Details

Time bar (total: 9.1s)

sample79.0ms

Algorithm
intervals
Results
22.0ms121×body160valid
22.0ms246×body80nan
13.0ms135×body80valid

simplify130.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
02910
15110
210710
329010
4105410
5444510
6500110

prune4.0ms

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: 12.2b

Counts
2 → 1

localize18.0ms

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))))))
11.2b
(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 (/ Om Omc) 2.0)
17.0ms
(/ (- 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))))))
13.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series625.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(pow (/ Om Omc) 2.0)
217.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
18.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
329.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify66.0ms

Algorithm
egg-herbie
Counts
150 → 150
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
06501948
120761846
250011827

prune521.0ms

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: 12.2b

Counts
151 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ Om Omc) 2.0)
0.3b
(/ 1 (fma (pow (/ t l) 2.0) 2.0 1.0))
0.6b
(asin (sqrt (* (- 1.0 (pow (/ Om Omc) 2.0)) (/ 1 (fma (pow (/ t l) 2.0) 2.0 1.0)))))
11.2b
(sqrt (* (- 1.0 (pow (/ Om Omc) 2.0)) (/ 1 (fma (pow (/ t l) 2.0) 2.0 1.0))))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×times-frac
13×unpow-prod-down
11×add-exp-log
9×pow1
6×sqrt-div add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow div-exp associate-/r* associate-/l*
2×frac-times flip3-- sqrt-pow1 associate-*l/ pow-exp flip-- div-inv
1×cbrt-undiv pow-to-exp rec-exp asin-acos pow-flip pow-pow frac-2neg pow1/2 1-exp associate-*r/ pow-prod-down clear-num sqrt-prod un-div-inv inv-pow sqr-pow
Counts
4 → 92
Calls
4 calls:
5.0ms
(pow (/ Om Omc) 2.0)
4.0ms
(/ 1 (fma (pow (/ t l) 2.0) 2.0 1.0))
1.0ms
(asin (sqrt (* (- 1.0 (pow (/ Om Omc) 2.0)) (/ 1 (fma (pow (/ t l) 2.0) 2.0 1.0)))))
12.0ms
(sqrt (* (- 1.0 (pow (/ Om Omc) 2.0)) (/ 1 (fma (pow (/ t l) 2.0) 2.0 1.0))))

series422.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(pow (/ Om Omc) 2.0)
85.0ms
(/ 1 (fma (pow (/ t l) 2.0) 2.0 1.0))
11.0ms
(asin (sqrt (* (- 1.0 (pow (/ Om Omc) 2.0)) (/ 1 (fma (pow (/ t l) 2.0) 2.0 1.0)))))
267.0ms
(sqrt (* (- 1.0 (pow (/ Om Omc) 2.0)) (/ 1 (fma (pow (/ t l) 2.0) 2.0 1.0))))

simplify51.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0447819
11565755
25001738

prune307.0ms

Filtered
104 candidates to 73 candidates (70.2%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1031104
Fresh156
Picked011
Done000
Total1047111

Merged error: 12.2b

Counts
111 → 7

localize29.0ms

Local error

Found 4 expressions with local error:

7.2b
(sqrt (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
7.2b
(sqrt (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
11.2b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
11.2b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
190×sqrt-prod
164×add-sqr-sqrt
112×times-frac
78×*-un-lft-identity
54×add-cube-cbrt
48×difference-of-squares
24×unpow-prod-down
12×distribute-lft-out-- sqr-pow
10×pow1 rem-sqrt-square sqrt-pow1
8×associate-/r/
6×pow1/2 sqrt-div
4×add-exp-log expm1-log1p-u flip3-+ add-cbrt-cube flip-+ log1p-expm1-u div-inv add-log-exp
Counts
4 → 188
Calls
4 calls:
15.0ms
(sqrt (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
15.0ms
(sqrt (sqrt (/ (- 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)))))
19.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series1.3s

Counts
4 → 12
Calls
4 calls:
341.0ms
(sqrt (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
343.0ms
(sqrt (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
316.0ms
(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)))))

simplify129.0ms

Algorithm
egg-herbie
Counts
200 → 200
Iterations

Useful iterations: 3 (93.0ms)

IterNodesCost
04213392
19453320
235693300
350033266

prune879.0ms

Filtered
200 candidates to 162 candidates (81.0%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New2000200
Fresh055
Picked011
Done011
Total2007207

Merged error: 12.2b

Counts
207 → 7

localize20.0ms

Local error

Found 4 expressions with local error:

11.2b
(sqrt (* (- 1.0 (pow (/ Om Omc) 2.0)) (* (* (cbrt (/ 1 (fma (pow (/ t l) 2.0) 2.0 1.0))) (cbrt (/ 1 (fma (pow (/ t l) 2.0) 2.0 1.0)))) (cbrt (/ 1 (fma (pow (/ t l) 2.0) 2.0 1.0))))))
17.3b
(cbrt (/ 1 (fma (pow (/ t l) 2.0) 2.0 1.0)))
17.3b
(cbrt (/ 1 (fma (pow (/ t l) 2.0) 2.0 1.0)))
17.3b
(cbrt (/ 1 (fma (pow (/ t l) 2.0) 2.0 1.0)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
39×cbrt-prod cbrt-div
29×frac-times
27×times-frac
25×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
23×sqrt-div
17×associate-*l/
16×associate-*r/
14×pow1
8×flip3-- flip--
6×pow-prod-down
4×add-exp-log expm1-log1p-u sqrt-pow1 add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/3 div-inv
1×pow1/2 sqrt-prod
Counts
4 → 110
Calls
4 calls:
25.0ms
(sqrt (* (- 1.0 (pow (/ Om Omc) 2.0)) (* (* (cbrt (/ 1 (fma (pow (/ t l) 2.0) 2.0 1.0))) (cbrt (/ 1 (fma (pow (/ t l) 2.0) 2.0 1.0)))) (cbrt (/ 1 (fma (pow (/ t l) 2.0) 2.0 1.0))))))
2.0ms
(cbrt (/ 1 (fma (pow (/ t l) 2.0) 2.0 1.0)))
3.0ms
(cbrt (/ 1 (fma (pow (/ t l) 2.0) 2.0 1.0)))
3.0ms
(cbrt (/ 1 (fma (pow (/ t l) 2.0) 2.0 1.0)))

series668.0ms

Counts
4 → 12
Calls
4 calls:
271.0ms
(sqrt (* (- 1.0 (pow (/ Om Omc) 2.0)) (* (* (cbrt (/ 1 (fma (pow (/ t l) 2.0) 2.0 1.0))) (cbrt (/ 1 (fma (pow (/ t l) 2.0) 2.0 1.0)))) (cbrt (/ 1 (fma (pow (/ t l) 2.0) 2.0 1.0))))))
134.0ms
(cbrt (/ 1 (fma (pow (/ t l) 2.0) 2.0 1.0)))
129.0ms
(cbrt (/ 1 (fma (pow (/ t l) 2.0) 2.0 1.0)))
133.0ms
(cbrt (/ 1 (fma (pow (/ t l) 2.0) 2.0 1.0)))

simplify132.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
03781810
19861748
240781697
350011697

prune407.0ms

Filtered
122 candidates to 84 candidates (68.9%)
Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New1211122
Fresh044
Picked011
Done022
Total1218129

Merged error: 12.2b

Counts
129 → 8

regimes765.0ms

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
02010
12010

end0.0ms

sample2.3s

Algorithm
intervals
Results
764.0ms8123×body80nan
692.0ms3803×body160valid
388.0ms4197×body80valid