Details

Time bar (total: 8.7s)

sample59.0ms

Algorithm
intervals
Results
16.0ms282×body80nan
13.0ms108×body160valid
9.0ms148×body80valid

simplify125.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02910
14910
210110
327910
4102910
5438410
6500210

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.9b

localize14.0ms

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))))
0.5b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
11.1b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite80.0ms

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×associate-/r/ 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 → 130
Calls
4 calls:
3.0ms
(pow (/ Om Omc) 2.0)
38.0ms
(/ (- 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)))))

series622.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(pow (/ Om Omc) 2.0)
216.0ms
(/ (- 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))))))
324.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify61.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
06341882
120171787
250011774

prune581.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 11.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.5b
(asin (sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
3.6b
(log (exp (pow (/ Om Omc) 2.0)))
11.1b
(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite187.0ms

Algorithm
rewrite-expression-head
Rules
55×*-un-lft-identity
51×add-sqr-sqrt
46×times-frac
34×add-cube-cbrt
25×log-pow
24×sqrt-prod
17×exp-prod
14×distribute-lft-out--
13×pow1 unpow-prod-down
7×difference-of-squares
6×add-exp-log add-cbrt-cube associate-/l*
4×associate-/r/ add-log-exp
3×log-prod associate-/r* div-inv
2×rem-sqrt-square flip3-+ flip-+ associate-/l/
1×cbrt-undiv asin-acos flip3-- frac-2neg sqrt-pow1 pow1/2 sqrt-div div-sub div-exp rem-log-exp clear-num flip-- sqr-pow
Counts
4 → 117
Calls
4 calls:
98.0ms
(/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.0ms
(asin (sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
12.0ms
(log (exp (pow (/ Om Omc) 2.0)))
71.0ms
(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series745.0ms

Counts
4 → 12
Calls
4 calls:
214.0ms
(/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
17.0ms
(asin (sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
59.0ms
(log (exp (pow (/ Om Omc) 2.0)))
454.0ms
(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify53.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
05521751
116571613
250021583

prune521.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 11.8b

localize22.0ms

Local error

Found 4 expressions with local error:

3.6b
(log (exp (pow (/ Om Omc) 2.0)))
11.1b
(sqrt (* (/ (sqrt (- 1.0 (log (exp (pow (/ Om Omc) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (sqrt (- 1.0 (log (exp (pow (/ Om Omc) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
11.1b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
11.1b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
18×log-pow
17×add-sqr-sqrt exp-prod
15×pow1 add-cube-cbrt *-un-lft-identity
13×unpow-prod-down
9×times-frac
8×sqrt-pow1
7×sqrt-div sqrt-prod
4×add-exp-log add-cbrt-cube add-log-exp
3×rem-sqrt-square log-prod pow1/2
2×flip3-+ flip-+
1×pow2 frac-times pow-plus associate-*r/ rem-log-exp pow-prod-down associate-*l/ pow-sqr pow-prod-up div-inv sqr-pow
Counts
4 → 78
Calls
4 calls:
12.0ms
(log (exp (pow (/ Om Omc) 2.0)))
81.0ms
(sqrt (* (/ (sqrt (- 1.0 (log (exp (pow (/ Om Omc) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (sqrt (- 1.0 (log (exp (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))))
3.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series733.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(log (exp (pow (/ Om Omc) 2.0)))
315.0ms
(sqrt (* (/ (sqrt (- 1.0 (log (exp (pow (/ Om Omc) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (sqrt (- 1.0 (log (exp (pow (/ Om Omc) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
175.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
180.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify119.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 3 (110.0ms)

IterNodesCost
0367774
11041719
24458719
35001713

prune494.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 11.8b

localize32.0ms

Local error

Found 4 expressions with local error:

11.1b
(sqrt (* (/ (sqrt (- 1.0 (log (exp (pow (/ Om Omc) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (sqrt (- 1.0 (log (exp (pow (/ Om Omc) 2.0))))) (* (fabs (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))))
11.1b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
17.2b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
17.2b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
8×pow1 add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×cbrt-prod
5×sqrt-div
4×add-exp-log cbrt-div sqrt-prod add-cbrt-cube add-log-exp
3×sqrt-pow1 flip3-+ flip-+
2×pow1/2 pow1/3
1×frac-times rem-sqrt-square associate-*r/ pow-prod-down associate-*l/
Counts
4 → 55
Calls
4 calls:
83.0ms
(sqrt (* (/ (sqrt (- 1.0 (log (exp (pow (/ Om Omc) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (sqrt (- 1.0 (log (exp (pow (/ Om Omc) 2.0))))) (* (fabs (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (cbrt (+ 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))))
2.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.1s

Counts
4 → 12
Calls
4 calls:
455.0ms
(sqrt (* (/ (sqrt (- 1.0 (log (exp (pow (/ Om Omc) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (sqrt (- 1.0 (log (exp (pow (/ Om Omc) 2.0))))) (* (fabs (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))))
181.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
241.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
241.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify101.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 3 (91.0ms)

IterNodesCost
0306966
1959902
23863894
35002893

prune481.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 11.8b

regimes658.0ms

Accuracy

0% (0.1b remaining)

Error of 10.4b against oracle of 10.4b and baseline of 10.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02012
12012

end0.0ms

sample1.6s

Algorithm
intervals
Results
476.0ms8052×body80nan
465.0ms3831×body160valid
246.0ms4169×body80valid