Details

Time bar (total: 9.2s)

sample61.0ms

Algorithm
intervals
Results
17.0ms119×body160valid
15.0ms211×body80nan
9.0ms137×body80valid

simplify147.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02910
15110
210710
329010
4105410
5444510
6500110

prune7.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 11.1b

Counts
2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (/ t l) 2.0)
0.3b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
0.6b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
10.1b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite41.0ms

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:
5.0ms
(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))))))
17.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
13.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series594.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(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))))))
206.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
310.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify67.0ms

Algorithm
egg-herbie
Counts
150 → 150
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
06641948
121061846
250011828

prune629.0ms

Filtered
150 candidates to 123 candidates (82.0%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1437150
Fresh000
Picked101
Done000
Total1447151

Merged error: 11.0b

Counts
151 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (/ t l) 2.0)
0.3b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* 1 (pow (/ t l) 2.0)))))))
0.6b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* 1 (pow (/ t l) 2.0)))))
10.1b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* 1 (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:
5.0ms
(pow (/ t l) 2.0)
1.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* 1 (pow (/ t l) 2.0)))))))
19.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* 1 (pow (/ t l) 2.0)))))
13.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* 1 (pow (/ t l) 2.0))))))

series590.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(pow (/ t l) 2.0)
17.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* 1 (pow (/ t l) 2.0)))))))
205.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* 1 (pow (/ t l) 2.0)))))
307.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* 1 (pow (/ t l) 2.0))))))

simplify71.0ms

Algorithm
egg-herbie
Counts
150 → 150
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
06682119
121621998
250011973

prune650.0ms

Filtered
150 candidates to 123 candidates (82.0%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1482150
Fresh246
Picked011
Done000
Total1507157

Merged error: 11.0b

Counts
157 → 7

localize21.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
10.1b
(sqrt (* (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
10.1b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
10.1b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
37×*-un-lft-identity
25×add-sqr-sqrt
24×times-frac
23×add-cube-cbrt
22×sqrt-prod
9×pow1 sqrt-div
7×distribute-lft-out
6×add-exp-log associate-/r* add-cbrt-cube
4×expm1-log1p-u sqrt-pow1 flip3-+ flip-+ log1p-expm1-u associate-/l* add-log-exp
3×pow1/2
2×rem-sqrt-square associate-/r/ associate-/l/
1×cbrt-undiv frac-times frac-2neg associate-*r/ div-exp pow-prod-down associate-*l/ clear-num div-inv
Counts
4 → 102
Calls
4 calls:
19.0ms
(/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
34.0ms
(sqrt (* (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
3.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
3.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.1s

Counts
4 → 12
Calls
4 calls:
306.0ms
(/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
406.0ms
(sqrt (* (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
178.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
178.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify50.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
03371665
112631572
250011548

prune534.0ms

Filtered
114 candidates to 82 candidates (71.9%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1131114
Fresh055
Picked011
Done011
Total1138121

Merged error: 11.0b

Counts
121 → 8

localize32.0ms

Local error

Found 4 expressions with local error:

10.1b
(sqrt (* (* (/ (* (cbrt (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2)))) (cbrt (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))))) (sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (/ (cbrt (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2)))) (sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))) (/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
10.1b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
10.1b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
10.1b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
13×pow1 sqrt-div
10×add-sqr-sqrt sqrt-prod
7×add-cube-cbrt *-un-lft-identity
6×sqrt-pow1
5×frac-times associate-*l/
4×add-exp-log expm1-log1p-u pow1/2 add-cbrt-cube log1p-expm1-u add-log-exp
3×rem-sqrt-square flip3-+ associate-*r/ pow-prod-down flip-+
Counts
4 → 72
Calls
4 calls:
70.0ms
(sqrt (* (* (/ (* (cbrt (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2)))) (cbrt (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))))) (sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (/ (cbrt (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2)))) (sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))) (/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
3.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
3.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
3.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series960.0ms

Counts
4 → 12
Calls
4 calls:
414.0ms
(sqrt (* (* (/ (* (cbrt (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2)))) (cbrt (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))))) (sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (/ (cbrt (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2)))) (sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))) (/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
179.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
181.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
185.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify101.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 3 (87.0ms)

IterNodesCost
02571365
18221294
238691294
350011281

prune528.0ms

Filtered
84 candidates to 68 candidates (81.0%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New82284
Fresh055
Picked101
Done022
Total83992

Merged error: 11.0b

Counts
92 → 9

regimes986.0ms

Accuracy

0% (0.1b remaining)

Error of 11.0b against oracle of 10.9b and baseline of 11.0b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02311
12511
22511

end0.0ms

sample1.9s

Algorithm
intervals
Results
562.0ms7924×body80nan
523.0ms3719×body160valid
307.0ms4281×body80valid