Details

Time bar (total: 3.0m)

sample167.0ms

Algorithm
intervals
Results
62.0ms195×body80nan
51.0ms115×body160valid
30.0ms141×body80valid

simplify331.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
331.0ms
(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: 10.6b

localize33.0ms

Local error

Found 4 expressions with local error:

10.0b
(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)))))
0.3b
(* (/ t l) (/ t l))
0.2b
(* (/ Om Omc) (/ Om Omc))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
113×add-sqr-sqrt
111×times-frac
86×*-un-lft-identity
79×add-cube-cbrt
30×add-cbrt-cube add-exp-log
26×swap-sqr associate-*r* associate-*l*
21×sqrt-prod
19×pow1
14×difference-of-squares
10×div-inv
9×cbrt-undiv div-exp
8×prod-exp cbrt-unprod unswap-sqr
5×associate-/l*
4×associate-/r/ insert-posit16 add-log-exp
3×associate-/r*
2×pow2 frac-times rem-sqrt-square flip3-+ pow-plus pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up flip-+ associate-/l/
1×clear-num frac-2neg sqrt-pow1 flip3-- pow1/2 sqrt-div div-sub flip--
Counts
4 → 211
Calls
4 calls:
Slowest
19.0ms
(* (/ t l) (/ t l))
15.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
13.0ms
(* (/ Om Omc) (/ Om Omc))
8.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))

series357.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
151.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
112.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
48.0ms
(* (/ Om Omc) (/ Om Omc))
46.0ms
(* (/ t l) (/ t l))

simplify17.1s

Counts
231 → 223
Calls
231 calls:
Slowest
444.0ms
(* (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))) (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))))
424.0ms
(- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3))
399.0ms
(* (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))))
327.0ms
(- 1 (* 2 (* (/ t l) (/ t l))))
326.0ms
(sqrt (* (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))))

prune3.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 10.5b

localize33.0ms

Local error

Found 4 expressions with local error:

10.3b
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
10.3b
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
10.0b
(sqrt (/ (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
0.3b
(* (/ t l) (/ t l))

rewrite78.0ms

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
Counts
4 → 340
Calls
4 calls:
Slowest
28.0ms
(sqrt (/ (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
23.0ms
(* (/ t l) (/ t l))
8.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
3.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

series419.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
167.0ms
(sqrt (/ (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
112.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
110.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
30.0ms
(* (/ t l) (/ t l))

simplify53.5s

Counts
332 → 352
Calls
332 calls:
Slowest
745.0ms
(sqrt (* (cbrt (/ (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))) (cbrt (/ (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))))
521.0ms
(sqrt (/ (/ (+ 1 (/ Om Omc)) (* (cbrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))) (cbrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))) (sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))
446.0ms
(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)))))))))
427.0ms
(sqrt (- (* 1 1) (* (* 2 (* (/ t l) (/ t l))) (* 2 (* (/ t l) (/ t l))))))
424.0ms
(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)))))))) (sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))

prune6.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 10.5b

localize71.0ms

Local error

Found 4 expressions with local error:

10.3b
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
10.3b
(sqrt (+ 1 (* 2 (* (/ (/ t l) (cbrt l)) (/ (/ t (cbrt l)) (cbrt l))))))
10.0b
(sqrt (/ (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))) (sqrt (+ 1 (* 2 (* (/ (/ t l) (cbrt l)) (/ (/ t (cbrt l)) (cbrt l))))))))
0.5b
(cbrt l)

