Details

Time bar (total: 40.0s)

sample164.0ms

Algorithm
intervals
Results
43.0ms286×body80nan
39.0ms127×body80valid
38.0ms129×body160valid

simplify2.9s

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: 10.2b

localize36.0ms

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))))
0.3b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
9.4b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite248.0ms

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:
11.0ms
(pow (/ Om Omc) 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))))))
102.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series930.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(pow (/ Om Omc) 2.0)
311.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
23.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
499.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify2.9s

Counts
142 → 142
Iterations

Useful iterations: done (2.9s)

IterNodesCost
03083657
16333542
214833367
344673355
done50013352

prune788.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 10.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ Om Omc) 2.0)
0.3b
(/ (- (* 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))))
0.3b
(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))))))
9.4b
(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)))))

rewrite97.0ms

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:
6.0ms
(pow (/ Om Omc) 2.0)
49.0ms
(/ (- (* 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))))
1.0ms
(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))))))
38.0ms
(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)))))

series2.1s

Counts
4 → 12
Calls
4 calls:
97.0ms
(pow (/ Om Omc) 2.0)
896.0ms
(/ (- (* 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))))
33.0ms
(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))))))
1.1s
(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)))))

simplify1.4s

Counts
109 → 109
Iterations

Useful iterations: 2 (576.0ms)

IterNodesCost
02993802
17863283
229132986
done50002986

prune891.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 10.1b

localize31.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
9.4b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
9.4b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
9.4b
(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))))))

rewrite256.0ms

Algorithm
rewrite-expression-head
Rules
713×times-frac
674×sqrt-prod
641×add-sqr-sqrt
364×*-un-lft-identity
278×add-cube-cbrt
172×difference-of-squares
86×unpow-prod-down
43×distribute-lft-out-- sqr-pow
21×sqrt-div
16×associate-/r/
10×flip3-+ flip-+
9×rem-sqrt-square
8×div-inv associate-/l*
7×pow1
6×add-exp-log associate-/r* add-cbrt-cube
4×add-log-exp
3×sqrt-pow1 pow1/2
2×associate-/l/
1×cbrt-undiv flip3-- frac-2neg div-sub div-exp clear-num flip--
Counts
4 → 456
Calls
4 calls:
89.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
10.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
8.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
106.0ms
(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))))))

series1.3s

Counts
4 → 12
Calls
4 calls:
385.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
221.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
280.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
462.0ms
(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))))))

simplify1.8s

Counts
468 → 468
Iterations

Useful iterations: done (1.7s)

IterNodesCost
087325718
1154523123
2302621844
done500020994

prune1.6s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 10.1b

localize30.0ms

Local error

Found 4 expressions with local error:

9.4b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
9.4b
(sqrt (/ (/ (+ (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0))) (/ (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (- (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
18.8b
(sqrt (pow (/ Om Omc) 2.0))
18.8b
(sqrt (pow (/ Om Omc) 2.0))

rewrite1.7s

Algorithm
rewrite-expression-head
Rules
9616×sqrt-prod
8888×times-frac
6320×add-sqr-sqrt
5708×*-un-lft-identity
2684×add-cube-cbrt
1800×difference-of-squares
1152×distribute-lft-out
750×unpow-prod-down
364×sqr-pow
360×distribute-lft-out--
68×associate-/r/
39×div-inv
30×flip3-- flip--
18×rem-sqrt-square
6×pow1
5×sqrt-div
4×add-exp-log sqrt-pow1 pow1/2 add-cbrt-cube add-log-exp
2×flip3-+ flip-+
Counts
4 → 3010
Calls
4 calls:
9.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
645.0ms
(sqrt (/ (/ (+ (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0))) (/ (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (- (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
9.0ms
(sqrt (pow (/ Om Omc) 2.0))
9.0ms
(sqrt (pow (/ Om Omc) 2.0))

series1.6s

Counts
4 → 12
Calls
4 calls:
207.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
785.0ms
(sqrt (/ (/ (+ (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0))) (/ (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (- (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
331.0ms
(sqrt (pow (/ Om Omc) 2.0))
314.0ms
(sqrt (pow (/ Om Omc) 2.0))

simplify2.5s

Counts
3022 → 3022
Iterations

Useful iterations: done (2.2s)

IterNodesCost
03292262061
done5000246641

prune11.5s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 10.1b

regimes936.0ms

Accuracy

0% (0.1b remaining)

Error of 10.3b against oracle of 10.2b and baseline of 10.3b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02035
12435
done2435

end0.0ms

sample4.0s

Algorithm
intervals
Results
1.4s8023×body80nan
1.2s3861×body160valid
700.0ms4139×body80valid