Details

Time bar (total: 11.7s)

sample61.0ms

Algorithm
intervals
Results
18.0ms305×body80nan
13.0ms110×body160valid
8.0ms146×body80valid

simplify127.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02910
15110
210710
329010
4105410
5444510
6500110

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ Om Omc) 2.0)
0.3b
(/ (- 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))))))
11.5b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite93.0ms

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 (/ Om Omc) 2.0)
50.0ms
(/ (- 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))))))
33.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series617.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(pow (/ Om Omc) 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))))))
321.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify63.0ms

Algorithm
egg-herbie
Counts
150 → 150
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
06501948
120761846
250011827

prune741.0ms

Filtered
150 candidates to 123 candidates (82.0%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 12.4b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ Om Omc) 2.0)
0.3b
(/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))
0.6b
(asin (sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))))
11.5b
(sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0)))))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt times-frac
16×add-cube-cbrt *-un-lft-identity sqrt-prod associate-/r/
13×unpow-prod-down
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 associate-/l* add-log-exp
3×pow-unpow div-exp div-inv difference-of-squares
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 sqr-pow
Counts
4 → 105
Calls
4 calls:
3.0ms
(pow (/ Om Omc) 2.0)
23.0ms
(/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))
0.0ms
(asin (sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))))
21.0ms
(sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0)))))

series1.5s

Counts
4 → 12
Calls
4 calls:
68.0ms
(pow (/ Om Omc) 2.0)
604.0ms
(/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))
30.0ms
(asin (sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))))
764.0ms
(sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0)))))

simplify91.0ms

Algorithm
egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 2 (73.0ms)

IterNodesCost
08101963
135541783
250011779

prune541.0ms

Filtered
117 candidates to 98 candidates (83.8%)
Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 12.4b

localize22.0ms

Local error

Found 4 expressions with local error:

6.2b
(sqrt (sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))))
6.2b
(sqrt (sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))))
11.5b
(sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0)))))
11.5b
(sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0)))))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
104×sqrt-prod
32×associate-/r/
24×flip3-+ flip-+
20×add-sqr-sqrt
16×frac-times times-frac
14×add-cube-cbrt *-un-lft-identity
10×pow1 sqrt-pow1
8×associate-*r/ associate-*l/
6×rem-sqrt-square pow1/2 sqrt-div
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u div-inv add-log-exp difference-of-squares
Counts
4 → 128
Calls
4 calls:
22.0ms
(sqrt (sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))))
22.0ms
(sqrt (sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))))
23.0ms
(sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0)))))
21.0ms
(sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0)))))

series3.0s

Counts
4 → 12
Calls
4 calls:
704.0ms
(sqrt (sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))))
708.0ms
(sqrt (sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))))
781.0ms
(sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0)))))
783.0ms
(sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0)))))

simplify67.0ms

Algorithm
egg-herbie
Counts
140 → 140
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
03963174
113503108
250013048

prune831.0ms

Filtered
140 candidates to 122 candidates (87.1%)
Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 12.4b

localize22.0ms

Local error

Found 4 expressions with local error:

11.7b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
11.7b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
19.1b
(sqrt (pow (/ Om Omc) 2.0))
19.1b
(sqrt (pow (/ Om Omc) 2.0))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
40×sqrt-prod
32×add-sqr-sqrt
30×unpow-prod-down
22×add-cube-cbrt *-un-lft-identity
20×times-frac
10×rem-sqrt-square
6×pow1
4×add-exp-log expm1-log1p-u sqrt-pow1 pow1/2 sqrt-div add-cbrt-cube log1p-expm1-u add-log-exp sqr-pow
2×flip3-+ flip-+ div-inv
Counts
4 → 98
Calls
4 calls:
3.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
3.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
6.0ms
(sqrt (pow (/ Om Omc) 2.0))
7.0ms
(sqrt (pow (/ Om Omc) 2.0))

series931.0ms

Counts
4 → 12
Calls
4 calls:
191.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
189.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
276.0ms
(sqrt (pow (/ Om Omc) 2.0))
275.0ms
(sqrt (pow (/ Om Omc) 2.0))

simplify94.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
0376850
1997828
23976828
35001828

prune632.0ms

Filtered
110 candidates to 92 candidates (83.6%)
Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 12.4b

regimes443.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02418
12418

end0.0ms

sample1.6s

Algorithm
intervals
Results
474.0ms7963×body80nan
455.0ms3782×body160valid
255.0ms4218×body80valid