Details

Time bar (total: 1.6m)

sample166.0ms

Algorithm
intervals
Results
79.0ms117×body160valid
41.0ms253×body80nan
22.0ms139×body80valid

simplify320.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
320.0ms
(asin (sqrt (/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (pow (/ t l) 2))))))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.4b

localize27.0ms

Local error

Found 4 expressions with local error:

10.4b
(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)))))))
0.2b
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
0.2b
(* (/ Om Omc) (/ Om Omc))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
73×add-sqr-sqrt
71×times-frac
58×*-un-lft-identity
51×add-cube-cbrt
21×sqrt-prod
18×add-cbrt-cube add-exp-log
14×difference-of-squares
13×swap-sqr associate-*r* associate-*l*
12×pow1
6×div-inv
5×cbrt-undiv div-exp associate-/l*
4×prod-exp associate-/r/ cbrt-unprod insert-posit16 add-log-exp unswap-sqr
3×associate-/r*
2×rem-sqrt-square flip3-+ flip-+ associate-/l/
1×pow2 frac-times asin-acos clear-num frac-2neg sqrt-pow1 pow-plus flip3-- pow1/2 sqrt-div div-sub pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up flip--
Counts
4 → 152
Calls
4 calls:
Slowest
31.0ms
(* (/ Om Omc) (/ Om Omc))
27.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
8.0ms
(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)))))))

series736.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
493.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
198.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
32.0ms
(* (/ Om Omc) (/ Om Omc))
12.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))

simplify15.9s

Counts
156 → 164
Calls
156 calls:
Slowest
445.0ms
(- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3))
423.0ms
(* (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))) (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))))
329.0ms
(- 1 (* 2 (* (/ t l) (/ t l))))
326.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
302.0ms
(/ (* (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)))))))

prune2.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 11.3b

localize33.0ms

Local error

Found 4 expressions with local error:

10.4b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1)))
0.6b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1))))
0.5b
(/ 2 (* (/ l t) (/ l t)))
0.2b
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
58×*-un-lft-identity
44×times-frac
39×add-sqr-sqrt
27×add-cube-cbrt
26×sqrt-prod
24×add-cbrt-cube add-exp-log
18×difference-of-squares
11×distribute-lft-out
10×cbrt-undiv div-exp
8×associate-/l*
7×associate-/r/
5×pow1 associate-/r*
4×prod-exp cbrt-unprod insert-posit16 add-log-exp
3×div-inv
2×rem-sqrt-square clear-num frac-2neg flip3-+ flip-+ associate-/l/
1×frac-times asin-acos sqrt-pow1 flip3-- pow1/2 sqrt-div div-sub associate-*l/ associate-*r/ flip--
Counts
4 → 126
Calls
4 calls:
Slowest
35.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1))
28.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1)))
15.0ms
(/ 2 (* (/ l t) (/ l t)))
1.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1))))

series338.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
175.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1)))
100.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1))
47.0ms
(/ 2 (* (/ l t) (/ l t)))
17.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1))))

simplify18.3s

Counts
117 → 138
Calls
117 calls:
Slowest
681.0ms
(/ (- (sqrt 1) (/ Om Omc)) (+ (/ 2 (* (/ l t) (/ l t))) 1))
628.0ms
(+ (* (/ 2 (* (/ l t) (/ l t))) (/ 2 (* (/ l t) (/ l t)))) (- (* 1 1) (* (/ 2 (* (/ l t) (/ l t))) 1)))
433.0ms
(- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3))
409.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (- (* (/ 2 (* (/ l t) (/ l t))) (/ 2 (* (/ l t) (/ l t)))) (* 1 1))))
378.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (+ (/ 2 (* (/ l t) (/ l t))) 1)))

prune2.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 11.3b

localize31.0ms

Local error

Found 4 expressions with local error:

