Details

Time bar (total: 1.1m)

sample147.0ms

Algorithm
intervals
Results
45.0ms234×body80nan
41.0ms99×body160valid
39.0ms157×body80valid

simplify276.0ms

Calls
1 calls:
Slowest
276.0ms
(asin (sqrt (/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (pow (/ t l) 2))))))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.7b

localize40.0ms

Local error

Found 4 expressions with local error:

10.6b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
0.6b
(asin (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)))))
0.2b
(* (/ Om Omc) (/ Om Omc))

rewrite16.0ms

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
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
4.0ms
(* (/ Om Omc) (/ Om Omc))
1.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))

series356.0ms

Calls
4 calls:
Slowest
156.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
132.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
47.0ms
(* (/ Om Omc) (/ Om Omc))
22.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))

simplify9.5s

Calls
75 calls:
Slowest
362.0ms
(- (* 1 1) (* (* (/ Om Omc) (/ Om Omc)) (* (/ Om Omc) (/ Om Omc))))
302.0ms
(- 1 (* 2 (* (/ t l) (/ t l))))
293.0ms
(sqrt (/ (* (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))))))))
278.0ms
(asin (sqrt (/ (- 1 (/ (pow Om 2) (pow Omc 2))) (+ (* 2 (/ (pow t 2) (pow l 2))) 1))))
273.0ms
(/ (* (* (- 1 (* (/ Om Omc) (/ Om Omc))) (- 1 (* (/ Om Omc) (/ Om Omc)))) (- 1 (* (/ Om Omc) (/ Om Omc)))) (* (* (+ 1 (* 2 (* (/ t l) (/ t l)))) (+ 1 (* 2 (* (/ t l) (/ t l))))) (+ 1 (* 2 (* (/ t l) (/ t l))))))

prune1.4s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 11.7b

localize10.0ms

Local error

Found 4 expressions with local error:

10.8b
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
0.6b
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
0.4b
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
0.2b
(* (/ Om Omc) (/ Om Omc))

rewrite13.0ms

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
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
1.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))

series319.0ms

Calls
4 calls:
Slowest
192.0ms
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
69.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
44.0ms
(* (/ Om Omc) (/ Om Omc))
13.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))

simplify19.5s

Calls
123 calls:
Slowest
822.0ms
(sqrt (- (* 1 1) (* (* (/ Om Omc) (/ Om Omc)) (* (/ Om Omc) (/ Om Omc)))))
534.0ms
(sqrt (+ (pow 1 3) (pow (* 2 (* (/ t l) (/ t l))) 3)))
397.0ms
(/ (* (* (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)))))))
339.0ms
(sqrt (- (* 1 1) (* (* 2 (* (/ t l) (/ t l))) (* 2 (* (/ t l) (/ t l))))))
308.0ms
(asin (sqrt (/ (- 1 (/ (pow Om 2) (pow Omc 2))) (+ (* 2 (/ (pow t 2) (pow l 2))) 1))))

prune1.8s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 6.3b

localize17.0ms

Local error

Found 4 expressions with local error:

11.2b
(sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
11.2b
(sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
10.8b
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
10.8b
(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)))))

series546.0ms

Calls
4 calls:
Slowest
191.0ms
(sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
185.0ms
(sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
85.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
85.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

simplify7.6s

Calls
44 calls:
Slowest
636.0ms
(sqrt (sqrt (+ (pow 1 3) (pow (* 2 (* (/ t l) (/ t l))) 3))))
591.0ms
(sqrt (sqrt (+ (pow 1 3) (pow (* 2 (* (/ t l) (/ t l))) 3))))
542.0ms
(sqrt (+ (pow 1 3) (pow (* 2 (* (/ t l) (/ t l))) 3)))
526.0ms
(sqrt (+ (pow 1 3) (pow (* 2 (* (/ t l) (/ t l))) 3)))
391.0ms
(sqrt (- (* 1 1) (* (* 2 (* (/ t l) (/ t l))) (* 2 (* (/ t l) (/ t l))))))

prune1.5s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 6.3b

localize38.0ms

Local error

Found 4 expressions with local error:

17.3b
(cbrt (* (* (sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))) (sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))) (sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))
11.2b
(sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
11.2b
(sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
11.2b
(sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
120×sqrt-div
30×flip3-+ sqrt-prod flip-+
28×frac-times
26×cbrt-div
16×add-sqr-sqrt
14×associate-*l/
10×*-un-lft-identity add-cube-cbrt
8×associate-*r/
6×rem-sqrt-square
4×pow1 add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×pow1/2
1×cbrt-prod pow1/3 pow3 rem-cbrt-cube
Calls
4 calls:
Slowest
30.0ms
(cbrt (* (* (sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))) (sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))) (sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))
2.0ms
(sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
2.0ms
(sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
2.0ms
(sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))

series737.0ms

Calls
4 calls:
Slowest
208.0ms
(sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
193.0ms
(cbrt (* (* (sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))) (sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))) (sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))
179.0ms
(sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
157.0ms
(sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))

simplify16.1s

Calls
70 calls:
Slowest
642.0ms
(sqrt (sqrt (+ (pow 1 3) (pow (* 2 (* (/ t l) (/ t l))) 3))))
582.0ms
(cbrt (* (* (sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))) (sqrt (sqrt (+ (pow 1 3) (pow (* 2 (* (/ t l) (/ t l))) 3))))) (sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))
541.0ms
(cbrt (* (* (sqrt (sqrt (+ (pow 1 3) (pow (* 2 (* (/ t l) (/ t l))) 3)))) (sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))) (sqrt (sqrt (+ (pow 1 3) (pow (* 2 (* (/ t l) (/ t l))) 3))))))
540.0ms
(sqrt (sqrt (+ (pow 1 3) (pow (* 2 (* (/ t l) (/ t l))) 3))))
517.0ms
(sqrt (sqrt (* (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))) (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))

prune2.3s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 6.3b

regimes452.0ms

Accuracy

98.9% (0.1b remaining)

Error of 5.5b against oracle of 5.5b and baseline of 10.3b

bsearch12.0ms

end0.0ms

sample4.9s

Algorithm
intervals
Results
2.1s3717×body160valid
1.5s7695×body80nan
906.0ms4283×body80valid