Details

Time bar (total: 51.2s)

sample107.0ms

Algorithm
intervals
Results
34.0ms116×body160valid
31.0ms201×body80nan
21.0ms140×body80valid

simplify335.0ms

Calls
1 calls:
Slowest
334.0ms
(asin (sqrt (/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (pow (/ t l) 2))))))

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.3b

localize53.0ms

Local error

Found 4 expressions with local error:

12.2b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
0.7b
(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
(* (/ Om Omc) (/ Om Omc))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
19×times-frac
15×sqrt-prod
9×pow1
8×add-cbrt-cube add-exp-log
4×associate-*r* associate-*l* associate-/r/ insert-posit16 div-inv add-log-exp
3×associate-/r* associate-/l*
2×rem-sqrt-square flip3-+ flip-+ associate-/l/
1×pow2 frac-times cbrt-undiv asin-acos clear-num frac-2neg pow-plus flip3-- pow1/2 sqrt-div div-sub div-exp pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative pow-prod-up cbrt-unprod flip--
Calls
4 calls:
Slowest
5.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
5.0ms
(* (/ Om Omc) (/ Om Omc))
2.0ms
(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)))))))

series242.0ms

Calls
4 calls:
Slowest
139.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
69.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
21.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
13.0ms
(* (/ Om Omc) (/ Om Omc))

simplify9.8s

Calls
75 calls:
Slowest
499.0ms
(- (* 1 1) (* (* (/ Om Omc) (/ Om Omc)) (* (/ Om Omc) (/ Om Omc))))
347.0ms
(- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3))
302.0ms
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (* (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))) (cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
282.0ms
(- 1 (* 2 (* (/ t l) (/ t l))))
275.0ms
(asin (sqrt (/ (- 1 (/ (pow Om 2) (pow Omc 2))) (+ (* 2 (/ (pow t 2) (pow l 2))) 1))))

prune1.7s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 13.3b

localize43.0ms

Local error

Found 4 expressions with local error:

17.9b
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
17.9b
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
17.9b
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
10.6b
(sqrt (/ 1 (* (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))) (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-div
12×sqrt-prod
9×cbrt-prod add-sqr-sqrt flip3-+ flip-+
8×*-un-lft-identity associate-/r/ add-cube-cbrt
4×frac-times pow1 add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×pow1/3
2×associate-*l/ associate-*r/
1×rem-sqrt-square pow1/2 sqrt-div div-inv
Calls
4 calls:
Slowest
10.0ms
(sqrt (/ 1 (* (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))) (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))
2.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
1.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
1.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

series589.0ms

Calls
4 calls:
Slowest
163.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
149.0ms
(sqrt (/ 1 (* (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))) (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))
139.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
138.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

simplify8.9s

Calls
41 calls:
Slowest
593.0ms
(sqrt (/ 1 (* (cbrt (+ (pow 1 3) (pow (* 2 (* (/ t l) (/ t l))) 3))) (cbrt (+ (pow 1 3) (pow (* 2 (* (/ t l) (/ t l))) 3))))))
563.0ms
(cbrt (+ (pow 1 3) (pow (* 2 (* (/ t l) (/ t l))) 3)))
548.0ms
(cbrt (+ (pow 1 3) (pow (* 2 (* (/ t l) (/ t l))) 3)))
526.0ms
(cbrt (+ (pow 1 3) (pow (* 2 (* (/ t l) (/ t l))) 3)))
522.0ms
(sqrt (/ 1 (* (cbrt (+ (pow 1 3) (pow (* 2 (* (/ t l) (/ t l))) 3))) (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))

prune1.4s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 13.3b

localize46.0ms

Local error

Found 4 expressions with local error:

17.9b
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
17.9b
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
17.9b
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
17.9b
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
8×add-sqr-sqrt cbrt-div *-un-lft-identity add-cube-cbrt
4×pow1 flip3-+ add-cbrt-cube pow1/3 add-exp-log flip-+ insert-posit16 add-log-exp
Calls
4 calls:
Slowest
1.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
1.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
1.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
1.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

series606.0ms

Calls
4 calls:
Slowest
170.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
148.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
147.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
141.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

simplify6.7s

Calls
32 calls:
Slowest
539.0ms
(cbrt (+ (pow 1 3) (pow (* 2 (* (/ t l) (/ t l))) 3)))
528.0ms
(cbrt (+ (pow 1 3) (pow (* 2 (* (/ t l) (/ t l))) 3)))
490.0ms
(cbrt (+ (pow 1 3) (pow (* 2 (* (/ t l) (/ t l))) 3)))
482.0ms
(cbrt (+ (pow 1 3) (pow (* 2 (* (/ t l) (/ t l))) 3)))
441.0ms
(cbrt (- (* 1 1) (* (* 2 (* (/ t l) (/ t l))) (* 2 (* (/ t l) (/ t l))))))

prune1.6s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 13.3b

localize14.0ms

Local error

Found 4 expressions with local error:

17.5b
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
17.5b
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
17.5b
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
12.2b
(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))))))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
45×cbrt-prod
27×times-frac
25×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
15×cbrt-div
7×sqrt-div
6×associate-/r/
5×frac-times associate-*l/
4×pow1 add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×flip3-+ pow1/3 associate-*r/ flip-+ div-inv
1×pow1/2 sqrt-prod
Calls
4 calls:
Slowest
4.0ms
(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))))))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))))
2.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
2.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
2.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))

series739.0ms

Calls
4 calls:
Slowest
220.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
203.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
191.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
124.0ms
(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))))))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))))

simplify11.1s

Calls
68 calls:
Slowest
641.0ms
(cbrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
311.0ms
(sqrt (* (* (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))))
299.0ms
(cbrt (/ (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
286.0ms
(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))))))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))))
283.0ms
(sqrt (* (* (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))))

prune1.6s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 13.3b

regimes403.0ms

Accuracy

0% (0.1b remaining)

Error of 10.4b against oracle of 10.3b and baseline of 10.4b

bsearch3.0ms

end0.0ms

sample5.2s

Algorithm
intervals
Results
2.1s7974×body80nan
1.7s3790×body160valid
867.0ms4210×body80valid