Details

Time bar (total: 1.7m)

sample162.0ms

Algorithm
intervals
Results
64.0ms257×body80nan
48.0ms126×body160valid
25.0ms130×body80valid

simplify408.0ms

Calls
1 calls:
Slowest
408.0ms
(asin (sqrt (/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (pow (/ t l) 2))))))

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.5b

localize50.0ms

Local error

Found 4 expressions with local error:

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

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
73×add-sqr-sqrt
71×times-frac
58×*-un-lft-identity
51×add-cube-cbrt
19×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×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×associate-/r*
2×rem-sqrt-square 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
31.0ms
(* (/ t l) (/ t l))
26.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
11.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
1.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))

series308.0ms

Calls
4 calls:
Slowest
151.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
117.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
30.0ms
(* (/ t l) (/ t l))
10.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))

simplify14.6s

Calls
152 calls:
Slowest
698.0ms
(/ (* (* (- 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)))
543.0ms
(- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3))
404.0ms
(* (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))))
274.0ms
(/ (- 1 (/ Om Omc)) (fma (* (/ t l) (/ t l)) 2 1))
269.0ms
(/ (- (sqrt 1) (/ Om Omc)) (fma (* (/ t l) (/ t l)) 2 1))

prune2.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 8.4b

localize50.0ms

Local error

Found 4 expressions with local error:

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

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
434×times-frac
411×sqrt-prod
272×add-sqr-sqrt
241×*-un-lft-identity
205×add-cube-cbrt
72×difference-of-squares
16×add-cbrt-cube add-exp-log
14×pow1
13×swap-sqr associate-*r* associate-*l*
11×div-inv
9×rem-sqrt-square
4×expm1-log1p-u cbrt-undiv div-exp prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×sqrt-pow1 pow1/2
1×pow2 frac-times pow-plus sqrt-div pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up
Calls
4 calls:
Slowest
13.0ms
(* (/ t l) (/ t l))
10.0ms
(sqrt (/ (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))) (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))

series347.0ms

Calls
4 calls:
Slowest
146.0ms
(sqrt (/ (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
90.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
79.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
32.0ms
(* (/ t l) (/ t l))

simplify46.5s

Calls
314 calls:
Slowest
668.0ms
(sqrt (/ (* (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))) (sqrt 1)))
589.0ms
(sqrt (/ (/ (+ 1 (/ Om Omc)) (* (cbrt (sqrt (fma (* (/ t l) (/ t l)) 2 1))) (cbrt (sqrt (fma (* (/ t l) (/ t l)) 2 1))))) (sqrt (* (cbrt (fma (* (/ t l) (/ t l)) 2 1)) (cbrt (fma (* (/ t l) (/ t l)) 2 1))))))
428.0ms
(sqrt (/ (/ (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (* (cbrt (sqrt (fma (* (/ t l) (/ t l)) 2 1))) (cbrt (sqrt (fma (* (/ t l) (/ t l)) 2 1))))) (sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))))
407.0ms
(sqrt (/ (/ (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (* (cbrt (sqrt (fma (* (/ t l) (/ t l)) 2 1))) (cbrt (sqrt (fma (* (/ t l) (/ t l)) 2 1))))) (sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))))
386.0ms
(sqrt (/ (/ (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))) (* (cbrt (sqrt (fma (* (/ t l) (/ t l)) 2 1))) (cbrt (sqrt (fma (* (/ t l) (/ t l)) 2 1))))))

prune6.4s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 8.4b

localize61.0ms

Local error

Found 4 expressions with local error:

13.4b
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
13.4b
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
8.2b
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
7.8b
(sqrt (/ (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (* (fabs (cbrt (fma (* (/ t l) (/ t l)) 2 1))) (sqrt (cbrt (fma (* (/ t l) (/ t l)) 2 1))))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
89×sqrt-prod
86×times-frac
50×add-sqr-sqrt
44×*-un-lft-identity
38×add-cube-cbrt
12×difference-of-squares
7×div-inv
6×cbrt-prod pow1
4×expm1-log1p-u rem-sqrt-square add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
2×sqrt-pow1 pow1/2 pow1/3
1×sqrt-div
Calls
4 calls:
Slowest
13.0ms
(sqrt (/ (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (* (fabs (cbrt (fma (* (/ t l) (/ t l)) 2 1))) (sqrt (cbrt (fma (* (/ t l) (/ t l)) 2 1))))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
1.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
1.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
1.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))

series762.0ms

Calls
4 calls:
Slowest
304.0ms
(sqrt (/ (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (* (fabs (cbrt (fma (* (/ t l) (/ t l)) 2 1))) (sqrt (cbrt (fma (* (/ t l) (/ t l)) 2 1))))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
189.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
169.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
99.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))

simplify16.7s

Calls
86 calls:
Slowest
581.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))))
460.0ms
(/ (* (sqrt (/ -1 (fabs (pow (fma (/ (pow t 2) (pow l 2)) 2 1) 1/3)))) (* (exp (* 1/3 (- (+ (log 1/2) (* 2 (log (/ 1 t)))) (* 2 (log (/ 1 l)))))) Om)) Omc)
445.0ms
(/ (* (sqrt (/ -1 (fabs (pow (fma (/ (pow t 2) (pow l 2)) 2 1) 1/3)))) (* (exp (* 1/3 (- (+ (* 2 (log (/ -1 t))) (log 1/2)) (* 2 (log (/ -1 l)))))) Om)) Omc)
371.0ms
(sqrt (* (cbrt (/ (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (* (fabs (cbrt (fma (* (/ t l) (/ t l)) 2 1))) (sqrt (cbrt (fma (* (/ t l) (/ t l)) 2 1))))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))) (cbrt (/ (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (* (fabs (cbrt (fma (* (/ t l) (/ t l)) 2 1))) (sqrt (cbrt (fma (* (/ t l) (/ t l)) 2 1))))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))))
369.0ms
(sqrt (sqrt (/ (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (* (fabs (cbrt (fma (* (/ t l) (/ t l)) 2 1))) (sqrt (cbrt (fma (* (/ t l) (/ t l)) 2 1))))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))))

prune2.4s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 8.4b

localize92.0ms

Local error

Found 4 expressions with local error:

13.4b
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
13.4b
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
8.2b
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
8.2b
(sqrt (fma (* (/ t l) (/ t l)) 2 1))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×cbrt-prod pow1 sqrt-prod
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 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
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
1.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))

series572.0ms

Calls
4 calls:
Slowest
232.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
188.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
85.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
68.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))

simplify2.6s

Calls
28 calls:
Slowest
273.0ms
(exp (* 1/3 (- (+ (log 2) (* 2 (log (/ -1 l)))) (* 2 (log (/ -1 t))))))
233.0ms
(exp (* 1/3 (- (+ (log 2) (* 2 (log (/ 1 l)))) (* 2 (log (/ 1 t))))))
216.0ms
(exp (* 1/3 (- (+ (log 2) (* 2 (log (/ -1 l)))) (* 2 (log (/ -1 t))))))
186.0ms
(exp (* 1/3 (- (+ (log 2) (* 2 (log (/ 1 l)))) (* 2 (log (/ 1 t))))))
174.0ms
(sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))

prune1.7s

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 8.4b

regimes525.0ms

Accuracy

0% (0.1b remaining)

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

bsearch4.0ms

end0.0ms

sample5.1s

Algorithm
intervals
Results
2.0s3781×body160valid
1.6s8244×body80nan
1.1s4219×body80valid