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
431×sqrt-prod
406×times-frac
237×add-sqr-sqrt
218×*-un-lft-identity
182×add-cube-cbrt
72×difference-of-squares
19×sqrt-div
14×associate-/r/
9×rem-sqrt-square flip3-+ flip-+
7×pow1 div-inv
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×cbrt-prod sqrt-pow1 pow1/2
1×pow1/3
Counts
4 → 284
Calls
4 calls:
Slowest
35.0ms
(sqrt (/ (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))) (sqrt (+ 1 (* 2 (* (/ (/ t l) (cbrt l)) (/ (/ t (cbrt l)) (cbrt l))))))))
7.0ms
(sqrt (+ 1 (* 2 (* (/ (/ t l) (cbrt l)) (/ (/ t (cbrt l)) (cbrt l))))))
6.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
1.0ms
(cbrt l)

series708.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
270.0ms
(cbrt l)
228.0ms
(sqrt (/ (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))) (sqrt (+ 1 (* 2 (* (/ (/ t l) (cbrt l)) (/ (/ t (cbrt l)) (cbrt l))))))))
112.0ms
(sqrt (+ 1 (* 2 (* (/ (/ t l) (cbrt l)) (/ (/ t (cbrt l)) (cbrt l))))))
97.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

simplify1.0m

Counts
260 → 296
Calls
260 calls:
Slowest
696.0ms
(sqrt (/ (/ (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (sqrt 1)) (* (cbrt (sqrt (+ 1 (* 2 (* (/ (/ t l) (cbrt l)) (/ (/ t (cbrt l)) (cbrt l))))))) (cbrt (sqrt (+ 1 (* 2 (* (/ (/ t l) (cbrt l)) (/ (/ t (cbrt l)) (cbrt l))))))))))
589.0ms
(sqrt (/ (/ (+ (sqrt 1) (/ Om Omc)) (sqrt 1)) (sqrt (* (cbrt (+ 1 (* 2 (* (/ (/ t l) (cbrt l)) (/ (/ t (cbrt l)) (cbrt l)))))) (cbrt (+ 1 (* 2 (* (/ (/ t l) (cbrt l)) (/ (/ t (cbrt l)) (cbrt l))))))))))
434.0ms
(sqrt (/ (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))) (sqrt (* (cbrt (+ 1 (* 2 (* (/ (/ t l) (cbrt l)) (/ (/ t (cbrt l)) (cbrt l)))))) (cbrt (+ 1 (* 2 (* (/ (/ t l) (cbrt l)) (/ (/ t (cbrt l)) (cbrt l))))))))))
429.0ms
(sqrt (/ (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))) (sqrt (- (* 1 1) (* (* 2 (* (/ (/ t l) (cbrt l)) (/ (/ t (cbrt l)) (cbrt l)))) (* 2 (* (/ (/ t l) (cbrt l)) (/ (/ t (cbrt l)) (cbrt l)))))))))
426.0ms
(sqrt (sqrt (/ (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))) (sqrt (+ 1 (* 2 (* (/ (/ t l) (cbrt l)) (/ (/ t (cbrt l)) (cbrt l)))))))))

prune7.0s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 10.5b

localize64.0ms

Local error

Found 4 expressions with local error:

10.0b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
10.0b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
4.8b
(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
4.8b
(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
136×sqrt-prod
68×add-sqr-sqrt
64×times-frac
54×*-un-lft-identity
42×add-cube-cbrt
24×difference-of-squares
10×pow1 rem-sqrt-square sqrt-pow1
8×associate-/r/
6×pow1/2 sqrt-div
4×flip3-+ add-cbrt-cube add-exp-log flip-+ insert-posit16 div-inv add-log-exp
Counts
4 → 148
Calls
4 calls:
Slowest
17.0ms
(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
16.0ms
(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
16.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
15.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))

series871.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
274.0ms
(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
272.0ms
(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
172.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
153.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))

simplify19.4s

Counts
124 → 160
Calls
124 calls:
Slowest
319.0ms
(sqrt (sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))))
303.0ms
(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
298.0ms
(sqrt (* (cbrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))) (cbrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))))
296.0ms
(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
293.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))

prune2.9s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 10.5b

regimes352.0ms

Accuracy

0% (0.1b remaining)

Error of 10.5b against oracle of 10.4b and baseline of 10.5b

bsearch7.0ms

end0.0ms

sample5.6s

Algorithm
intervals
Results
2.2s3853×body160valid
1.8s7980×body80nan
982.0ms4147×body80valid