Details

Time bar (total: 1.6m)

sample116.0ms

Algorithm
intervals
Results
48.0ms228×body80nan
34.0ms131×body160valid
17.0ms125×body80valid

simplify773.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
773.0ms
(asin (sqrt (/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (pow (/ t l) 2))))))

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.9b

localize58.0ms

Local error

Found 4 expressions with local error:

9.8b
(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)))))))
0.5b
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
0.2b
(* (/ Om Omc) (/ Om Omc))

rewrite41.0ms

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
14.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
14.0ms
(* (/ Om Omc) (/ Om Omc))
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)))))))

series313.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
162.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
93.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
45.0ms
(* (/ Om Omc) (/ Om Omc))
13.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))

simplify15.7s

Counts
156 → 164
Calls
156 calls:
Slowest
401.0ms
(* (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))) (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))))
399.0ms
(- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3))
345.0ms
(asin (sqrt (/ (- 1 (/ (pow Om 2) (pow Omc 2))) (+ (* 2 (/ (pow t 2) (pow l 2))) 1))))
326.0ms
(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
325.0ms
(asin (sqrt (/ (- 1 (/ (pow Om 2) (pow Omc 2))) (+ (* 2 (/ (pow t 2) (pow l 2))) 1))))

prune2.3s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 10.9b

localize49.0ms

Local error

Found 4 expressions with local error:

9.8b
(sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
2.8b
(log (exp (* (/ Om Omc) (/ Om Omc))))
0.5b
(asin (sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
0.5b
(/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (+ 1 (* 2 (* (/ t l) (/ t l)))))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
56×*-un-lft-identity
52×add-sqr-sqrt
43×times-frac
28×add-cube-cbrt
27×sqrt-prod
14×distribute-lft-out-- difference-of-squares
13×pow1
10×log-pow
7×associate-/l*
6×add-cbrt-cube add-exp-log
5×add-log-exp
4×associate-/r/ insert-posit16
3×log-prod associate-/r*
2×rem-sqrt-square flip3-+ flip-+ div-inv associate-/l/
1×cbrt-undiv asin-acos exp-prod clear-num frac-2neg sqrt-pow1 flip3-- exp-to-pow pow1/2 sqrt-div div-sub div-exp rem-log-exp flip--
Counts
4 → 113
Calls
4 calls:
Slowest
24.0ms
(/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
12.0ms
(sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
3.0ms
(log (exp (* (/ Om Omc) (/ Om Omc))))
1.0ms
(asin (sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))

series332.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
169.0ms
(sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
125.0ms
(/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
27.0ms
(log (exp (* (/ Om Omc) (/ Om Omc))))
12.0ms
(asin (sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))

simplify22.6s

Counts
105 → 125
Calls
105 calls:
Slowest
810.0ms
(/ (- (sqrt 1) (sqrt (log (exp (* (/ Om Omc) (/ Om Omc)))))) (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
537.0ms
(- (* 1 1) (* (log (exp (* (/ Om Omc) (/ Om Omc)))) (log (exp (* (/ Om Omc) (/ Om Omc))))))
467.0ms
(sqrt (/ (+ (sqrt 1) (sqrt (log (exp (* (/ Om Omc) (/ Om Omc)))))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
408.0ms
(/ (- (sqrt 1) (sqrt (log (exp (* (/ Om Omc) (/ Om Omc)))))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
405.0ms
(- (pow 1 3) (pow (log (exp (* (/ Om Omc) (/ Om Omc)))) 3))

prune2.0s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 10.9b

localize37.0ms

Local error

Found 4 expressions with local error:

9.8b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1)))
0.5b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1))))
0.5b
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1))
0.4b
(/ 2 (* (/ l t) (/ l t)))

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
39.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1))
31.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1)))
9.0ms
(/ 2 (* (/ l t) (/ l t)))
1.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1))))

series349.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
178.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1)))
103.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1))
48.0ms
(/ 2 (* (/ l t) (/ l t)))
20.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1))))

simplify17.2s

Counts
117 → 138
Calls
117 calls:
Slowest
607.0ms
(+ (* (/ 2 (* (/ l t) (/ l t))) (/ 2 (* (/ l t) (/ l t)))) (- (* 1 1) (* (/ 2 (* (/ l t) (/ l t))) 1)))
467.0ms
(- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3))
384.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (cbrt (+ (/ 2 (* (/ l t) (/ l t))) 1)))
377.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (+ (/ 2 (* (/ l t) (/ l t))) 1)))
355.0ms
(/ (* (* 2 2) 2) (* (/ (* (* l l) l) (* (* t t) t)) (/ (* (* l l) l) (* (* t t) t))))

prune1.9s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 10.9b

localize35.0ms

Local error

Found 4 expressions with local error:

9.8b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (/ (sqrt 2) (/ l t)) (/ (sqrt 2) (/ l t))) 1)))
0.5b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (/ (sqrt 2) (/ l t)) (/ (sqrt 2) (/ l t))) 1))))
0.5b
(/ (sqrt 2) (/ l t))
0.5b
(/ (sqrt 2) (/ l t))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
298×times-frac
173×add-sqr-sqrt
170×*-un-lft-identity
167×add-cube-cbrt
105×sqrt-prod
26×associate-/r*
17×div-inv
14×add-cbrt-cube add-exp-log
12×associate-/l*
6×cbrt-undiv div-exp difference-of-squares
5×pow1
4×associate-/r/ insert-posit16 add-log-exp
2×rem-sqrt-square clear-num frac-2neg
1×asin-acos sqrt-pow1 flip3-+ pow1/2 sqrt-div flip-+
Counts
4 → 269
Calls
4 calls:
Slowest
41.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (/ (sqrt 2) (/ l t)) (/ (sqrt 2) (/ l t))) 1)))
6.0ms
(/ (sqrt 2) (/ l t))
6.0ms
(/ (sqrt 2) (/ l t))
1.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (/ (sqrt 2) (/ l t)) (/ (sqrt 2) (/ l t))) 1))))

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
830.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (/ (sqrt 2) (/ l t)) (/ (sqrt 2) (/ l t))) 1)))
96.0ms
(/ (sqrt 2) (/ l t))
69.0ms
(/ (sqrt 2) (/ l t))
49.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (/ (sqrt 2) (/ l t)) (/ (sqrt 2) (/ l t))) 1))))

simplify21.4s

Counts
393 → 281
Calls
393 calls:
Slowest
537.0ms
(/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (* (cbrt l) (cbrt l)) (* (cbrt t) (cbrt t))))
526.0ms
(/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (* (cbrt l) (cbrt l)) (* (cbrt t) (cbrt t))))
467.0ms
(sqrt (/ (+ (sqrt 1) (/ Om Omc)) (sqrt (+ (* (/ (sqrt 2) (/ l t)) (/ (sqrt 2) (/ l t))) 1))))
445.0ms
(sqrt (/ (+ (sqrt 1) (/ Om Omc)) (* (cbrt (+ (* (/ (sqrt 2) (/ l t)) (/ (sqrt 2) (/ l t))) 1)) (cbrt (+ (* (/ (sqrt 2) (/ l t)) (/ (sqrt 2) (/ l t))) 1)))))
420.0ms
(sqrt (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ (* (/ (sqrt 2) (/ l t)) (/ (sqrt 2) (/ l t))) 1))))

prune4.5s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 10.8b

regimes478.0ms

Accuracy

0% (0.1b remaining)

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

bsearch6.0ms

end0.0ms

sample5.2s

Algorithm
intervals
Results
2.0s7880×body80nan
1.8s3835×body160valid
865.0ms4165×body80valid