Details

Time bar (total: 25.1s)

sample112.0ms

Algorithm
intervals
Results
37.0ms108×body160valid
33.0ms262×body80nan
21.0ms148×body80valid

simplify1.1s

Counts
1 → 1
Iterations
IterNodes
63345
5901
4307
3122
259
132
016

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.8b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ Om Omc) (/ Om Omc))
0.4b
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (/ 2 (* (/ l t) (/ l t)))))
0.5b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (/ 2 (* (/ l t) (/ l t)))))))
10.9b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (/ 2 (* (/ l t) (/ l t))))))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
84×*-un-lft-identity
81×times-frac
77×add-sqr-sqrt
53×add-cube-cbrt
26×sqrt-prod
18×add-cbrt-cube add-exp-log difference-of-squares
13×swap-sqr associate-*r* associate-*l*
12×pow1
11×distribute-lft-out
6×div-inv
5×cbrt-undiv div-exp associate-/l*
4×associate-/r* prod-exp associate-/r/ cbrt-unprod insert-posit16 add-log-exp unswap-sqr
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 → 163
Calls
4 calls:
12.0ms
(* (/ Om Omc) (/ Om Omc))
22.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (/ 2 (* (/ l t) (/ l t)))))
1.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (/ 2 (* (/ l t) (/ l t)))))))
19.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (/ 2 (* (/ l t) (/ l t))))))

series348.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (/ Om Omc) (/ Om Omc))
126.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (/ 2 (* (/ l t) (/ l t)))))
18.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (/ 2 (* (/ l t) (/ l t)))))))
158.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (/ 2 (* (/ l t) (/ l t))))))

simplify876.0ms

Counts
175 → 175
Iterations
IterNodes
22093
1710
0267

prune2.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 11.8b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ t l) (/ t l))
0.4b
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (* (/ t l) (/ t l)) 2) 1))
0.5b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (* (/ t l) (/ t l)) 2) 1))))
10.9b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (* (/ t l) (/ t l)) 2) 1)))

rewrite132.0ms

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:
12.0ms
(* (/ t l) (/ t l))
58.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (* (/ t l) (/ t l)) 2) 1))
1.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (* (/ t l) (/ t l)) 2) 1))))
59.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (* (/ t l) (/ t l)) 2) 1)))

series294.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(* (/ t l) (/ t l))
81.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (* (/ t l) (/ t l)) 2) 1))
20.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (* (/ t l) (/ t l)) 2) 1))))
147.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (* (/ t l) (/ t l)) 2) 1)))

simplify809.0ms

Counts
164 → 164
Iterations
IterNodes
22170
1703
0268

prune2.4s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 11.8b

localize58.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ Om Omc) (/ Om Omc))
0.2b
(* (/ t l) (/ t l))
0.5b
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ (* (* (/ t l) (/ t l)) 2) 1))))
11.3b
(sqrt (+ (* (* (/ t l) (/ t l)) 2) 1))

rewrite132.0ms

Algorithm
rewrite-expression-head
Rules
86×add-sqr-sqrt
80×times-frac
61×*-un-lft-identity add-cube-cbrt
28×add-cbrt-cube add-exp-log
26×swap-sqr associate-*r* associate-*l*
19×pow1
8×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
4×insert-posit16 add-log-exp
3×sqrt-prod
2×pow2 frac-times pow-plus sqrt-div pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up
1×rem-sqrt-square asin-acos sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 161
Calls
4 calls:
13.0ms
(* (/ Om Omc) (/ Om Omc))
18.0ms
(* (/ t l) (/ t l))
2.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ (* (* (/ t l) (/ t l)) 2) 1))))
97.0ms
(sqrt (+ (* (* (/ t l) (/ t l)) 2) 1))

series235.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(* (/ Om Omc) (/ Om Omc))
47.0ms
(* (/ t l) (/ t l))
21.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ (* (* (/ t l) (/ t l)) 2) 1))))
118.0ms
(sqrt (+ (* (* (/ t l) (/ t l)) 2) 1))

simplify913.0ms

Counts
173 → 173
Iterations
IterNodes
22742
1841
0268

prune2.6s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 8.1b

localize83.0ms

Local error

Found 4 expressions with local error:

9.4b
(cbrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (* (/ t l) (/ t l)) 2) 1)))))
10.9b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (* (/ t l) (/ t l)) 2) 1)))
10.9b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (* (/ t l) (/ t l)) 2) 1)))
10.9b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (* (/ t l) (/ t l)) 2) 1)))

rewrite266.0ms

Algorithm
rewrite-expression-head
Rules
63×sqrt-prod
50×add-sqr-sqrt
48×times-frac
41×*-un-lft-identity
32×add-cube-cbrt
18×difference-of-squares
7×pow1
6×rem-sqrt-square associate-/r/
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×cbrt-prod sqrt-pow1 flip3-+ pow1/2 sqrt-div flip-+ div-inv
1×pow1/3
Counts
4 → 114
Calls
4 calls:
1.0ms
(cbrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (* (/ t l) (/ t l)) 2) 1)))))
69.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (* (/ t l) (/ t l)) 2) 1)))
94.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (* (/ t l) (/ t l)) 2) 1)))
101.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (* (/ t l) (/ t l)) 2) 1)))

series712.0ms

Counts
4 → 12
Calls
4 calls:
132.0ms
(cbrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (* (/ t l) (/ t l)) 2) 1)))))
192.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (* (/ t l) (/ t l)) 2) 1)))
195.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (* (/ t l) (/ t l)) 2) 1)))
193.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (* (/ t l) (/ t l)) 2) 1)))

simplify4.6s

Counts
126 → 126
Iterations
IterNodes
47472
31671
2534
1269
0143

prune2.0s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 8.0b

regimes561.0ms

Accuracy

98.3% (0.1b remaining)

Error of 5.5b against oracle of 5.4b and baseline of 10.6b

bsearch2.0ms

simplify6.0ms

Iterations
IterNodes
230
130
026

end0.0ms

sample4.4s

Algorithm
intervals
Results
1.8s3739×body160valid
1.4s8027×body80nan
759.0ms4261×body80valid