Details

Time bar (total: 1.8m)

sample153.0ms

Algorithm
intervals
Results
49.0ms126×body160valid
48.0ms257×body80nan
27.0ms130×body80valid

simplify440.0ms

Calls
1 calls:
Slowest
439.0ms
(asin (sqrt (/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (pow (/ t l) 2))))))

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.5b

localize37.0ms

Local error

Found 4 expressions with local error:

7.8b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
0.4b
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
0.2b
(* (/ t l) (/ t l))
0.2b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
73×add-sqr-sqrt
71×times-frac
58×*-un-lft-identity
51×add-cube-cbrt
21×sqrt-prod
18×add-cbrt-cube add-exp-log
14×difference-of-squares
13×swap-sqr associate-*r* associate-*l*
12×pow1
6×div-inv
5×cbrt-undiv div-exp associate-/l*
4×prod-exp associate-/r/ cbrt-unprod insert-posit16 add-log-exp unswap-sqr
3×associate-/r*
2×rem-sqrt-square flip3-+ flip-+ associate-/l/
1×pow2 frac-times asin-acos clear-num frac-2neg sqrt-pow1 pow-plus flip3-- pow1/2 sqrt-div div-sub pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up flip--
Calls
4 calls:
Slowest
24.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
13.0ms
(* (/ t l) (/ t l))
11.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
1.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))

series346.0ms

Calls
4 calls:
Slowest
164.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
111.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
50.0ms
(* (/ t l) (/ t l))
22.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))

simplify16.0s

Calls
156 calls:
Slowest
410.0ms
(* (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))))
396.0ms
(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
395.0ms
(- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3))
320.0ms
(asin (sqrt (/ (- 1 (/ (pow Om 2) (pow Omc 2))) (+ (* 2 (/ (pow t 2) (pow l 2))) 1))))
299.0ms
(- 1 (* 2 (* (/ t l) (/ t l))))

prune2.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 8.4b

localize58.0ms

Local error

Found 4 expressions with local error:

8.2b
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
8.2b
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
7.8b
(sqrt (/ (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
0.2b
(* (/ t l) (/ t l))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
446×times-frac
431×sqrt-prod
276×add-sqr-sqrt
245×*-un-lft-identity
209×add-cube-cbrt
72×difference-of-squares
19×sqrt-div
16×add-cbrt-cube add-exp-log
14×pow1 associate-/r/
13×swap-sqr associate-*r* associate-*l*
11×div-inv
9×rem-sqrt-square flip3-+ flip-+
4×cbrt-undiv div-exp prod-exp cbrt-unprod insert-posit16 add-log-exp unswap-sqr
3×sqrt-pow1 pow1/2
1×pow2 frac-times pow-plus pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up
Calls
4 calls:
Slowest
18.0ms
(* (/ t l) (/ t l))
15.0ms
(sqrt (/ (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
5.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
3.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

series372.0ms

Calls
4 calls:
Slowest
191.0ms
(sqrt (/ (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
75.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
75.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
30.0ms
(* (/ t l) (/ t l))

simplify54.9s

Calls
332 calls:
Slowest
722.0ms
(sqrt (/ (/ (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (* (cbrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))) (cbrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))) (* (cbrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))) (cbrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))))
483.0ms
(sqrt (- (* 1 1) (* (* 2 (* (/ t l) (/ t l))) (* 2 (* (/ t l) (/ t l))))))
465.0ms
(sqrt (/ (/ (+ 1 (/ Om Omc)) (sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))) (sqrt 1)))
442.0ms
(sqrt (/ (/ (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (sqrt (* (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))) (cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))) (* (cbrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))) (cbrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))))
429.0ms
(sqrt (- (* 1 1) (* (* 2 (* (/ t l) (/ t l))) (* 2 (* (/ t l) (/ t l))))))

prune6.8s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 8.4b

localize77.0ms

Local error

Found 4 expressions with local error:

13.4b
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
13.4b
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
13.4b
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
8.7b
(sqrt (* (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))) (cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-div
12×pow1
9×cbrt-prod sqrt-pow1 flip3-+ pow1/3 flip-+
8×sqrt-div
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×frac-times add-cbrt-cube add-exp-log insert-posit16 add-log-exp
2×pow-prod-down associate-*l/ associate-*r/ pow-sqr pow-prod-up
1×pow2 rem-sqrt-square pow-plus pow1/2 sqrt-prod
Calls
4 calls:
Slowest
15.0ms
(sqrt (* (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))) (cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
2.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
2.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
2.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

series774.0ms

Calls
4 calls:
Slowest
205.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
197.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
188.0ms
(sqrt (* (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))) (cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
185.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

simplify8.9s

Calls
46 calls:
Slowest
660.0ms
(sqrt (* (cbrt (+ (pow 1 3) (pow (* 2 (* (/ t l) (/ t l))) 3))) (cbrt (+ (pow 1 3) (pow (* 2 (* (/ t l) (/ t l))) 3)))))
564.0ms
(cbrt (- (* 1 1) (* (* 2 (* (/ t l) (/ t l))) (* 2 (* (/ t l) (/ t l))))))
538.0ms
(sqrt (* (cbrt (- (* 1 1) (* (* 2 (* (/ t l) (/ t l))) (* 2 (* (/ t l) (/ t l)))))) (cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
512.0ms
(sqrt (* (cbrt (- (* 1 1) (* (* 2 (* (/ t l) (/ t l))) (* 2 (* (/ t l) (/ t l)))))) (cbrt (- (* 1 1) (* (* 2 (* (/ t l) (/ t l))) (* 2 (* (/ t l) (/ t l))))))))
505.0ms
(sqrt (* (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))) (cbrt (- (* 1 1) (* (* 2 (* (/ t l) (/ t l))) (* 2 (* (/ t l) (/ t l))))))))

prune2.3s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 8.4b

localize94.0ms

Local error

Found 4 expressions with local error:

13.4b
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
13.4b
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
13.4b
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
8.7b
(sqrt (* (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))) (cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-div
12×pow1
9×cbrt-prod sqrt-pow1 flip3-+ pow1/3 flip-+
8×sqrt-div
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×frac-times add-cbrt-cube add-exp-log insert-posit16 add-log-exp
2×pow-prod-down associate-*l/ associate-*r/ pow-sqr pow-prod-up
1×pow2 rem-sqrt-square pow-plus pow1/2 sqrt-prod
Calls
4 calls:
Slowest
11.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
7.0ms
(sqrt (* (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))) (cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
2.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
2.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

series720.0ms

Calls
4 calls:
Slowest
198.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
179.0ms
(sqrt (* (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))) (cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
174.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
169.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

simplify8.5s

Calls
46 calls:
Slowest
561.0ms
(sqrt (* (cbrt (+ (pow 1 3) (pow (* 2 (* (/ t l) (/ t l))) 3))) (cbrt (+ (pow 1 3) (pow (* 2 (* (/ t l) (/ t l))) 3)))))
516.0ms
(cbrt (- (* 1 1) (* (* 2 (* (/ t l) (/ t l))) (* 2 (* (/ t l) (/ t l))))))
512.0ms
(sqrt (* (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))) (cbrt (- (* 1 1) (* (* 2 (* (/ t l) (/ t l))) (* 2 (* (/ t l) (/ t l))))))))
507.0ms
(cbrt (- (* 1 1) (* (* 2 (* (/ t l) (/ t l))) (* 2 (* (/ t l) (/ t l))))))
495.0ms
(sqrt (* (cbrt (- (* 1 1) (* (* 2 (* (/ t l) (/ t l))) (* 2 (* (/ t l) (/ t l)))))) (cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))

prune2.0s

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 8.4b

regimes580.0ms

Accuracy

0% (0.1b remaining)

Error of 10.1b against oracle of 10.0b and baseline of 10.1b

bsearch3.0ms

end0.0ms

sample5.3s

Algorithm
intervals
Results
2.2s8244×body80nan
1.7s3781×body160valid
894.0ms4219×body80valid