Details

Time bar (total: 3.3m)

sample182.0ms

Algorithm
intervals
Results
72.0ms122×body160valid
56.0ms268×body80nan
31.0ms134×body80valid

simplify474.0ms

Calls
1 calls:
Slowest
473.0ms
(asin (sqrt (/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (pow (/ t l) 2))))))

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.6b

localize51.0ms

Local error

Found 4 expressions with local error:

10.6b
(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
(* (/ t l) (/ t l))
0.2b
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))

rewrite632.0ms

Algorithm
rewrite-expression-head
Rules
712×add-sqr-sqrt
482×*-un-lft-identity
415×times-frac
216×difference-of-squares
133×add-cube-cbrt
121×sqrt-prod
107×associate-/l*
100×unswap-sqr
96×distribute-lft-out
81×frac-times
73×associate-*l*
70×associate-/r*
61×swap-sqr
33×sqrt-div
25×*-commutative
24×distribute-lft-out--
23×clear-num
22×frac-2neg
18×add-cbrt-cube add-exp-log
13×associate-*r*
12×pow1
9×associate-*l/ associate-*r/
6×div-inv
5×cbrt-undiv div-exp
4×prod-exp associate-/r/ cbrt-unprod insert-posit16 add-log-exp associate-/l/
2×rem-sqrt-square flip3-+ flip3-- un-div-inv flip-+ flip--
1×pow2 asin-acos sqrt-pow1 pow-plus pow1/2 div-sub pow-prod-down pow-sqr pow-prod-up
Calls
4 calls:
Slowest
301.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
270.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
29.0ms
(* (/ t l) (/ t l))
1.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))

series334.0ms

Calls
4 calls:
Slowest
166.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
121.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
36.0ms
(* (/ t l) (/ t l))
11.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))

simplify1.2m

Calls
683 calls:
Slowest
636.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
506.0ms
(/ 1 (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
436.0ms
(/ (- 1 (* (sqrt (/ Om Omc)) (/ (sqrt Om) (sqrt Omc)))) (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
432.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (* (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))) (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))
425.0ms
(sqrt (- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3)))

prune7.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 11.6b

localize60.0ms

Local error

Found 4 expressions with local error:

10.3b
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
0.7b
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
0.7b
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
0.3b
(* (/ t l) (/ t l))

rewrite450.0ms

Algorithm
rewrite-expression-head
Rules
581×add-sqr-sqrt
375×*-un-lft-identity
356×times-frac
347×sqrt-prod
162×difference-of-squares
145×add-cube-cbrt
87×associate-/l*
81×frac-times
76×unswap-sqr
68×associate-/r*
56×distribute-lft-out
50×associate-*l*
49×swap-sqr
22×clear-num
21×frac-2neg
19×*-commutative
18×add-cbrt-cube add-exp-log distribute-lft-out--
13×associate-*r*
12×pow1
9×associate-*l/ associate-*r/
6×sqrt-div
5×cbrt-undiv div-exp div-inv
4×prod-exp cbrt-unprod insert-posit16 add-log-exp
2×flip3-+ associate-/r/ un-div-inv flip-+ associate-/l/
1×pow2 rem-sqrt-square asin-acos sqrt-undiv sqrt-pow1 pow-plus flip3-- pow1/2 pow-prod-down pow-sqr pow-prod-up flip--
Calls
4 calls:
Slowest
250.0ms
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
168.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
18.0ms
(* (/ t l) (/ t l))
2.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))

series362.0ms

Calls
4 calls:
Slowest
209.0ms
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
93.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
40.0ms
(* (/ t l) (/ t l))
20.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))

simplify1.4m

Calls
729 calls:
Slowest
565.0ms
(/ (sqrt (- (sqrt 1) (* (/ (sqrt Om) (sqrt Omc)) (/ (sqrt Om) (sqrt Omc))))) (cbrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
540.0ms
(/ (sqrt 1) (sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
468.0ms
(* (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))))
466.0ms
(/ (* (* (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)))))))
451.0ms
(sqrt (- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3)))

