Details

Time bar (total: 14.3s)

sample62.0ms

Algorithm
intervals
Results
17.0ms273×body80nan
15.0ms118×body160valid
8.0ms138×body80valid

simplify127.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02910
15110
210710
329010
4105410
5444510
6500110

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (/ t l) 2.0)
0.4b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.6b
(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)))))

rewrite90.0ms

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×expm1-log1p-u associate-/r/ log1p-expm1-u 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 → 138
Calls
4 calls:
4.0ms
(pow (/ t l) 2.0)
49.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
31.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series610.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(pow (/ t l) 2.0)
214.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
17.0ms
(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)))))

simplify65.0ms

Algorithm
egg-herbie
Counts
150 → 150
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
06641948
121061846
250011828

prune625.0ms

Filtered
150 candidates to 123 candidates (82.0%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 11.4b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (/ t l) 2.0)
0.4b
(/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
0.6b
(asin (sqrt (/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
10.4b
(sqrt (/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

rewrite358.0ms

Algorithm
rewrite-expression-head
Rules
215×add-sqr-sqrt
151×unpow-prod-down
131×times-frac
120×difference-of-squares
90×cube-prod
67×sqr-pow
61×sqrt-prod
49×associate-/l*
46×*-un-lft-identity
16×add-cube-cbrt associate-/r/
15×distribute-lft-out--
12×add-exp-log flip3-+ flip-+
9×add-cbrt-cube
8×frac-times
6×pow1
4×expm1-log1p-u associate-*r/ associate-*l/ log1p-expm1-u add-log-exp
3×difference-cubes pow-unpow div-exp div-inv
2×cbrt-undiv pow-exp associate-/l/
1×pow-to-exp rem-sqrt-square asin-acos flip3-- pow-pow frac-2neg sqrt-pow1 pow1/2 sqrt-div div-sub prod-exp clear-num associate-/r* flip-- cbrt-unprod
Counts
4 → 240
Calls
4 calls:
3.0ms
(pow (/ t l) 2.0)
214.0ms
(/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
0.0ms
(asin (sqrt (/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
122.0ms
(sqrt (/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

series1.7s

Counts
4 → 12
Calls
4 calls:
64.0ms
(pow (/ t l) 2.0)
716.0ms
(/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
40.0ms
(asin (sqrt (/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
889.0ms
(sqrt (/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

simplify78.0ms

Algorithm
egg-herbie
Counts
252 → 252
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
011735721
150025421

prune1.1s

Filtered
252 candidates to 154 candidates (61.1%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 11.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (/ t l) 2.0)
0.4b
(/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
0.6b
(asin (sqrt (/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
10.4b
(sqrt (/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

rewrite362.0ms

Algorithm
rewrite-expression-head
Rules
215×add-sqr-sqrt
151×unpow-prod-down
131×times-frac
120×difference-of-squares
90×cube-prod
67×sqr-pow
61×sqrt-prod
49×associate-/l*
46×*-un-lft-identity
16×add-cube-cbrt associate-/r/
15×distribute-lft-out--
12×add-exp-log flip3-+ flip-+
9×add-cbrt-cube
8×frac-times
6×pow1
4×expm1-log1p-u associate-*r/ associate-*l/ log1p-expm1-u add-log-exp
3×difference-cubes pow-unpow div-exp div-inv
2×cbrt-undiv pow-exp associate-/l/
1×pow-to-exp rem-sqrt-square asin-acos flip3-- pow-pow frac-2neg sqrt-pow1 pow1/2 sqrt-div div-sub prod-exp clear-num associate-/r* flip-- cbrt-unprod
Counts
4 → 240
Calls
4 calls:
3.0ms
(pow (/ t l) 2.0)
218.0ms
(/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
0.0ms
(asin (sqrt (/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
124.0ms
(sqrt (/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

series1.9s

Counts
4 → 12
Calls
4 calls:
59.0ms
(pow (/ t l) 2.0)
717.0ms
(/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
39.0ms
(asin (sqrt (/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
1.0s
(sqrt (/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

simplify84.0ms

Algorithm
egg-herbie
Counts
252 → 252
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
011735721
150025421

prune1.2s

Filtered
252 candidates to 154 candidates (61.1%)
Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 11.4b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (/ t l) 2.0)
0.6b
(asin (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (sqrt (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
0.6b
(/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (sqrt (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
10.3b
(sqrt (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite225.0ms

Algorithm
rewrite-expression-head
Rules
405×add-sqr-sqrt
299×sqrt-prod
257×times-frac
243×unpow-prod-down
200×difference-of-squares
150×cube-prod
125×*-un-lft-identity
111×sqr-pow
75×add-cube-cbrt
52×associate-/l*
25×distribute-lft-out--
18×sqrt-div
12×flip3-+ flip-+
9×add-exp-log
8×pow1 frac-times associate-/r/
6×add-cbrt-cube
5×difference-cubes
4×expm1-log1p-u associate-*r/ associate-*l/ associate-/r* log1p-expm1-u add-log-exp
3×pow-unpow
2×sqrt-pow1 div-exp pow-exp div-inv associate-/l/
1×cbrt-undiv pow-to-exp asin-acos sqrt-undiv flip3-- pow-pow frac-2neg pow1/2 pow-prod-down clear-num flip--
Counts
4 → 350
Calls
4 calls:
3.0ms
(pow (/ t l) 2.0)
0.0ms
(asin (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (sqrt (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
167.0ms
(/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (sqrt (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
27.0ms
(sqrt (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series1.5s

Counts
4 → 12
Calls
4 calls:
59.0ms
(pow (/ t l) 2.0)
43.0ms
(asin (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (sqrt (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
892.0ms
(/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (sqrt (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
459.0ms
(sqrt (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify201.0ms

Algorithm
egg-herbie
Counts
362 → 362
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
0120011959
1457811755
2500111755

prune1.7s

Filtered
362 candidates to 201 candidates (55.5%)
Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 11.4b

regimes676.0ms

Accuracy

0% (0.1b remaining)

Error of 10.9b against oracle of 10.8b and baseline of 10.9b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03223
13223

end0.0ms

sample1.7s

Algorithm
intervals
Results
497.0ms7813×body80nan
476.0ms3742×body160valid
266.0ms4258×body80valid