Details

Time bar (total: 12.4s)

sample132.0ms

Algorithm
intervals
Results
33.0ms249×body80nan
32.0ms121×body160valid
17.0ms135×body80valid

simplify156.0ms

Counts
1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.2b

localize66.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ Om Omc) 2.0)
0.2b
(pow (/ t l) 2.0)
0.5b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
7.6b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
59×add-sqr-sqrt
46×times-frac
38×*-un-lft-identity
32×add-cube-cbrt unpow-prod-down
30×sqrt-prod
12×difference-of-squares
10×add-exp-log
7×pow1
6×pow-unpow
5×sqr-pow
4×pow-exp add-cbrt-cube add-log-exp
3×div-inv distribute-lft-out--
2×pow-to-exp rem-sqrt-square pow-pow div-exp associate-/r/
1×asin-acos sqrt-pow1 flip3-+ pow1/2 sqrt-div flip-+
Counts
4 → 106
Calls
4 calls:
16.0ms
(pow (/ Om Omc) 2.0)
13.0ms
(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))))))
43.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series750.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(pow (/ Om Omc) 2.0)
102.0ms
(pow (/ t l) 2.0)
24.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
531.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify38.0ms

Counts
118 → 118

prune689.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 8.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ t l) 2.0)
0.2b
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
0.5b
(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
7.5b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite132.0ms

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:
16.0ms
(pow (/ t l) 2.0)
94.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
1.0ms
(asin (fabs (/ (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))))

series781.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(pow (/ t l) 2.0)
429.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
22.0ms
(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
252.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify55.0ms

Counts
163 → 163

prune919.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 8.1b

localize32.0ms

Local error

Found 4 expressions with local error:

7.5b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
7.5b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
8.1b
(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
8.1b
(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
26×sqrt-prod
16×add-sqr-sqrt
12×sqrt-div
10×pow1 add-cube-cbrt *-un-lft-identity sqrt-pow1
6×rem-sqrt-square pow1/2
4×add-exp-log flip3-+ add-cbrt-cube flip-+ add-log-exp
Counts
4 → 72
Calls
4 calls:
5.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
5.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
6.0ms
(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
7.0ms
(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series1.1s

Counts
4 → 12
Calls
4 calls:
271.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
221.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
307.0ms
(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
281.0ms
(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify112.0ms

Counts
84 → 84

prune666.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 8.1b

localize49.0ms

Local error

Found 4 expressions with local error:

8.7b
(sqrt (/ 1 (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
13.4b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
13.4b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
13.4b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-div
15×sqrt-prod
13×pow1
11×add-sqr-sqrt sqrt-pow1
10×*-un-lft-identity
9×cbrt-prod add-cube-cbrt pow-flip flip3-+ pow1/3 flip-+
8×associate-/r/
5×times-frac
4×add-exp-log frac-times add-cbrt-cube add-log-exp
3×rem-sqrt-square
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus pow1/2 sqrt-div div-inv inv-pow
Counts
4 → 77
Calls
4 calls:
37.0ms
(sqrt (/ 1 (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
5.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
4.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
5.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.3s

Counts
4 → 12
Calls
4 calls:
332.0ms
(sqrt (/ 1 (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
336.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
321.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
306.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify85.0ms

Counts
89 → 89

prune556.0ms

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 8.1b

regimes862.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify103.0ms

end0.0ms

sample3.7s

Algorithm
intervals
Results
1.2s7828×body80nan
948.0ms3785×body160valid
551.0ms4215×body80valid