Details

Time bar (total: 2.5m)

sample106.0ms

Algorithm
intervals
Results
36.0ms131×body160valid
31.0ms248×body80nan
16.0ms125×body80valid

simplify472.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
472.0ms
(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: 9.3b

localize60.0ms

Local error

Found 4 expressions with local error:

8.8b
(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)))))))
0.2b
(* (/ t l) (/ t l))
0.2b
(* (/ Om Omc) (/ Om Omc))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
99×add-sqr-sqrt
96×times-frac
72×*-un-lft-identity
69×add-cube-cbrt
28×add-cbrt-cube add-exp-log
26×swap-sqr associate-*r* associate-*l*
21×sqrt-prod
19×pow1
9×div-inv
8×cbrt-undiv div-exp prod-exp cbrt-unprod unswap-sqr
6×difference-of-squares
4×insert-posit16 add-log-exp
2×pow2 frac-times rem-sqrt-square pow-plus pow-prod-down associate-*l/ associate-*r/ associate-/r/ pow-sqr *-commutative pow-prod-up
1×asin-acos sqrt-pow1 flip3-+ pow1/2 sqrt-div flip-+
Counts
4 → 179
Calls
4 calls:
Slowest
24.0ms
(* (/ t l) (/ t l))
24.0ms
(* (/ Om Omc) (/ Om Omc))
15.0ms
(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)))))))

series293.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
203.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
42.0ms
(* (/ t l) (/ t l))
28.0ms
(* (/ Om Omc) (/ Om Omc))
20.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))

simplify24.3s

Counts
243 → 191
Calls
243 calls:
Slowest
540.0ms
(* (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))) (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))))
443.0ms
(* (* (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))) (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))) (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
390.0ms
(* (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))))
357.0ms
(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
347.0ms
(* (/ t l) (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))))

prune2.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 9.2b

localize59.0ms

Local error

Found 4 expressions with local error:

8.8b
(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))))
0.4b
(/ 2 (* (/ l t) (/ l t)))
0.2b
(* (/ l t) (/ l t))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
64×times-frac
63×add-sqr-sqrt
58×*-un-lft-identity
44×add-cube-cbrt
34×add-cbrt-cube add-exp-log
26×sqrt-prod
13×cbrt-undiv swap-sqr div-exp associate-*r* associate-*l*
12×pow1
8×prod-exp cbrt-unprod difference-of-squares
6×div-inv
5×associate-/r/ distribute-lft-out
4×insert-posit16 add-log-exp unswap-sqr
3×associate-/l*
2×frac-times rem-sqrt-square associate-*l/ associate-*r/
1×pow2 asin-acos clear-num associate-/r* frac-2neg sqrt-pow1 flip3-+ pow-plus pow1/2 sqrt-div pow-prod-down pow-sqr *-commutative pow-prod-up flip-+
Counts
4 → 147
Calls
4 calls:
Slowest
29.0ms
(* (/ l t) (/ l t))
27.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1)))
10.0ms
(/ 2 (* (/ l t) (/ l t)))
1.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1))))

series271.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
176.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1)))
49.0ms
(/ 2 (* (/ l t) (/ l t)))
28.0ms
(* (/ l t) (/ l t))
19.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1))))

simplify27.1s

Counts
204 → 159
Calls
204 calls:
Slowest
1.2s
(* (* (/ 2 (* (/ l t) (/ l t))) (/ 2 (* (/ l t) (/ l t)))) (/ 2 (* (/ l t) (/ l t))))
567.0ms
(sqrt (/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (+ (/ 2 (* (/ l t) (/ l t))) 1))))
564.0ms
(sqrt (+ (* (/ 2 (* (/ l t) (/ l t))) (/ 2 (* (/ l t) (/ l t)))) (- (* 1 1) (* (/ 2 (* (/ l t) (/ l t))) 1))))
538.0ms
(* (/ (* (cbrt l) (cbrt l)) (* (cbrt t) (cbrt t))) (/ (* (cbrt l) (cbrt l)) (* (cbrt t) (cbrt t))))
424.0ms
(* (* (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1))) (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1)))) (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1))))

prune2.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 9.2b

localize44.0ms

Local error

Found 4 expressions with local error:

