Details

Time bar (total: 8.5s)

sample63.0ms

Algorithm
intervals
Results
18.0ms309×body80nan
15.0ms130×body160valid
7.0ms126×body80valid

simplify124.0ms

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: 9.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (/ t l) 2.0)
0.3b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.8b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.2b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite91.0ms

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)
49.0ms
(/ (- 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)))))

series605.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(pow (/ t l) 2.0)
211.0ms
(/ (- 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))))))
313.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify65.0ms

Algorithm
egg-herbie
Counts
150 → 150
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
06641948
121061846
250011828

prune749.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 9.4b

localize23.0ms

Local error

Found 4 expressions with local error:

0.8b
(asin (* (fabs (/ 1 (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
1.4b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
14.1b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
14.1b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
82×add-sqr-sqrt
56×times-frac
54×sqrt-prod
41×*-un-lft-identity
31×cbrt-prod
29×add-cube-cbrt
24×difference-of-squares
12×unpow-prod-down
6×cbrt-div distribute-lft-out-- sqr-pow
5×pow1
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×rem-sqrt-square flip3-+ flip-+
2×pow1/3 associate-/r/
1×asin-acos sqrt-pow1 pow1/2 sqrt-div div-inv
Counts
4 → 109
Calls
4 calls:
0.0ms
(asin (* (fabs (/ 1 (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
31.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
2.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
2.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series869.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(asin (* (fabs (/ 1 (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
348.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
243.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
243.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify53.0ms

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
05582127
114022035
250022026

prune686.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 9.4b

localize23.0ms

Local error

Found 4 expressions with local error:

0.8b
(asin (* (fabs (/ 1 (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))))
7.9b
(cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
8.0b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
14.1b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×sqrt-prod
5×pow1
4×add-exp-log expm1-log1p-u cbrt-div sqrt-div add-cbrt-cube log1p-expm1-u add-log-exp
3×flip3-+ flip-+
2×pow1/3
1×rem-sqrt-square asin-acos sqrt-pow1 pow1/2
Counts
4 → 60
Calls
4 calls:
0.0ms
(asin (* (fabs (/ 1 (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))))
2.0ms
(cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
3.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
2.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series705.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(asin (* (fabs (/ 1 (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))))
239.0ms
(cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
186.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
245.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify130.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0368942
11125865
24777858
35001858

prune472.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 9.4b

localize29.0ms

Local error

Found 4 expressions with local error:

7.9b
(cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
8.0b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
8.0b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
14.1b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×cbrt-prod add-cube-cbrt *-un-lft-identity sqrt-prod
6×pow1 sqrt-div
4×add-exp-log expm1-log1p-u cbrt-div flip3-+ add-cbrt-cube flip-+ log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 67
Calls
4 calls:
2.0ms
(cbrt (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))))
2.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series858.0ms

Counts
4 → 12
Calls
4 calls:
250.0ms
(cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
181.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
180.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
246.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify114.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 3 (105.0ms)

IterNodesCost
0257730
1859692
23910685
35001682

prune576.0ms

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 9.4b

regimes560.0ms

Accuracy

0% (0.0b remaining)

Error of 10.3b against oracle of 10.2b and baseline of 10.3b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01810
11810

end0.0ms

sample1.6s

Algorithm
intervals
Results
479.0ms8008×body80nan
444.0ms3733×body160valid
259.0ms4267×body80valid