10.4b
(sqrt (+ (/ 2 (* (/ l t) (/ l t))) 1))
0.6b
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ (/ 2 (* (/ l t) (/ l t))) 1))))
0.5b
(/ 2 (* (/ l t) (/ l t)))
0.4b
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ (/ 2 (* (/ l t) (/ l t))) 1)))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
80×sqrt-prod
69×*-un-lft-identity
59×times-frac
50×add-sqr-sqrt
41×add-cube-cbrt
24×add-cbrt-cube add-exp-log
16×difference-of-squares
11×associate-/l*
10×cbrt-undiv div-exp distribute-lft-out
8×associate-/r*
6×sqrt-div
5×pow1 associate-/r/
4×prod-exp cbrt-unprod insert-posit16 add-log-exp
2×clear-num frac-2neg flip3-+ flip-+ div-inv associate-/l/
1×frac-times rem-sqrt-square asin-acos sqrt-undiv sqrt-pow1 flip3-- pow1/2 associate-*l/ associate-*r/ flip--
Counts
4 → 146
Calls
4 calls:
Slowest
44.0ms
(sqrt (+ (/ 2 (* (/ l t) (/ l t))) 1))
38.0ms
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ (/ 2 (* (/ l t) (/ l t))) 1)))
20.0ms
(/ 2 (* (/ l t) (/ l t)))
2.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ (/ 2 (* (/ l t) (/ l t))) 1))))

series284.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
162.0ms
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ (/ 2 (* (/ l t) (/ l t))) 1)))
59.0ms
(sqrt (+ (/ 2 (* (/ l t) (/ l t))) 1))
51.0ms
(/ 2 (* (/ l t) (/ l t)))
12.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ (/ 2 (* (/ l t) (/ l t))) 1))))

simplify28.5s

Counts
173 → 158
Calls
173 calls:
Slowest
828.0ms
(sqrt (- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3)))
533.0ms
(sqrt (+ (* (/ 2 (* (/ l t) (/ l t))) (/ 2 (* (/ l t) (/ l t)))) (- (* 1 1) (* (/ 2 (* (/ l t) (/ l t))) 1))))
473.0ms
(sqrt (+ (pow (/ 2 (* (/ l t) (/ l t))) 3) (pow 1 3)))
418.0ms
(/ (* (* (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (sqrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (* (* (sqrt (+ (/ 2 (* (/ l t) (/ l t))) 1)) (sqrt (+ (/ 2 (* (/ l t) (/ l t))) 1))) (sqrt (+ (/ 2 (* (/ l t) (/ l t))) 1))))
415.0ms
(/ (* (* 2 2) 2) (* (/ (* (* l l) l) (* (* t t) t)) (/ (* (* l l) l) (* (* t t) t))))

prune2.5s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 6.6b

localize75.0ms

Local error

Found 4 expressions with local error:

10.4b
(sqrt (/ (- 1 (* (* (/ Om Omc) (/ Om Omc)) (* (/ Om Omc) (/ Om Omc)))) (* (+ (/ 2 (* (/ l t) (/ l t))) 1) (+ 1 (* (/ Om Omc) (/ Om Omc))))))
0.6b
(asin (sqrt (/ (- 1 (* (* (/ Om Omc) (/ Om Omc)) (* (/ Om Omc) (/ Om Omc)))) (* (+ (/ 2 (* (/ l t) (/ l t))) 1) (+ 1 (* (/ Om Omc) (/ Om Omc)))))))
0.5b
(/ 2 (* (/ l t) (/ l t)))
0.3b
(/ (- 1 (* (* (/ Om Omc) (/ Om Omc)) (* (/ Om Omc) (/ Om Omc)))) (* (+ (/ 2 (* (/ l t) (/ l t))) 1) (+ 1 (* (/ Om Omc) (/ Om Omc)))))

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
27×add-cbrt-cube add-exp-log
19×associate-/r/
17×sqrt-prod
14×add-sqr-sqrt
13×*-un-lft-identity times-frac
12×flip3-+ flip-+
11×cbrt-undiv div-exp
10×add-cube-cbrt
9×frac-times
8×associate-/l*
6×difference-of-squares
5×pow1 associate-*l/ prod-exp associate-*r/ cbrt-unprod
4×insert-posit16 add-log-exp
3×div-inv
2×clear-num associate-/r* frac-2neg associate-/l/
1×rem-sqrt-square asin-acos sqrt-pow1 flip3-- pow1/2 sqrt-div div-sub flip--
Counts
4 → 106
Calls
4 calls:
Slowest
41.0ms
(sqrt (/ (- 1 (* (* (/ Om Omc) (/ Om Omc)) (* (/ Om Omc) (/ Om Omc)))) (* (+ (/ 2 (* (/ l t) (/ l t))) 1) (+ 1 (* (/ Om Omc) (/ Om Omc))))))
41.0ms
(/ (- 1 (* (* (/ Om Omc) (/ Om Omc)) (* (/ Om Omc) (/ Om Omc)))) (* (+ (/ 2 (* (/ l t) (/ l t))) 1) (+ 1 (* (/ Om Omc) (/ Om Omc)))))
13.0ms
(/ 2 (* (/ l t) (/ l t)))
1.0ms
(asin (sqrt (/ (- 1 (* (* (/ Om Omc) (/ Om Omc)) (* (/ Om Omc) (/ Om Omc)))) (* (+ (/ 2 (* (/ l t) (/ l t))) 1) (+ 1 (* (/ Om Omc) (/ Om Omc)))))))

