Details

Time bar (total: 11.7s)

sample112.0ms

Algorithm
intervals
Results
37.0ms254×body80nan
33.0ms120×body160valid
20.0ms136×body80valid

simplify129.0ms

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: 10.0b

localize15.0ms

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))))
0.6b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.8b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite79.0ms

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:
4.0ms
(pow (/ t l) 2.0)
38.0ms
(/ (- 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))))))
31.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series620.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(pow (/ t l) 2.0)
214.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
18.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
322.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify65.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
06481882
120471787
250011774

prune582.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 9.9b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ t l) 2.0)
0.4b
(/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))
0.6b
(asin (sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))))
8.8b
(sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0)))))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt times-frac
16×add-cube-cbrt *-un-lft-identity sqrt-prod associate-/r/
13×unpow-prod-down
12×add-exp-log flip3-+ flip-+
9×add-cbrt-cube
8×frac-times
6×pow1
4×associate-*r/ associate-*l/ associate-/l* add-log-exp
3×pow-unpow div-exp div-inv difference-of-squares
2×cbrt-undiv pow-exp associate-/l/
1×pow-to-exp rem-sqrt-square asin-acos flip3-- pow-pow frac-2neg sqrt-pow1 pow1/2 sqrt-div div-sub prod-exp clear-num associate-/r* flip-- cbrt-unprod sqr-pow
Counts
4 → 97
Calls
4 calls:
3.0ms
(pow (/ t l) 2.0)
23.0ms
(/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))
0.0ms
(asin (sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))))
20.0ms
(sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0)))))

series1.5s

Counts
4 → 12
Calls
4 calls:
65.0ms
(pow (/ t l) 2.0)
603.0ms
(/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))
27.0ms
(asin (sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))))
785.0ms
(sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0)))))

simplify90.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 1 (18.0ms)

IterNodesCost
07921852
134551677
250011677

prune527.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 9.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b
(asin (sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
8.8b
(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.9b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
8.9b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite120.0ms

Algorithm
rewrite-expression-head
Rules
658×times-frac
647×sqrt-prod
560×add-sqr-sqrt
325×*-un-lft-identity
253×add-cube-cbrt
144×difference-of-squares
72×unpow-prod-down
36×distribute-lft-out-- sqr-pow
19×sqrt-div
14×associate-/r/
9×rem-sqrt-square flip3-+ flip-+
7×pow1 div-inv
4×add-exp-log add-cbrt-cube add-log-exp
3×sqrt-pow1 pow1/2
1×asin-acos
Counts
4 → 385
Calls
4 calls:
0.0ms
(asin (sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
73.0ms
(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 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))))

series839.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(asin (sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
313.0ms
(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
319.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
187.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify166.0ms

Algorithm
egg-herbie
Counts
397 → 397
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
0153913238
1465412782
2500212550

prune899.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 9.9b

localize22.0ms

Local error

Found 4 expressions with local error:

8.8b
(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (* (fabs (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
8.9b
(sqrt (+ 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))))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
108×times-frac
87×sqrt-prod
81×add-sqr-sqrt
43×*-un-lft-identity
31×add-cube-cbrt
24×difference-of-squares
12×unpow-prod-down
7×sqrt-div
6×pow1 cbrt-prod cbrt-div distribute-lft-out-- sqr-pow
5×flip3-+ flip-+
4×add-exp-log associate-/r/ add-cbrt-cube add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3 associate-*r/ div-inv
Counts
4 → 112
Calls
4 calls:
46.0ms
(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 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:
452.0ms
(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (* (fabs (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
185.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
250.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
243.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify67.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
07233060
119733009
250012971

prune641.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 9.9b

regimes741.0ms

Accuracy

0% (0.1b remaining)

Error of 10.1b against oracle of 10.1b and baseline of 10.1b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02418
12418

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.2s7974×body80nan
976.0ms3812×body160valid
615.0ms4188×body80valid