Details

Time bar (total: 59.3s)

sample158.0ms

Algorithm
intervals
Results
59.0ms270×body80nan
44.0ms117×body160valid
28.0ms139×body80valid

simplify334.0ms

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.2b

localize36.0ms

Local error

Found 4 expressions with local error:

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

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))
3.0ms
(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)))))))

series291.0ms

Calls
4 calls:
Slowest
153.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
87.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
29.0ms
(* (/ Om Omc) (/ Om Omc))
21.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))

simplify9.7s

Calls
75 calls:
Slowest
507.0ms
(- (* 1 1) (* (* (/ Om Omc) (/ Om Omc)) (* (/ Om Omc) (/ Om Omc))))
315.0ms
(- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3))
309.0ms
(sqrt (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
272.0ms
(/ (* (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)))))))
271.0ms
(asin (sqrt (/ (- 1 (/ (pow Om 2) (pow Omc 2))) (+ (* 2 (/ (pow t 2) (pow l 2))) 1))))

prune1.5s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 10.1b

localize10.0ms

Local error

Found 4 expressions with local error:

8.9b
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
0.7b
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
0.5b
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
0.2b
(* (/ Om Omc) (/ Om Omc))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
45×sqrt-prod
36×add-sqr-sqrt times-frac
35×*-un-lft-identity add-cube-cbrt
9×pow1
8×add-cbrt-cube add-exp-log
6×associate-/r* sqrt-div associate-/l*
4×associate-*r* associate-*l* insert-posit16 add-log-exp
3×div-inv
2×flip3-+ associate-/r/ flip-+ associate-/l/
1×pow2 frac-times cbrt-undiv rem-sqrt-square asin-acos sqrt-undiv clear-num frac-2neg pow-plus flip3-- pow1/2 div-exp pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative pow-prod-up cbrt-unprod flip--
Calls
4 calls:
Slowest
6.0ms
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
4.0ms
(* (/ Om Omc) (/ Om Omc))
1.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
1.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

series312.0ms

Calls
4 calls:
Slowest
180.0ms
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
85.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
27.0ms
(* (/ Om Omc) (/ Om Omc))
21.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))

simplify20.0s

Calls
123 calls:
Slowest
761.0ms
(sqrt (- (* 1 1) (* (* 2 (* (/ t l) (/ t l))) (* 2 (* (/ t l) (/ t l))))))
486.0ms
(sqrt (+ (pow 1 3) (pow (* 2 (* (/ t l) (/ t l))) 3)))
483.0ms
(sqrt (- (* 1 1) (* (* (/ Om Omc) (/ Om Omc)) (* (/ Om Omc) (/ Om Omc)))))
369.0ms
(/ (* (* (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (sqrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (* (* (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
325.0ms
(/ (* (cbrt (sqrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (cbrt (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))))) (sqrt (* (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))) (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))

prune2.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.1b

localize24.0ms

Local error

Found 4 expressions with local error:

8.9b
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
8.9b
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
7.4b
(sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
7.4b
(sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
26×sqrt-prod
16×add-sqr-sqrt
12×sqrt-div
10×*-un-lft-identity add-cube-cbrt
6×rem-sqrt-square
4×pow1 flip3-+ add-cbrt-cube pow1/2 add-exp-log flip-+ insert-posit16 add-log-exp
Calls
4 calls:
Slowest
2.0ms
(sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
2.0ms
(sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
2.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
2.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

series575.0ms

Calls
4 calls:
Slowest
202.0ms
(sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
194.0ms
(sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
92.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
87.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

simplify7.2s

Calls
44 calls:
Slowest
537.0ms
(sqrt (+ (pow 1 3) (pow (* 2 (* (/ t l) (/ t l))) 3)))
516.0ms
(sqrt (sqrt (+ (pow 1 3) (pow (* 2 (* (/ t l) (/ t l))) 3))))
505.0ms
(sqrt (+ (pow 1 3) (pow (* 2 (* (/ t l) (/ t l))) 3)))
490.0ms
(sqrt (sqrt (+ (pow 1 3) (pow (* 2 (* (/ t l) (/ t l))) 3))))
407.0ms
(sqrt (- (* 1 1) (* (* 2 (* (/ t l) (/ t l))) (* 2 (* (/ t l) (/ t l))))))

prune1.5s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.1b

localize10.0ms

Local error

Found 4 expressions with local error:

8.9b
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
8.9b
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
7.4b
(sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
7.4b
(sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))

rewrite4.0ms

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

series624.0ms

Calls
4 calls:
Slowest
233.0ms
(sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
192.0ms
(sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
108.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
92.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

simplify7.6s

Calls
44 calls:
Slowest
565.0ms
(sqrt (+ (pow 1 3) (pow (* 2 (* (/ t l) (/ t l))) 3)))
556.0ms
(sqrt (sqrt (+ (pow 1 3) (pow (* 2 (* (/ t l) (/ t l))) 3))))
534.0ms
(sqrt (sqrt (+ (pow 1 3) (pow (* 2 (* (/ t l) (/ t l))) 3))))
528.0ms
(sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
462.0ms
(sqrt (+ (pow 1 3) (pow (* 2 (* (/ t l) (/ t l))) 3)))

prune1.5s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 6.1b

regimes587.0ms

Accuracy

98.6% (0.1b remaining)

Error of 6.0b against oracle of 6.0b and baseline of 10.6b

bsearch14.0ms

end0.0ms

sample5.3s

Algorithm
intervals
Results
1.9s3746×body160valid
1.7s7815×body80nan
878.0ms4254×body80valid