Details

Time bar (total: 8.9s)

sample65.0ms

Algorithm
intervals
Results
17.0ms245×body80nan
17.0ms125×body160valid
9.0ms131×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

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ t l) 2.0)
0.3b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.4b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.7b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite34.0ms

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:
5.0ms
(pow (/ t l) 2.0)
12.0ms
(/ (- 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))))))
11.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series595.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(pow (/ t l) 2.0)
206.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
19.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
311.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify67.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
06481882
120471787
250011774

prune556.0ms

Filtered
142 candidates to 114 candidates (80.3%)
Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 9.4b

localize20.0ms

Local error

Found 4 expressions with local error:

8.5b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
8.5b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
8.8b
(sqrt (/ 1 (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))))))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
120×sqrt-prod
104×add-sqr-sqrt
78×times-frac
56×*-un-lft-identity
42×add-cube-cbrt
24×difference-of-squares
12×unpow-prod-down
10×pow1 rem-sqrt-square sqrt-div
9×sqrt-pow1
6×distribute-lft-out-- sqr-pow
5×pow1/2
4×add-exp-log flip3-+ associate-/r/ add-cbrt-cube flip-+ add-log-exp
3×pow-flip
2×div-inv
1×inv-pow
Counts
4 → 140
Calls
4 calls:
2.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
2.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
8.0ms
(sqrt (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
14.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

series935.0ms

Counts
4 → 12
Calls
4 calls:
174.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
175.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
253.0ms
(sqrt (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
332.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

simplify56.0ms

Algorithm
egg-herbie
Counts
152 → 152
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
05442246
114492186
250012138

prune609.0ms

Filtered
152 candidates to 102 candidates (67.1%)
Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 9.4b

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
8.5b
(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))))))
18.1b
(pow (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (- 1/4))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
167×add-sqr-sqrt
111×times-frac
109×sqrt-prod
83×*-un-lft-identity
57×add-cube-cbrt
52×difference-of-squares
29×unpow-prod-down
14×sqr-pow
13×distribute-lft-out--
10×pow-unpow
8×associate-/l*
7×pow1 add-exp-log sqrt-div
6×associate-/r* add-cbrt-cube
4×rem-sqrt-square associate-/r/ add-log-exp
3×distribute-lft-neg-in distribute-rgt-neg-in flip3-+ flip-+
2×sqrt-pow1 pow1/2 div-inv associate-/l/
1×cbrt-undiv neg-sub0 pow-to-exp pow-neg neg-mul-1 flip3-- pow-pow frac-2neg div-sub div-exp pow-exp clear-num flip-- pow-sub
Counts
4 → 187
Calls
4 calls:
13.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
2.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
14.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
4.0ms
(pow (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (- 1/4))

series1.1s

Counts
4 → 12
Calls
4 calls:
322.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
174.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
338.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
239.0ms
(pow (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (- 1/4))

simplify77.0ms

Algorithm
egg-herbie
Counts
199 → 199
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
06623264
120883115
250013092

prune782.0ms

Filtered
199 candidates to 134 candidates (67.3%)
Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 9.4b

localize22.0ms

Local error

Found 4 expressions with local error:

8.7b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
9.5b
(cbrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
9.5b
(cbrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
9.5b
(cbrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
46×add-sqr-sqrt
30×sqrt-prod
28×times-frac
25×*-un-lft-identity
19×add-cube-cbrt
12×difference-of-squares
9×cbrt-prod
6×unpow-prod-down
5×pow1
4×add-exp-log add-cbrt-cube add-log-exp
3×pow1/3 distribute-lft-out-- sqr-pow
2×rem-sqrt-square associate-/r/
1×sqrt-pow1 flip3-+ pow1/2 sqrt-div flip-+ div-inv
Counts
4 → 75
Calls
4 calls:
12.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
1.0ms
(cbrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
1.0ms
(cbrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
1.0ms
(cbrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))

series629.0ms

Counts
4 → 12
Calls
4 calls:
321.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
103.0ms
(cbrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
101.0ms
(cbrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
105.0ms
(cbrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))

simplify95.0ms

Algorithm
egg-herbie
Counts
87 → 87
Iterations

Useful iterations: 3 (80.0ms)

IterNodesCost
03981463
19401367
233901358
350021343

prune443.0ms

Filtered
87 candidates to 73 candidates (83.9%)
Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 9.4b

regimes632.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01810
11810

end0.0ms

sample1.9s

Algorithm
intervals
Results
603.0ms8227×body80nan
532.0ms3766×body160valid
315.0ms4234×body80valid