Details

Time bar (total: 10.1s)

sample61.0ms

Algorithm
intervals
Results
16.0ms274×body80nan
14.0ms115×body160valid
8.0ms141×body80valid

simplify128.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02910
15110
210710
329010
4105410
5444510
6500110

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ t l) 2.0)
0.4b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.7b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
10.6b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite96.0ms

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)
50.0ms
(/ (- 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))))))
34.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series632.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(pow (/ t l) 2.0)
217.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (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))))))
331.0ms
(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

prune651.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 11.7b

localize18.0ms

Local error

Found 4 expressions with local error:

10.6b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0)))))))
29.9b
(cbrt (pow (/ t l) 2.0))
29.9b
(cbrt (pow (/ t l) 2.0))
29.9b
(cbrt (pow (/ t l) 2.0))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
67×add-sqr-sqrt
55×times-frac
51×cbrt-prod
46×*-un-lft-identity
45×unpow-prod-down
40×add-cube-cbrt
30×sqrt-prod
12×difference-of-squares
6×sqr-pow
5×pow1
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u div-inv add-log-exp
3×pow1/3 distribute-lft-out--
2×rem-sqrt-square associate-/r/
1×sqrt-pow1 flip3-+ pow1/2 sqrt-div flip-+
Counts
4 → 125
Calls
4 calls:
31.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0)))))))
3.0ms
(cbrt (pow (/ t l) 2.0))
3.0ms
(cbrt (pow (/ t l) 2.0))
8.0ms
(cbrt (pow (/ t l) 2.0))

series1.3s

Counts
4 → 12
Calls
4 calls:
329.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0)))))))
273.0ms
(cbrt (pow (/ t l) 2.0))
413.0ms
(cbrt (pow (/ t l) 2.0))
281.0ms
(cbrt (pow (/ t l) 2.0))

simplify56.0ms

Algorithm
egg-herbie
Counts
137 → 137
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
05232251
112332182
250012146

prune734.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 11.7b

localize26.0ms

Local error

Found 4 expressions with local error:

29.9b
(cbrt (pow (/ t l) 2.0))
29.9b
(cbrt (pow (/ t l) 2.0))
29.9b
(cbrt (pow (/ t l) 2.0))
29.9b
(cbrt (pow (/ t l) 2.0))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
68×cbrt-prod
52×unpow-prod-down
36×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac
4×pow1 add-exp-log expm1-log1p-u pow1/3 add-cbrt-cube log1p-expm1-u div-inv add-log-exp sqr-pow
Counts
4 → 108
Calls
4 calls:
3.0ms
(cbrt (pow (/ t l) 2.0))
3.0ms
(cbrt (pow (/ t l) 2.0))
3.0ms
(cbrt (pow (/ t l) 2.0))
4.0ms
(cbrt (pow (/ t l) 2.0))

series1.1s

Counts
4 → 12
Calls
4 calls:
272.0ms
(cbrt (pow (/ t l) 2.0))
269.0ms
(cbrt (pow (/ t l) 2.0))
273.0ms
(cbrt (pow (/ t l) 2.0))
278.0ms
(cbrt (pow (/ t l) 2.0))

simplify89.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 3 (27.0ms)

IterNodesCost
02391096
14911068
213051060
333391048
450011048

prune751.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 11.7b

localize29.0ms

Local error

Found 4 expressions with local error:

29.9b
(cbrt (pow (/ t l) 2.0))
29.9b
(cbrt (pow (/ t l) 2.0))
29.9b
(cbrt (pow (/ t l) 2.0))
29.9b
(cbrt (pow (/ t l) 2.0))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
68×cbrt-prod
52×unpow-prod-down
36×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac
4×pow1 add-exp-log expm1-log1p-u pow1/3 add-cbrt-cube log1p-expm1-u div-inv add-log-exp sqr-pow
Counts
4 → 108
Calls
4 calls:
4.0ms
(cbrt (pow (/ t l) 2.0))
3.0ms
(cbrt (pow (/ t l) 2.0))
4.0ms
(cbrt (pow (/ t l) 2.0))
4.0ms
(cbrt (pow (/ t l) 2.0))

series1.1s

Counts
4 → 12
Calls
4 calls:
272.0ms
(cbrt (pow (/ t l) 2.0))
280.0ms
(cbrt (pow (/ t l) 2.0))
275.0ms
(cbrt (pow (/ t l) 2.0))
278.0ms
(cbrt (pow (/ t l) 2.0))

simplify85.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 3 (26.0ms)

IterNodesCost
02391096
14911068
213051060
333391048
450011048

prune781.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 11.7b

regimes642.0ms

Accuracy

0% (0.1b remaining)

Error of 10.8b against oracle of 10.8b and baseline of 10.8b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01810
11810

end0.0ms

sample1.6s

Algorithm
intervals
Results
484.0ms7961×body80nan
451.0ms3742×body160valid
258.0ms4258×body80valid