Details

Time bar (total: 7.5s)

sample55.0ms

Algorithm
intervals
Results
14.0ms124×body160valid
13.0ms236×body80nan
8.0ms132×body80valid

simplify126.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02910
14910
210110
327910
4102910
5438410
6500210

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ t l) 2.0)
0.2b
(pow (/ Om Omc) 2.0)
0.7b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
10.5b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
59×add-sqr-sqrt
46×times-frac
38×*-un-lft-identity
32×add-cube-cbrt unpow-prod-down
30×sqrt-prod
12×difference-of-squares
10×add-exp-log
7×pow1
6×pow-unpow
5×sqr-pow
4×pow-exp add-cbrt-cube add-log-exp
3×div-inv distribute-lft-out--
2×pow-to-exp rem-sqrt-square pow-pow div-exp associate-/r/
1×asin-acos sqrt-pow1 flip3-+ pow1/2 sqrt-div flip-+
Counts
4 → 106
Calls
4 calls:
5.0ms
(pow (/ t l) 2.0)
4.0ms
(pow (/ Om Omc) 2.0)
1.0ms
(asin (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)))))

series463.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(pow (/ t l) 2.0)
63.0ms
(pow (/ Om Omc) 2.0)
18.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
318.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify54.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
06951235
120431164
250021152

prune460.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 11.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ Om Omc) 2.0)
0.4b
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
0.7b
(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
10.3b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
108×add-sqr-sqrt
95×sqrt-prod
82×times-frac
65×*-un-lft-identity
51×add-cube-cbrt
28×difference-of-squares
27×unpow-prod-down
11×associate-/l*
9×add-exp-log
8×sqr-pow
7×distribute-lft-out--
6×pow1 sqrt-div associate-/r* add-cbrt-cube
4×add-log-exp
3×pow-unpow
2×flip3-+ div-exp pow-exp associate-/r/ flip-+ div-inv associate-/l/
1×cbrt-undiv pow-to-exp rem-sqrt-square asin-acos sqrt-undiv flip3-- pow-pow frac-2neg sqrt-pow1 pow1/2 clear-num flip--
Counts
4 → 151
Calls
4 calls:
4.0ms
(pow (/ Om Omc) 2.0)
15.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
1.0ms
(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
3.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series577.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(pow (/ Om Omc) 2.0)
317.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
17.0ms
(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
180.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify62.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
06092507
119582333
250012323

prune747.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 11.3b

localize19.0ms

Local error

Found 4 expressions with local error:

7.9b
(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
7.9b
(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
10.3b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
10.3b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
26×sqrt-prod
16×add-sqr-sqrt
12×sqrt-div
10×pow1 add-cube-cbrt *-un-lft-identity sqrt-pow1
6×rem-sqrt-square pow1/2
4×add-exp-log flip3-+ add-cbrt-cube flip-+ add-log-exp
Counts
4 → 72
Calls
4 calls:
5.0ms
(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
3.0ms
(sqrt (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))))

series823.0ms

Counts
4 → 12
Calls
4 calls:
239.0ms
(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
233.0ms
(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
175.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
175.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify84.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 3 (76.0ms)

IterNodesCost
0201726
1658700
22858696
35002688

prune424.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 11.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.7b
(asin (fabs (* (/ 1 (fabs (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))))
2.7b
(sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
15.7b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
15.7b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
10×cbrt-prod add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×cbrt-div sqrt-prod
5×pow1
4×add-exp-log add-cbrt-cube add-log-exp
3×flip3-+ pow1/3 flip-+
2×rem-sqrt-square sqrt-pow1 sqrt-div
1×asin-acos pow1/2
Counts
4 → 54
Calls
4 calls:
1.0ms
(asin (fabs (* (/ 1 (fabs (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))))
3.0ms
(sqrt (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))))

series750.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(asin (fabs (* (/ 1 (fabs (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))))
243.0ms
(sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
234.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
241.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify126.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 3 (112.0ms)

IterNodesCost
0327862
11012789
24465779
35002778

prune403.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 11.3b

regimes615.0ms

Accuracy

0% (0.1b remaining)

Error of 10.7b against oracle of 10.6b and baseline of 10.7b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01810
11810

end0.0ms

sample1.6s

Algorithm
intervals
Results
464.0ms7956×body80nan
427.0ms3753×body160valid
243.0ms4247×body80valid