Details

Time bar (total: 2.4m)

sample151.0ms

Algorithm
intervals
Results
56.0ms122×body160valid
47.0ms268×body80nan
25.0ms134×body80valid

simplify381.0ms

Calls
1 calls:
Slowest
381.0ms
(asin (sqrt (/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (pow (/ t l) 2))))))

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.6b

localize27.0ms

Local error

Found 4 expressions with local error:

10.6b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
0.7b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
0.3b
(* (/ t l) (/ t l))
0.2b
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))

rewrite322.0ms

Algorithm
rewrite-expression-head
Rules
520×add-sqr-sqrt
275×times-frac
234×*-un-lft-identity
144×difference-of-squares
129×add-cube-cbrt
107×associate-/l*
81×frac-times
73×sqrt-prod
68×unswap-sqr
66×associate-/r*
45×swap-sqr
31×sqrt-div
23×clear-num
22×frac-2neg
21×associate-*l*
18×add-cbrt-cube add-exp-log
17×*-commutative
16×distribute-lft-out--
13×associate-*r*
12×pow1
9×associate-*l/ associate-*r/
6×div-inv
5×cbrt-undiv div-exp
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp associate-/l/
2×rem-sqrt-square flip3-- un-div-inv flip--
1×pow2 asin-acos sqrt-pow1 pow-plus pow1/2 div-sub pow-prod-down pow-sqr pow-prod-up
Calls
4 calls:
Slowest
149.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
139.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
22.0ms
(* (/ t l) (/ t l))
1.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))

series357.0ms

Calls
4 calls:
Slowest
172.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
122.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
47.0ms
(* (/ t l) (/ t l))
17.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))

simplify49.2s

Calls
537 calls:
Slowest
671.0ms
(/ (* (* (- 1 (* (/ Om Omc) (/ Om Omc))) (- 1 (* (/ Om Omc) (/ Om Omc)))) (- 1 (* (/ Om Omc) (/ Om Omc)))) (* (* (fma (* (/ t l) (/ t l)) 2 1) (fma (* (/ t l) (/ t l)) 2 1)) (fma (* (/ t l) (/ t l)) 2 1)))
612.0ms
(/ (- (sqrt 1) (/ Om Omc)) (fma (* (/ t l) (/ t l)) 2 1))
471.0ms
(sqrt (- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3)))
462.0ms
(- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3))
411.0ms
(* (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))))

prune6.7s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 11.6b

localize47.0ms

Local error

Found 4 expressions with local error:

10.3b
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
0.7b
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
0.7b
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
0.3b
(* (/ t l) (/ t l))

rewrite142.0ms

Algorithm
rewrite-expression-head
Rules
483×add-sqr-sqrt
280×times-frac
245×sqrt-prod
233×*-un-lft-identity
141×add-cube-cbrt
126×difference-of-squares
87×associate-/l*
81×frac-times
66×associate-/r*
60×unswap-sqr
41×swap-sqr
22×clear-num
21×frac-2neg
20×associate-*l*
18×add-cbrt-cube add-exp-log
15×*-commutative
14×distribute-lft-out--
13×associate-*r*
12×pow1
9×associate-*l/ associate-*r/
5×cbrt-undiv div-exp div-inv
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
2×sqrt-div un-div-inv associate-/l/
1×pow2 rem-sqrt-square asin-acos sqrt-undiv sqrt-pow1 pow-plus flip3-- pow1/2 pow-prod-down pow-sqr pow-prod-up flip--
Calls
4 calls:
Slowest
97.0ms
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
19.0ms
(* (/ t l) (/ t l))
1.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
1.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))

series341.0ms

Calls
4 calls:
Slowest
199.0ms
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
84.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
48.0ms
(* (/ t l) (/ t l))
10.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))

simplify1.1m

Calls
617 calls:
Slowest
578.0ms
(/ (sqrt (- 1 (sqrt (* (/ Om Omc) (/ Om Omc))))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
516.0ms
(sqrt (- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3)))
449.0ms
(/ (* (* (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (sqrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (* (* (sqrt (fma (* (/ t l) (/ t l)) 2 1)) (sqrt (fma (* (/ t l) (/ t l)) 2 1))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
411.0ms
(* (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))))
290.0ms
(/ (sqrt (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1))))

prune7.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 6.5b

localize69.0ms

Local error

Found 4 expressions with local error:

10.3b
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
10.3b
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
10.3b
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
8.8b
(cbrt (asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×sqrt-prod
8×*-un-lft-identity add-cube-cbrt
7×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-prod rem-sqrt-square sqrt-pow1 pow1/2
1×pow1/3
Calls
4 calls:
Slowest
1.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
1.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
1.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
1.0ms
(cbrt (asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))))

series360.0ms

Calls
4 calls:
Slowest
100.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
89.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
87.0ms
(cbrt (asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))))
84.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))

simplify3.3s

Calls
30 calls:
Slowest
400.0ms
(pow (asin (sqrt (/ (- 1 (/ (pow Om 2) (pow Omc 2))) (fma (/ (pow t 2) (pow l 2)) 2 1)))) 1/3)
363.0ms
(pow (asin (sqrt (/ (- 1 (/ (pow Om 2) (pow Omc 2))) (fma (/ (pow t 2) (pow l 2)) 2 1)))) 1/3)
362.0ms
(pow (asin (sqrt (/ (- 1 (/ (pow Om 2) (pow Omc 2))) (fma (/ (pow t 2) (pow l 2)) 2 1)))) 1/3)
287.0ms
(cbrt (* (cbrt (asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))) (cbrt (asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))))))
224.0ms
(cbrt (sqrt (asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))))

prune1.4s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.5b

localize81.0ms

Local error

Found 4 expressions with local error:

10.3b
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
10.3b
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
10.3b
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
10.0b
(pow (asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))) 1/3)

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
9×*-un-lft-identity add-cube-cbrt sqrt-prod
8×pow1
5×add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp
3×rem-sqrt-square pow-unpow unpow-prod-down sqrt-pow1 pow1/2
1×pow-to-exp pow-pow unpow1/3 pow-exp sqr-pow
Calls
4 calls:
Slowest
4.0ms
(pow (asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))) 1/3)
3.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
2.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
2.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))

series355.0ms

Calls
4 calls:
Slowest
111.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
95.0ms
(pow (asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))) 1/3)
80.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
70.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))

simplify3.7s

Calls
34 calls:
Slowest
363.0ms
(pow (asin (sqrt (/ (- 1 (/ (pow Om 2) (pow Omc 2))) (fma (/ (pow t 2) (pow l 2)) 2 1)))) 1/3)
346.0ms
(pow (asin (sqrt (/ (- 1 (/ (pow Om 2) (pow Omc 2))) (fma (/ (pow t 2) (pow l 2)) 2 1)))) 1/3)
310.0ms
(pow (asin (sqrt (/ (- 1 (/ (pow Om 2) (pow Omc 2))) (fma (/ (pow t 2) (pow l 2)) 2 1)))) 1/3)
270.0ms
(* (log (asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))) 1/3)
269.0ms
(pow (sqrt (asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))) 1/3)

prune1.7s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 6.5b

regimes557.0ms

Accuracy

98.1% (0.1b remaining)

Error of 5.4b against oracle of 5.3b and baseline of 10.2b

bsearch12.0ms

end0.0ms

sample5.4s

Algorithm
intervals
Results
2.3s3806×body160valid
1.7s7901×body80nan
1.0s4194×body80valid