Details

Time bar (total: 22.5s)

sample132.0ms

Algorithm
intervals
Results
43.0ms132×body160valid
28.0ms240×body80nan
16.0ms124×body80valid

simplify1.9s

Counts
1 → 1

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.7b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite184.0ms

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×associate-/r/ add-log-exp
3×pow-unpow associate-/r* div-inv
2×rem-sqrt-square flip3-+ div-exp pow-exp flip-+ 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 → 130
Calls
4 calls:
13.0ms
(pow (/ Om Omc) 2.0)
1.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
89.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
68.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series998.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(pow (/ Om Omc) 2.0)
40.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
303.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
534.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify972.0ms

Counts
142 → 142

prune897.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 10.6b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ Om Omc) 2.0)
0.4b
(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
0.8b
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
9.6b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite139.0ms

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 sqrt-div associate-/r* add-cbrt-cube
4×add-log-exp
3×pow-unpow
2×flip3-+ div-exp pow-exp associate-/r/ flip-+ div-inv associate-/l/
1×cbrt-undiv pow-to-exp rem-sqrt-square asin-acos sqrt-undiv flip3-- pow-pow frac-2neg sqrt-pow1 pow1/2 clear-num flip--
Counts
4 → 151
Calls
4 calls:
8.0ms
(pow (/ Om Omc) 2.0)
1.0ms
(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
113.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
11.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series930.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(pow (/ Om Omc) 2.0)
39.0ms
(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
504.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
287.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify898.0ms

Counts
163 → 163

prune958.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 10.6b

localize49.0ms

Local error

Found 4 expressions with local error:

4.9b
(sqrt (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
4.9b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
9.6b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
9.6b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
120×sqrt-prod
104×add-sqr-sqrt
78×times-frac
56×*-un-lft-identity
42×add-cube-cbrt
24×difference-of-squares
12×unpow-prod-down
10×pow1 rem-sqrt-square sqrt-div
9×sqrt-pow1
6×distribute-lft-out-- sqr-pow
5×pow1/2
4×add-exp-log flip3-+ associate-/r/ add-cbrt-cube flip-+ add-log-exp
3×pow-flip
2×div-inv
1×inv-pow
Counts
4 → 140
Calls
4 calls:
16.0ms
(sqrt (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
62.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
5.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
12.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.4s

Counts
4 → 12
Calls
4 calls:
446.0ms
(sqrt (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
526.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
227.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
238.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify832.0ms

Counts
152 → 152

prune1.1s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 10.6b

localize48.0ms

Local error

Found 4 expressions with local error:

5.2b
(cbrt (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
9.6b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
9.6b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
9.6b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
24×cbrt-prod
23×add-sqr-sqrt
20×add-cube-cbrt *-un-lft-identity
18×times-frac sqrt-prod
8×sqrt-div
7×pow1
4×add-exp-log flip3-+ add-cbrt-cube flip-+ add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×associate-/r/
1×cbrt-div pow1/3 div-inv
Counts
4 → 78
Calls
4 calls:
7.0ms
(cbrt (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
5.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
5.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
5.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.3s

Counts
4 → 12
Calls
4 calls:
428.0ms
(cbrt (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
304.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
246.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
315.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify1.9s

Counts
90 → 90

prune715.0ms

Pruning

10 alts after pruning (6 fresh and 4 done)

Merged error: 10.6b

regimes1.1s

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.8s

end0.0ms

sample4.1s

Algorithm
intervals
Results
1.1s3838×body160valid
1.0s7960×body80nan
946.0ms4162×body80valid