Details

Time bar (total: 25.8s)

sample123.0ms

Algorithm
intervals
Results
45.0ms121×body160valid
24.0ms225×body80nan
17.0ms135×body80valid

simplify3.1s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01619
12919
24919
310019
426519
579819
6301619
done500119

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.7b

localize18.0ms

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))))
0.8b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
10.3b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite202.0ms

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:
6.0ms
(pow (/ t l) 2.0)
122.0ms
(/ (- 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))))))
66.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series905.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(pow (/ t l) 2.0)
314.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
22.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
502.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify3.0s

Counts
142 → 142
Iterations

Useful iterations: done (2.9s)

IterNodesCost
03173657
16473534
215073367
346953363
done50003360

prune884.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 11.6b

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ -1 l) (/ -1 t))
0.4b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0))))
0.8b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0))))))
10.3b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0)))))

rewrite228.0ms

Algorithm
rewrite-expression-head
Rules
477×times-frac
284×add-sqr-sqrt
239×*-un-lft-identity
225×add-cube-cbrt
31×div-inv
30×sqrt-prod
28×difference-of-squares
21×associate-/l*
18×add-exp-log add-cbrt-cube
16×associate-/r*
14×unpow-prod-down
9×cbrt-undiv div-exp
7×distribute-lft-out-- sqr-pow
5×pow1 associate-/r/
4×add-log-exp
3×associate-/l/
2×rem-sqrt-square frac-2neg flip3-+ clear-num flip-+
1×asin-acos flip3-- sqrt-pow1 pow1/2 sqrt-div div-sub flip--
Counts
4 → 317
Calls
4 calls:
30.0ms
(/ (/ -1 l) (/ -1 t))
81.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0))))
1.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0))))))
82.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0)))))

series714.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(/ (/ -1 l) (/ -1 t))
301.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0))))
21.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0))))))
377.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0)))))

simplify1.3s

Counts
329 → 329
Iterations

Useful iterations: done (1.3s)

IterNodesCost
06508068
116357589
done50006700

prune1.9s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 11.6b

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ 1 (* 1 (/ l t))) 2.0))))
0.6b
(/ 1 (* 1 (/ l t)))
0.8b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ 1 (* 1 (/ l t))) 2.0))))))
10.3b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ 1 (* 1 (/ l t))) 2.0)))))

rewrite165.0ms

Algorithm
rewrite-expression-head
Rules
90×add-sqr-sqrt
59×times-frac
45×*-un-lft-identity
38×add-exp-log
31×add-cube-cbrt
30×sqrt-prod
28×difference-of-squares
17×div-exp
15×add-cbrt-cube
14×unpow-prod-down
12×prod-exp
11×1-exp associate-/l*
8×pow1
7×distribute-lft-out-- sqr-pow
5×cbrt-undiv rec-exp associate-/r/
4×associate-/r* add-log-exp
3×div-inv
2×rem-sqrt-square pow-flip frac-2neg flip3-+ clear-num cbrt-unprod flip-+ associate-/l/
1×asin-acos flip3-- sqrt-pow1 pow1/2 sqrt-div div-sub associate-*r/ pow-prod-down flip-- inv-pow
Counts
4 → 141
Calls
4 calls:
73.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ 1 (* 1 (/ l t))) 2.0))))
28.0ms
(/ 1 (* 1 (/ l t)))
1.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ 1 (* 1 (/ l t))) 2.0))))))
55.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ 1 (* 1 (/ l t))) 2.0)))))

series730.0ms

Counts
4 → 12
Calls
4 calls:
268.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ 1 (* 1 (/ l t))) 2.0))))
14.0ms
(/ 1 (* 1 (/ l t)))
21.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ 1 (* 1 (/ l t))) 2.0))))))
426.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ 1 (* 1 (/ l t))) 2.0)))))

simplify2.9s

Counts
153 → 153
Iterations

Useful iterations: 3 (1.5s)

IterNodesCost
03004378
16223795
214813585
343873233
done50013233

prune677.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 11.6b

localize37.0ms

Local error

Found 4 expressions with local error:

0.8b
(asin (* (fabs (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ (* (pow (* (/ 1 l) t) 2.0) 2.0) 1.0)))) (sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ (* (pow (* (/ 1 l) t) 2.0) 2.0) 1.0))))))
1.5b
(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ (* (pow (* (/ 1 l) t) 2.0) 2.0) 1.0))))
15.6b
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ (* (pow (* (/ 1 l) t) 2.0) 2.0) 1.0)))
15.6b
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ (* (pow (* (/ 1 l) t) 2.0) 2.0) 1.0)))

rewrite188.0ms

Algorithm
rewrite-expression-head
Rules
117×add-sqr-sqrt
92×cbrt-prod
82×times-frac
59×*-un-lft-identity
41×add-cube-cbrt
36×difference-of-squares
33×sqrt-prod
18×unpow-prod-down
9×distribute-lft-out-- sqr-pow
6×associate-/r/
5×pow1
4×add-exp-log add-cbrt-cube add-log-exp
3×rem-sqrt-square cbrt-div flip3-+ pow1/3 flip-+ div-inv
2×sqrt-pow1
1×asin-acos pow1/2 sqrt-div
Counts
4 → 133
Calls
4 calls:
1.0ms
(asin (* (fabs (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ (* (pow (* (/ 1 l) t) 2.0) 2.0) 1.0)))) (sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ (* (pow (* (/ 1 l) t) 2.0) 2.0) 1.0))))))
87.0ms
(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ (* (pow (* (/ 1 l) t) 2.0) 2.0) 1.0))))
40.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ (* (pow (* (/ 1 l) t) 2.0) 2.0) 1.0)))
48.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ (* (pow (* (/ 1 l) t) 2.0) 2.0) 1.0)))

series1.4s

Counts
4 → 12
Calls
4 calls:
42.0ms
(asin (* (fabs (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ (* (pow (* (/ 1 l) t) 2.0) 2.0) 1.0)))) (sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ (* (pow (* (/ 1 l) t) 2.0) 2.0) 1.0))))))
461.0ms
(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ (* (pow (* (/ 1 l) t) 2.0) 2.0) 1.0))))
501.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ (* (pow (* (/ 1 l) t) 2.0) 2.0) 1.0)))
426.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ (* (pow (* (/ 1 l) t) 2.0) 2.0) 1.0)))

simplify1.4s

Counts
145 → 145
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02975688
15395561
210814866
326324799
done50004784

prune1.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 11.6b

regimes870.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
01923
12421
done2421

end0.0ms

sample3.8s

Algorithm
intervals
Results
1.0s3767×body160valid
1.0s7895×body80nan
841.0ms4233×body80valid