Details

Time bar (total: 1.3m)

sample170.0ms

Algorithm
intervals
Results
79.0ms304×body80nan
42.0ms119×body160valid
24.0ms137×body80valid

simplify389.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
388.0ms
(asin (sqrt (/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (pow (/ t l) 2))))))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.6b

localize26.0ms

Local error

Found 4 expressions with local error:

9.5b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
0.8b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
0.3b
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
0.2b
(* (/ t l) (/ t l))

rewrite71.0ms

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--
Counts
4 → 152
Calls
4 calls:
Slowest
31.0ms
(* (/ t l) (/ t l))
29.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
7.0ms
(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)))))))

series339.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
163.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
110.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
45.0ms
(* (/ t l) (/ t l))
21.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))

simplify15.3s

Counts
156 → 164
Calls
156 calls:
Slowest
457.0ms
(* (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))))
397.0ms
(- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3))
349.0ms
(- 1 (* 2 (* (/ t l) (/ t l))))
318.0ms
(/ (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (* (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))) (cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
305.0ms
(/ (- 1 (/ Om Omc)) (+ 1 (* 2 (* (/ t l) (/ t l)))))

prune2.3s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 10.5b

localize26.0ms

Local error

Found 4 expressions with local error:

9.5b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1)))
0.8b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1))))
0.4b
(/ 2 (* (/ l t) (/ l t)))
0.3b
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
58×*-un-lft-identity
44×times-frac
39×add-sqr-sqrt
27×add-cube-cbrt
26×sqrt-prod
24×add-cbrt-cube add-exp-log
18×difference-of-squares
11×distribute-lft-out
10×cbrt-undiv div-exp
8×associate-/l*
7×associate-/r/
5×pow1 associate-/r*
4×prod-exp cbrt-unprod insert-posit16 add-log-exp
3×div-inv
2×rem-sqrt-square clear-num frac-2neg flip3-+ flip-+ associate-/l/
1×frac-times asin-acos sqrt-pow1 flip3-- pow1/2 sqrt-div div-sub associate-*l/ associate-*r/ flip--
Counts
4 → 126
Calls
4 calls:
Slowest
38.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1)))
37.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1))
10.0ms
(/ 2 (* (/ l t) (/ l t)))
1.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1))))

series346.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
183.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1)))
95.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1))
48.0ms
(/ 2 (* (/ l t) (/ l t)))
20.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1))))

simplify17.0s

Counts
117 → 138
Calls
117 calls:
Slowest
545.0ms
(+ (* (/ 2 (* (/ l t) (/ l t))) (/ 2 (* (/ l t) (/ l t)))) (- (* 1 1) (* (/ 2 (* (/ l t) (/ l t))) 1)))
507.0ms
(/ (+ 1 (/ Om Omc)) (* (cbrt (+ (/ 2 (* (/ l t) (/ l t))) 1)) (cbrt (+ (/ 2 (* (/ l t) (/ l t))) 1))))
435.0ms
(- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3))
353.0ms
(/ (* (* 2 2) 2) (* (/ (* (* l l) l) (* (* t t) t)) (/ (* (* l l) l) (* (* t t) t))))
335.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (cbrt (+ (/ 2 (* (/ l t) (/ l t))) 1)))

prune1.9s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 10.5b

localize62.0ms

Local error

Found 4 expressions with local error:

9.5b
(sqrt (- (/ 1 (+ (/ 2 (* (/ l t) (/ l t))) 1)) (/ (* (/ Om Omc) (/ Om Omc)) (+ (/ 2 (* (/ l t) (/ l t))) 1))))
0.8b
(asin (sqrt (- (/ 1 (+ (/ 2 (* (/ l t) (/ l t))) 1)) (/ (* (/ Om Omc) (/ Om Omc)) (+ (/ 2 (* (/ l t) (/ l t))) 1)))))
0.4b
(/ 2 (* (/ l t) (/ l t)))
0.4b
(/ 2 (* (/ l t) (/ l t)))

rewrite287.0ms

Algorithm
rewrite-expression-head
Rules
40×add-cbrt-cube add-exp-log
24×add-sqr-sqrt
20×*-un-lft-identity
18×cbrt-undiv div-exp
17×sqrt-prod
15×times-frac
10×associate-/r/
9×add-cube-cbrt
8×prod-exp cbrt-unprod div-inv
6×distribute-rgt-out-- associate-/l* difference-of-squares
5×pow1
4×sqrt-div insert-posit16 add-log-exp
2×frac-times clear-num associate-/r* frac-2neg flip3-+ associate-*l/ associate-*r/ flip-+ distribute-lft-out--
1×rem-sqrt-square asin-acos sqrt-pow1 flip3-- pow1/2 frac-sub flip-- distribute-lft-out sub-div
Counts
4 → 103
Calls
4 calls:
Slowest
257.0ms
(sqrt (- (/ 1 (+ (/ 2 (* (/ l t) (/ l t))) 1)) (/ (* (/ Om Omc) (/ Om Omc)) (+ (/ 2 (* (/ l t) (/ l t))) 1))))
16.0ms
(/ 2 (* (/ l t) (/ l t)))
9.0ms
(/ 2 (* (/ l t) (/ l t)))
1.0ms
(asin (sqrt (- (/ 1 (+ (/ 2 (* (/ l t) (/ l t))) 1)) (/ (* (/ Om Omc) (/ Om Omc)) (+ (/ 2 (* (/ l t) (/ l t))) 1)))))