series565.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
291.0ms
(sqrt (/ (- 1 (* (* (/ Om Omc) (/ Om Omc)) (* (/ Om Omc) (/ Om Omc)))) (* (+ (/ 2 (* (/ l t) (/ l t))) 1) (+ 1 (* (/ Om Omc) (/ Om Omc))))))
201.0ms
(/ (- 1 (* (* (/ Om Omc) (/ Om Omc)) (* (/ Om Omc) (/ Om Omc)))) (* (+ (/ 2 (* (/ l t) (/ l t))) 1) (+ 1 (* (/ Om Omc) (/ Om Omc)))))
45.0ms
(/ 2 (* (/ l t) (/ l t)))
28.0ms
(asin (sqrt (/ (- 1 (* (* (/ Om Omc) (/ Om Omc)) (* (/ Om Omc) (/ Om Omc)))) (* (+ (/ 2 (* (/ l t) (/ l t))) 1) (+ 1 (* (/ Om Omc) (/ Om Omc)))))))

simplify15.0s

Counts
82 → 118
Calls
82 calls:
Slowest
827.0ms
(/ (* (* (- 1 (* (* (/ Om Omc) (/ Om Omc)) (* (/ Om Omc) (/ Om Omc)))) (- 1 (* (* (/ Om Omc) (/ Om Omc)) (* (/ Om Omc) (/ Om Omc))))) (- 1 (* (* (/ Om Omc) (/ Om Omc)) (* (/ Om Omc) (/ Om Omc))))) (* (* (* (+ (/ 2 (* (/ l t) (/ l t))) 1) (+ (/ 2 (* (/ l t) (/ l t))) 1)) (+ (/ 2 (* (/ l t) (/ l t))) 1)) (* (* (+ 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (/ Om Omc) (/ Om Omc)))) (+ 1 (* (/ Om Omc) (/ Om Omc))))))
688.0ms
(/ (* (* (- 1 (* (* (/ Om Omc) (/ Om Omc)) (* (/ Om Omc) (/ Om Omc)))) (- 1 (* (* (/ Om Omc) (/ Om Omc)) (* (/ Om Omc) (/ Om Omc))))) (- 1 (* (* (/ Om Omc) (/ Om Omc)) (* (/ Om Omc) (/ Om Omc))))) (* (* (* (+ (/ 2 (* (/ l t) (/ l t))) 1) (+ 1 (* (/ Om Omc) (/ Om Omc)))) (* (+ (/ 2 (* (/ l t) (/ l t))) 1) (+ 1 (* (/ Om Omc) (/ Om Omc))))) (* (+ (/ 2 (* (/ l t) (/ l t))) 1) (+ 1 (* (/ Om Omc) (/ Om Omc))))))
605.0ms
(+ (* (/ 2 (* (/ l t) (/ l t))) (/ 2 (* (/ l t) (/ l t)))) (- (* 1 1) (* (/ 2 (* (/ l t) (/ l t))) 1)))
581.0ms
(- (* 1 1) (* (* (* (/ Om Omc) (/ Om Omc)) (* (/ Om Omc) (/ Om Omc))) (* (* (/ Om Omc) (/ Om Omc)) (* (/ Om Omc) (/ Om Omc)))))
469.0ms
(sqrt (/ (- 1 (* (* (/ Om Omc) (/ Om Omc)) (* (/ Om Omc) (/ Om Omc)))) (* (+ (pow (/ 2 (* (/ l t) (/ l t))) 3) (pow 1 3)) (+ (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3)))))

prune1.9s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 6.6b

regimes599.0ms

Accuracy

97.7% (0.1b remaining)

Error of 5.8b against oracle of 5.7b and baseline of 10.4b

bsearch13.0ms

end0.0ms

sample6.0s

Algorithm
intervals
Results
2.2s3779×body160valid
1.7s8013×body80nan
1.3s4221×body80valid