Details

Time bar (total: 8.9s)

sample77.0ms

Algorithm
intervals
Results
22.0ms246×body80nan
22.0ms121×body160valid
12.0ms135×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

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 12.2b

Counts
2 → 1

localize19.0ms

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)))))

rewrite40.0ms

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)
16.0ms
(/ (- 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)))))

series601.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(pow (/ Om Omc) 2.0)
207.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
19.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
315.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify71.0ms

Algorithm
egg-herbie
Counts
150 → 150
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
06501948
120761846
250011827

prune506.0ms

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

localize15.0ms

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))))

rewrite25.0ms

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:
4.0ms
(pow (/ Om Omc) 2.0)
3.0ms
(/ 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)))))
14.0ms
(sqrt (* (- 1.0 (pow (/ Om Omc) 2.0)) (/ 1 (fma (pow (/ t l) 2.0) 2.0 1.0))))

series407.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(pow (/ Om Omc) 2.0)
78.0ms
(/ 1 (fma (pow (/ t l) 2.0) 2.0 1.0))
14.0ms
(asin (sqrt (* (- 1.0 (pow (/ Om Omc) 2.0)) (/ 1 (fma (pow (/ t l) 2.0) 2.0 1.0)))))
253.0ms
(sqrt (* (- 1.0 (pow (/ Om Omc) 2.0)) (/ 1 (fma (pow (/ t l) 2.0) 2.0 1.0))))

simplify45.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0447819
11565755
25001738

prune313.0ms

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

localize17.0ms

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)))))

rewrite64.0ms

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:
14.0ms
(sqrt (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
13.0ms
(sqrt (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)))))
15.0ms
(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:
335.0ms
(sqrt (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
335.0ms
(sqrt (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
308.0ms
(sqrt (/ (- 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)))))

simplify119.0ms

Algorithm
egg-herbie
Counts
200 → 200
Iterations

Useful iterations: 3 (88.0ms)

IterNodesCost
04213392
19453320
235693300
350033266

prune871.0ms

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

localize22.0ms

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)))

rewrite34.0ms

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:
23.0ms
(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)))
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)))

series654.0ms

Counts
4 → 12
Calls
4 calls:
266.0ms
(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))))))
129.0ms
(cbrt (/ 1 (fma (pow (/ t l) 2.0) 2.0 1.0)))
131.0ms
(cbrt (/ 1 (fma (pow (/ t l) 2.0) 2.0 1.0)))
128.0ms
(cbrt (/ 1 (fma (pow (/ t l) 2.0) 2.0 1.0)))

simplify127.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
03781810
19861748
240781697
350011697

prune399.0ms

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

regimes766.0ms

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
734.0ms8123×body80nan
694.0ms3803×body160valid
378.0ms4197×body80valid