series522.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
406.0ms
(sqrt (- (/ 1 (+ (/ 2 (* (/ l t) (/ l t))) 1)) (/ (* (/ Om Omc) (/ Om Omc)) (+ (/ 2 (* (/ l t) (/ l t))) 1))))
54.0ms
(/ 2 (* (/ l t) (/ l t)))
44.0ms
(/ 2 (* (/ l t) (/ l t)))
18.0ms
(asin (sqrt (- (/ 1 (+ (/ 2 (* (/ l t) (/ l t))) 1)) (/ (* (/ Om Omc) (/ Om Omc)) (+ (/ 2 (* (/ l t) (/ l t))) 1)))))

simplify11.9s

Counts
75 → 115
Calls
75 calls:
Slowest
641.0ms
(sqrt (- (* (/ 1 (+ (/ 2 (* (/ l t) (/ l t))) 1)) (/ 1 (+ (/ 2 (* (/ l t) (/ l t))) 1))) (* (/ (* (/ Om Omc) (/ Om Omc)) (+ (/ 2 (* (/ l t) (/ l t))) 1)) (/ (* (/ Om Omc) (/ Om Omc)) (+ (/ 2 (* (/ l t) (/ l t))) 1)))))
591.0ms
(sqrt (+ (* (/ 2 (* (/ l t) (/ l t))) (/ 2 (* (/ l t) (/ l t)))) (- (* 1 1) (* (/ 2 (* (/ l t) (/ l t))) 1))))
353.0ms
(- (log 2) (+ (- (log l) (log t)) (- (log l) (log t))))
353.0ms
(sqrt (+ (/ 1 (sqrt (+ (/ 2 (* (/ l t) (/ l t))) 1))) (sqrt (/ (* (/ Om Omc) (/ Om Omc)) (+ (/ 2 (* (/ l t) (/ l t))) 1)))))
350.0ms
(sqrt (+ (/ (sqrt 1) (sqrt (+ (/ 2 (* (/ l t) (/ l t))) 1))) (sqrt (/ (* (/ Om Omc) (/ Om Omc)) (+ (/ 2 (* (/ l t) (/ l t))) 1)))))

prune1.7s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 10.5b

localize31.0ms

Local error

Found 4 expressions with local error:

9.5b
(sqrt (* (+ (/ Om Omc) 1) (/ (- 1 (/ Om Omc)) (+ (/ 2 (* (/ l t) (/ l t))) 1))))
0.8b
(asin (sqrt (* (+ (/ Om Omc) 1) (/ (- 1 (/ Om Omc)) (+ (/ 2 (* (/ l t) (/ l t))) 1)))))
0.4b
(/ 2 (* (/ l t) (/ l t)))
0.3b
(/ (- 1 (/ Om Omc)) (+ (/ 2 (* (/ l t) (/ l t))) 1))

rewrite113.0ms

Algorithm
rewrite-expression-head
Rules
60×add-sqr-sqrt
58×*-un-lft-identity
45×times-frac
24×add-cbrt-cube add-exp-log
20×add-cube-cbrt difference-of-squares
11×associate-/l*
10×cbrt-undiv div-exp
9×distribute-lft-out
7×pow1
5×associate-/r* sqrt-div associate-/r/ distribute-lft-out--
4×prod-exp cbrt-unprod insert-posit16 add-log-exp
3×frac-times flip3-+ associate-*l/ flip-+
2×clear-num frac-2neg sqrt-pow1 associate-*r/ div-inv associate-/l/
1×asin-acos flip3-- pow1/2 div-sub pow-prod-down sqrt-prod flip--
Counts
4 → 119
Calls
4 calls:
Slowest
53.0ms
(sqrt (* (+ (/ Om Omc) 1) (/ (- 1 (/ Om Omc)) (+ (/ 2 (* (/ l t) (/ l t))) 1))))
47.0ms
(/ (- 1 (/ Om Omc)) (+ (/ 2 (* (/ l t) (/ l t))) 1))
9.0ms
(/ 2 (* (/ l t) (/ l t)))
2.0ms
(asin (sqrt (* (+ (/ Om Omc) 1) (/ (- 1 (/ Om Omc)) (+ (/ 2 (* (/ l t) (/ l t))) 1)))))

series345.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
174.0ms
(sqrt (* (+ (/ Om Omc) 1) (/ (- 1 (/ Om Omc)) (+ (/ 2 (* (/ l t) (/ l t))) 1))))
88.0ms
(/ (- 1 (/ Om Omc)) (+ (/ 2 (* (/ l t) (/ l t))) 1))
62.0ms
(/ 2 (* (/ l t) (/ l t)))
20.0ms
(asin (sqrt (* (+ (/ Om Omc) 1) (/ (- 1 (/ Om Omc)) (+ (/ 2 (* (/ l t) (/ l t))) 1)))))

simplify16.4s

Counts
121 → 131
Calls
121 calls:
Slowest
521.0ms
(/ (- 1 (/ Om Omc)) (sqrt (+ (/ 2 (* (/ l t) (/ l t))) 1)))
517.0ms
(+ (* (/ 2 (* (/ l t) (/ l t))) (/ 2 (* (/ l t) (/ l t)))) (- (* 1 1) (* (/ 2 (* (/ l t) (/ l t))) 1)))
437.0ms
(sqrt (* (+ (/ Om Omc) 1) (- 1 (/ Om Omc))))
397.0ms
(sqrt (* (- (* (/ Om Omc) (/ Om Omc)) (* 1 1)) (- 1 (/ Om Omc))))
391.0ms
(* (+ (/ Om Omc) 1) (/ (- 1 (/ Om Omc)) (+ (/ 2 (* (/ l t) (/ l t))) 1)))

prune1.7s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 10.5b

regimes388.0ms

Accuracy

0% (0.1b remaining)

Error of 9.8b against oracle of 9.7b and baseline of 9.8b

bsearch5.0ms

end0.0ms

sample5.2s

Algorithm
intervals
Results
1.8s8129×body80nan
1.7s3836×body160valid
1.3s4164×body80valid