8.5b
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
0.5b
(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
(* (/ t l) (/ t l))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
88×times-frac
85×add-sqr-sqrt
72×*-un-lft-identity
65×add-cube-cbrt sqrt-prod
18×add-cbrt-cube add-exp-log
14×difference-of-squares
13×swap-sqr associate-*r* associate-*l*
12×pow1
8×associate-/l*
6×associate-/r* sqrt-div
5×cbrt-undiv div-exp div-inv
4×prod-exp cbrt-unprod insert-posit16 add-log-exp unswap-sqr
2×flip3-+ associate-/r/ flip-+ associate-/l/
1×pow2 frac-times rem-sqrt-square asin-acos sqrt-undiv clear-num frac-2neg sqrt-pow1 pow-plus flip3-- pow1/2 pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up flip--
Counts
4 → 173
Calls
4 calls:
Slowest
25.0ms
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
24.0ms
(* (/ t l) (/ t l))
7.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
2.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))

series312.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
165.0ms
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
90.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
38.0ms
(* (/ t l) (/ t l))
19.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))

simplify37.9s

Counts
254 → 185
Calls
254 calls:
Slowest
600.0ms
(sqrt (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
538.0ms
(* (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))))
469.0ms
(sqrt (- (* 1 1) (* (* 2 (* (/ t l) (/ t l))) (* 2 (* (/ t l) (/ t l))))))
464.0ms
(/ (* (* (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)))))))
380.0ms
(* (/ t l) (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))))

prune2.7s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.6b

localize70.0ms

Local error

Found 4 expressions with local error:

14.7b
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1)))
14.7b
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1)))
14.7b
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1)))
9.7b
(sqrt (* (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1)))))

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
78×cbrt-prod
76×*-un-lft-identity
60×times-frac
46×add-sqr-sqrt
34×add-cube-cbrt
24×difference-of-squares
15×distribute-lft-out
12×pow1
9×sqrt-pow1 pow1/3
7×cbrt-div
6×associate-/r/
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×flip3-+ sqrt-div flip-+ div-inv
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 frac-times rem-sqrt-square pow-plus pow1/2 associate-*l/ associate-*r/ sqrt-prod
Counts
4 → 131
Calls
4 calls:
Slowest
48.0ms
(sqrt (* (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1)))))
26.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1)))
14.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1)))
13.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1)))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
280.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1)))
273.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1)))
272.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1)))
265.0ms
(sqrt (* (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1)))))

simplify42.6s

Counts
223 → 143
Calls
223 calls:
Slowest
704.0ms
(* (* (sqrt (* (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1))))) (sqrt (* (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1)))))) (sqrt (* (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1))))))
645.0ms
(cbrt (+ (* (/ 2 (* (/ l t) (/ l t))) (/ 2 (* (/ l t) (/ l t)))) (- (* 1 1) (* (/ 2 (* (/ l t) (/ l t))) 1))))
606.0ms
(cbrt (/ (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (sqrt (+ (/ 2 (* (/ l t) (/ l t))) 1))))
523.0ms
(cbrt (+ (* (/ 2 (* (/ l t) (/ l t))) (/ 2 (* (/ l t) (/ l t)))) (- (* 1 1) (* (/ 2 (* (/ l t) (/ l t))) 1))))
521.0ms
(cbrt (+ (* (/ 2 (* (/ l t) (/ l t))) (/ 2 (* (/ l t) (/ l t)))) (- (* 1 1) (* (/ 2 (* (/ l t) (/ l t))) 1))))

prune2.7s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 4.6b

regimes522.0ms

Accuracy

92.9% (0.3b remaining)

Error of 5.7b against oracle of 5.3b and baseline of 10.0b

bsearch11.0ms

end0.0ms

sample5.1s

Algorithm
intervals
Results
1.7s7934×body80nan
1.5s3805×body160valid
903.0ms4195×body80valid