prune7.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 6.5b

localize51.0ms

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)))))
10.3b
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
8.8b
(cbrt (asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))

rewrite481.0ms

Algorithm
rewrite-expression-head
Rules
20×*-un-lft-identity
15×sqrt-prod
11×add-sqr-sqrt
8×add-cube-cbrt
7×pow1
6×sqrt-div distribute-lft-out
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×cbrt-prod rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 associate-*l* flip-+
1×pow1/3
Calls
4 calls:
Slowest
163.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
159.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
156.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
1.0ms
(cbrt (asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))

series386.0ms

Calls
4 calls:
Slowest
111.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
104.0ms
(cbrt (asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))
91.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
80.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

simplify5.3s

Calls
42 calls:
Slowest
465.0ms
(sqrt (- (* 1 1) (* (* 2 (* (/ t l) (/ t l))) (* 2 (* (/ t l) (/ t l))))))
453.0ms
(sqrt (- (* 1 1) (* (* 2 (* (/ t l) (/ t l))) (* 2 (* (/ t l) (/ t l))))))
426.0ms
(pow (asin (sqrt (/ (- 1 (/ (pow Om 2) (pow Omc 2))) (+ (* 2 (/ (pow t 2) (pow l 2))) 1)))) 1/3)
414.0ms
(sqrt (- (* 1 1) (* (* 2 (* (/ t l) (/ t l))) (* 2 (* (/ t l) (/ t l))))))
397.0ms
(pow (asin (sqrt (/ (- 1 (/ (pow Om 2) (pow Omc 2))) (+ (* 2 (/ (pow t 2) (pow l 2))) 1)))) 1/3)

prune1.5s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.5b

localize74.0ms

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)))))
10.3b
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
10.0b
(pow (asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))) 1/3)

rewrite799.0ms

Algorithm
rewrite-expression-head
Rules
21×*-un-lft-identity
15×sqrt-prod
12×add-sqr-sqrt
9×add-cube-cbrt
8×pow1
6×sqrt-div distribute-lft-out
5×add-exp-log
4×add-cbrt-cube insert-posit16 add-log-exp
3×rem-sqrt-square pow-unpow unpow-prod-down sqrt-pow1 flip3-+ pow1/2 associate-*l* flip-+
1×pow-to-exp pow-pow unpow1/3 pow-exp sqr-pow
Calls
4 calls:
Slowest
515.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
169.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
108.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
5.0ms
(pow (asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))) 1/3)

series368.0ms

Calls
4 calls:
Slowest
107.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
104.0ms
(pow (asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))) 1/3)
82.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
75.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

simplify5.9s

Calls
46 calls:
Slowest
468.0ms
(sqrt (- (* 1 1) (* (* 2 (* (/ t l) (/ t l))) (* 2 (* (/ t l) (/ t l))))))
456.0ms
(sqrt (- (* 1 1) (* (* 2 (* (/ t l) (/ t l))) (* 2 (* (/ t l) (/ t l))))))
427.0ms
(pow (asin (sqrt (/ (- 1 (/ (pow Om 2) (pow Omc 2))) (+ (* 2 (/ (pow t 2) (pow l 2))) 1)))) 1/3)
417.0ms
(sqrt (- (* 1 1) (* (* 2 (* (/ t l) (/ t l))) (* 2 (* (/ t l) (/ t l))))))
379.0ms
(pow (asin (sqrt (/ (- 1 (/ (pow Om 2) (pow Omc 2))) (+ (* 2 (/ (pow t 2) (pow l 2))) 1)))) 1/3)

prune1.6s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 6.5b

regimes549.0ms

Accuracy

98.1% (0.1b remaining)

Error of 5.4b against oracle of 5.3b and baseline of 10.2b

bsearch7.0ms

end0.0ms

sample5.0s

Algorithm
intervals
Results
1.9s3806×body160valid
1.7s7901×body80nan
903.0ms4194×body80valid