Details

Time bar (total: 20.9s)

sample87.0ms

Algorithm
intervals
Results
22.0ms257×body80nan
20.0ms129×body160valid
12.0ms127×body80valid

simplify2.2s

Counts
1 → 1

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.1b

localize37.0ms

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))))
0.7b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
9.1b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite222.0ms

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:
13.0ms
(pow (/ Om Omc) 2.0)
106.0ms
(/ (- 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))))))
91.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series972.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(pow (/ Om Omc) 2.0)
358.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
24.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
480.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify932.0ms

Counts
142 → 142

prune830.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 10.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ Om Omc) 2.0)
0.3b
(/ 1.0 (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.7b
(asin (sqrt (- (/ 1.0 (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (/ (pow (/ Om Omc) 2.0) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
9.1b
(sqrt (- (/ 1.0 (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (/ (pow (/ Om Omc) 2.0) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

rewrite232.0ms

Algorithm
rewrite-expression-head
Rules
57×add-sqr-sqrt
39×times-frac
31×*-un-lft-identity
23×add-cube-cbrt
20×sqrt-prod
17×unpow-prod-down
10×difference-of-squares
9×add-exp-log
6×pow1 associate-/r/ add-cbrt-cube
4×sqrt-div div-inv distribute-lft-out-- add-log-exp
3×pow-unpow distribute-rgt-out-- flip3-+ associate-/r* flip-+ associate-/l* sqr-pow
2×div-exp pow-exp
1×cbrt-undiv pow-to-exp rem-sqrt-square asin-acos flip3-- pow-pow frac-2neg sqrt-pow1 pow1/2 clear-num frac-sub flip-- sub-div
Counts
4 → 99
Calls
4 calls:
11.0ms
(pow (/ Om Omc) 2.0)
18.0ms
(/ 1.0 (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
1.0ms
(asin (sqrt (- (/ 1.0 (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (/ (pow (/ Om Omc) 2.0) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
194.0ms
(sqrt (- (/ 1.0 (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (/ (pow (/ Om Omc) 2.0) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

series1.1s

Counts
4 → 12
Calls
4 calls:
104.0ms
(pow (/ Om Omc) 2.0)
237.0ms
(/ 1.0 (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
45.0ms
(asin (sqrt (- (/ 1.0 (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (/ (pow (/ Om Omc) 2.0) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
711.0ms
(sqrt (- (/ 1.0 (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (/ (pow (/ Om Omc) 2.0) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

simplify1.1s

Counts
111 → 111

prune687.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 10.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.7b
(asin (sqrt (- (* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (cbrt 1.0) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (/ (pow (/ Om Omc) 2.0) (+ 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))))
9.1b
(sqrt (- (* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (cbrt 1.0) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (/ (pow (/ Om Omc) 2.0) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

rewrite181.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-div sqrt-prod
7×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log add-cbrt-cube add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2 frac-sub
2×flip3-+ flip-+
1×frac-times asin-acos flip3-- associate-*r/ associate-*l/ flip--
Counts
4 → 56
Calls
4 calls:
1.0ms
(asin (sqrt (- (* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (cbrt 1.0) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (/ (pow (/ Om Omc) 2.0) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
9.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
11.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
158.0ms
(sqrt (- (* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (cbrt 1.0) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (/ (pow (/ Om Omc) 2.0) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

series1.4s

Counts
4 → 12
Calls
4 calls:
76.0ms
(asin (sqrt (- (* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (cbrt 1.0) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (/ (pow (/ Om Omc) 2.0) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
245.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
271.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
842.0ms
(sqrt (- (* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (cbrt 1.0) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (/ (pow (/ Om Omc) 2.0) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

simplify687.0ms

Counts
68 → 68

prune503.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 10.0b

localize63.0ms

Local error

Found 4 expressions with local error:

8.9b
(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))))
9.1b
(sqrt (- (* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (cbrt 1.0) (* (* (cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))) (/ (pow (/ Om Omc) 2.0) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

rewrite477.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
11×sqrt-div
8×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log rem-sqrt-square sqrt-pow1 pow1/2 add-cbrt-cube add-log-exp
3×flip3-+ frac-sub flip-+
1×frac-times flip3-- associate-*r/ associate-*l/ flip--
Counts
4 → 63
Calls
4 calls:
9.0ms
(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))))
448.0ms
(sqrt (- (* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (cbrt 1.0) (* (* (cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))) (/ (pow (/ Om Omc) 2.0) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

series1.6s

Counts
4 → 12
Calls
4 calls:
277.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
253.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
254.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
783.0ms
(sqrt (- (* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (cbrt 1.0) (* (* (cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))) (/ (pow (/ Om Omc) 2.0) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

simplify675.0ms

Counts
75 → 75

prune496.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 10.0b

regimes764.0ms

Accuracy

0% (0.1b remaining)

Error of 10.7b against oracle of 10.6b and baseline of 10.7b

bsearch0.0ms

simplify1.6s

end0.0ms

sample3.9s

Algorithm
intervals
Results
1.3s8081×body80nan
1.1s3755×body160valid
558.0ms4245×body80valid