Details

Time bar (total: 14.1s)

sample72.0ms

Algorithm
intervals
Results
20.0ms273×body80nan
16.0ms118×body160valid
14.0ms138×body80valid

simplify125.0ms

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: 11.5b

localize14.0ms

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)))))

rewrite44.0ms

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)
20.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (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))))))
12.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series618.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(pow (/ t l) 2.0)
214.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
16.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
320.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify64.0ms

Algorithm
egg-herbie
Counts
150 → 150
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
06641948
121061846
250011828

prune629.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 11.4b

localize27.0ms

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))))))

rewrite302.0ms

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:
5.0ms
(pow (/ t l) 2.0)
231.0ms
(/ (- (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)))))
1.0ms
(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)))))))
50.0ms
(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:
60.0ms
(pow (/ t l) 2.0)
713.0ms
(/ (- (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)))))
42.0ms
(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)))))))
897.0ms
(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))))))

simplify83.0ms

Algorithm
egg-herbie
Counts
252 → 252
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
011735721
150025421

prune1.0s

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))))))

rewrite160.0ms

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:
5.0ms
(pow (/ t l) 2.0)
84.0ms
(/ (- (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)))))
1.0ms
(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)))))))
54.0ms
(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:
59.0ms
(pow (/ t l) 2.0)
706.0ms
(/ (- (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)))))))
890.0ms
(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))))))

simplify84.0ms

Algorithm
egg-herbie
Counts
252 → 252
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
011735721
150025421

prune1.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 11.4b

localize32.0ms

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)))))

rewrite114.0ms

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:
5.0ms
(pow (/ t l) 2.0)
1.0ms
(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)))))))
61.0ms
(/ (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))))))
18.0ms
(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:
62.0ms
(pow (/ t l) 2.0)
45.0ms
(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)))))))
912.0ms
(/ (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))))))
471.0ms
(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)))))

simplify203.0ms

Algorithm
egg-herbie
Counts
362 → 362
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
0120011831
1457911548
2500111548

prune1.6s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 11.4b

regimes847.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03223
13223

end0.0ms

sample1.9s

Algorithm
intervals
Results
566.0ms7813×body80nan
556.0ms3742×body160valid
322.0ms4258×body80valid