0) 2.0 1.0)))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (fma (pow (/ t l) 2.0) 2.0 1.0)))))
224.0ms
(cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))
203.0ms
(cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))
162.0ms
(cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))

simplify2.2s

Counts
67 → 67
Iterations
IterNodes
done5003
42487
3817
2329
1171
094

prune594.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 10.8b

localize73.0ms

Local error

Found 4 expressions with local error:

17.1b
(cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))
17.1b
(cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))
17.1b
(cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))
17.1b
(cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube pow1/3 add-exp-log log1p-expm1-u add-log-exp
Counts
4 → 52
Calls
4 calls:
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))
1.0ms
(cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))

series731.0ms

Counts
4 → 12
Calls
4 calls:
198.0ms
(cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))
179.0ms
(cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))
186.0ms
(cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))
167.0ms
(cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))

simplify3.2s

Counts
64 → 64
Iterations
IterNodes
done5000
53040
4999
3408
2186
1101
052

prune572.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 10.8b

regimes935.0ms

Accuracy

0% (0.1b remaining)

Error of 10.1b against oracle of 10.1b and baseline of 10.1b

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
done15
015

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.3s7945×body80nan
944.0ms3771×body160valid
611.0ms4229×body80valid