Details

Time bar (total: 55.9s)

sample103.0ms

Algorithm
intervals
Results
34.0ms115×body160valid
30.0ms216×body80nan
21.0ms141×body80valid

simplify316.0ms

Calls
1 calls:
Slowest
316.0ms
(asin (sqrt (/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (pow (/ t l) 2))))))

prune27.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.1b

localize31.0ms

Local error

Found 4 expressions with local error:

9.2b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
0.5b
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
0.4b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
0.3b
(* (/ Om Omc) (/ Om Omc))

rewrite13.0ms

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)))))
4.0ms
(* (/ 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)))))))

series256.0ms

Calls
4 calls:
Slowest
122.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
92.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
21.0ms
(* (/ Om Omc) (/ Om Omc))
21.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))

simplify9.4s

Calls
75 calls:
Slowest
372.0ms
(- (* 1 1) (* (* (/ Om Omc) (/ Om Omc)) (* (/ Om Omc) (/ Om Omc))))
308.0ms
(- 1 (* 2 (* (/ t l) (/ t l))))
281.0ms
(- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3))
280.0ms
(/ (* (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)))))))
277.0ms
(sqrt (/ (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))

prune1.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 10.0b

localize27.0ms

Local error

Found 4 expressions with local error:

9.2b
(sqrt (* (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
0.5b
(/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
0.4b
(asin (sqrt (* (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (+ 1 (* 2 (* (/ t l) (/ t l))))))))
0.3b
(* (/ Om Omc) (/ Om Omc))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
26×cbrt-div
21×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
18×times-frac
17×frac-times sqrt-div
13×flip3-- associate-*l/ flip--
12×cbrt-prod
9×pow1
8×add-exp-log
7×add-cbrt-cube
6×associate-*r/ associate-/l*
4×associate-*r* associate-*l* insert-posit16 add-log-exp
3×associate-/r* div-inv
2×associate-/r/ associate-/l/
1×pow2 cbrt-undiv asin-acos clear-num frac-2neg flip3-+ pow-plus pow1/2 div-exp pow-prod-down prod-exp *-commutative pow-prod-up sqrt-prod cbrt-unprod flip-+
Calls
4 calls:
Slowest
10.0ms
(* (/ Om Omc) (/ Om Omc))
9.0ms
(/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
9.0ms
(sqrt (* (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
1.0ms
(asin (sqrt (* (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (+ 1 (* 2 (* (/ t l) (/ t l))))))))

series392.0ms

Calls
4 calls:
Slowest
237.0ms
(/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
113.0ms
(sqrt (* (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
21.0ms
(* (/ Om Omc) (/ Om Omc))
20.0ms
(asin (sqrt (* (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (+ 1 (* 2 (* (/ t l) (/ t l))))))))

simplify16.1s

Calls
95 calls:
Slowest
691.0ms
(asin (sqrt (/ (- 1 (/ (pow Om 2) (pow Omc 2))) (+ (* 2 (/ (pow t 2) (pow l 2))) 1))))
462.0ms
(sqrt (* (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3)))) (/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
428.0ms
(cbrt (- (* 1 1) (* (* (/ Om Omc) (/ Om Omc)) (* (/ Om Omc) (/ Om Omc)))))
422.0ms
(sqrt (* (* (cbrt (- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
401.0ms
(sqrt (* (* (cbrt (- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3))) (cbrt (- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3)))) (/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))

prune2.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 10.0b

localize29.0ms

Local error

Found 4 expressions with local error:

9.6b
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
9.6b
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
9.2b
(sqrt (* (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (/ (/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))
0.4b
(asin (sqrt (* (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (/ (/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
24×cbrt-div
21×sqrt-div
16×frac-times
12×flip3-- associate-*l/ flip--
8×add-sqr-sqrt
7×sqrt-prod
6×*-un-lft-identity add-cube-cbrt
5×associate-*r/
4×pow1 add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×pow1/2
2×rem-sqrt-square flip3-+ flip-+
1×asin-acos
Calls
4 calls:
Slowest
10.0ms
(sqrt (* (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (/ (/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))
2.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
1.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
1.0ms
(asin (sqrt (* (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (/ (/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))))

series218.0ms

Calls
4 calls:
Slowest
112.0ms
(sqrt (* (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (/ (/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))
50.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
43.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
12.0ms
(asin (sqrt (* (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (/ (/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))))

simplify8.3s

Calls
42 calls:
Slowest
583.0ms
(sqrt (+ (pow 1 3) (pow (* 2 (* (/ t l) (/ t l))) 3)))
505.0ms
(sqrt (+ (pow 1 3) (pow (* 2 (* (/ t l) (/ t l))) 3)))
491.0ms
(sqrt (* (* (cbrt (- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3))) (cbrt (- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3)))) (/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))
477.0ms
(sqrt (* (* (cbrt (- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))
408.0ms
(sqrt (* (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3)))) (/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))

prune1.6s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 10.0b

localize6.0ms

Local error

Found 4 expressions with local error:

9.6b
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
9.6b
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
9.2b
(sqrt (* (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (/ (/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))
0.4b
(asin (sqrt (* (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (/ (/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
24×cbrt-div
21×sqrt-div
16×frac-times
12×flip3-- associate-*l/ flip--
8×add-sqr-sqrt
7×sqrt-prod
6×*-un-lft-identity add-cube-cbrt
5×associate-*r/
4×pow1 add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×pow1/2
2×rem-sqrt-square flip3-+ flip-+
1×asin-acos
Calls
4 calls:
Slowest
5.0ms
(sqrt (* (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (/ (/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))
1.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
1.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
1.0ms
(asin (sqrt (* (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (/ (/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))))

series274.0ms

Calls
4 calls:
Slowest
151.0ms
(sqrt (* (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (/ (/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))
54.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
45.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
25.0ms
(asin (sqrt (* (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (/ (/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))))

simplify8.0s

Calls
42 calls:
Slowest
572.0ms
(sqrt (+ (pow 1 3) (pow (* 2 (* (/ t l) (/ t l))) 3)))
482.0ms
(sqrt (+ (pow 1 3) (pow (* 2 (* (/ t l) (/ t l))) 3)))
441.0ms
(sqrt (* (* (cbrt (- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3))) (cbrt (- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3)))) (/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))
432.0ms
(sqrt (* (* (cbrt (- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))
423.0ms
(sqrt (* (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3)))) (/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))

prune1.5s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 10.0b

regimes464.0ms

Accuracy

0% (0.1b remaining)

Error of 10.2b against oracle of 10.1b and baseline of 10.2b

bsearch3.0ms

end0.0ms

sample5.4s

Algorithm
intervals
Results
2.0s3819×body160valid
1.7s8068×body80nan
855.0ms4181×body80valid