Details

Time bar (total: 8.5s)

sample92.0ms

Algorithm
intervals
Results
29.0ms273×body80nan
27.0ms129×body160valid
15.0ms127×body80valid

simplify128.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02910
15110
210710
329010
4105410
5444510
6500110

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.4b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ t l) 2.0)
0.2b
(pow (/ Om Omc) 2.0)
0.8b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
10.4b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite40.0ms

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×expm1-log1p-u pow-exp add-cbrt-cube log1p-expm1-u 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 → 114
Calls
4 calls:
3.0ms
(pow (/ t l) 2.0)
3.0ms
(pow (/ Om Omc) 2.0)
0.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
28.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series455.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(pow (/ t l) 2.0)
57.0ms
(pow (/ Om Omc) 2.0)
16.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
317.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify59.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
07091289
120871218
250011206

prune505.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 11.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ t l) 2.0)
0.2b
(pow (/ Om Omc) 2.0)
0.8b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
10.4b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite40.0ms

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×expm1-log1p-u pow-exp add-cbrt-cube log1p-expm1-u 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 → 114
Calls
4 calls:
3.0ms
(pow (/ t l) 2.0)
4.0ms
(pow (/ Om Omc) 2.0)
0.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
28.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series592.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(pow (/ t l) 2.0)
59.0ms
(pow (/ Om Omc) 2.0)
17.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
454.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify58.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
07091289
120871218
250011206

prune560.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 11.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ t l) 2.0)
0.2b
(pow (/ Om Omc) 2.0)
0.8b
(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
10.6b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
26×unpow-prod-down
22×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity
18×times-frac
10×add-exp-log
7×pow1
6×pow-unpow
4×expm1-log1p-u pow-exp add-cbrt-cube log1p-expm1-u add-log-exp
3×sqrt-prod
2×pow-to-exp pow-pow sqrt-div div-exp div-inv sqr-pow
1×rem-sqrt-square asin-acos sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 87
Calls
4 calls:
4.0ms
(pow (/ t l) 2.0)
3.0ms
(pow (/ Om Omc) 2.0)
0.0ms
(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
3.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series315.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(pow (/ t l) 2.0)
62.0ms
(pow (/ Om Omc) 2.0)
17.0ms
(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
179.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify50.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0560690
11818640
25001640

prune412.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 11.3b

localize19.0ms

Local error

Found 4 expressions with local error:

10.4b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0)))))))
32.8b
(cbrt (pow (/ t l) 2.0))
32.8b
(cbrt (pow (/ t l) 2.0))
32.8b
(cbrt (pow (/ t l) 2.0))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
67×add-sqr-sqrt
55×times-frac
51×cbrt-prod
46×*-un-lft-identity
45×unpow-prod-down
40×add-cube-cbrt
30×sqrt-prod
12×difference-of-squares
6×sqr-pow
5×pow1
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u div-inv add-log-exp
3×pow1/3 distribute-lft-out--
2×rem-sqrt-square associate-/r/
1×sqrt-pow1 flip3-+ pow1/2 sqrt-div flip-+
Counts
4 → 125
Calls
4 calls:
31.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0)))))))
3.0ms
(cbrt (pow (/ t l) 2.0))
3.0ms
(cbrt (pow (/ t l) 2.0))
3.0ms
(cbrt (pow (/ t l) 2.0))

series1.1s

Counts
4 → 12
Calls
4 calls:
312.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0)))))))
262.0ms
(cbrt (pow (/ t l) 2.0))
260.0ms
(cbrt (pow (/ t l) 2.0))
262.0ms
(cbrt (pow (/ t l) 2.0))

simplify54.0ms

Algorithm
egg-herbie
Counts
137 → 137
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
05232251
112332182
250012146

prune667.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 11.3b

regimes553.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02012
12012

end0.0ms

sample2.6s

Algorithm
intervals
Results
885.0ms8086×body80nan
852.0ms3915×body160valid
444.0ms4085×body80valid