Details

Time bar (total: 22.5s)

sample111.0ms

Algorithm
intervals
Results
33.0ms242×body80nan
32.0ms128×body160valid
16.0ms128×body80valid

simplify3.4s

Counts
1 → 1
Iterations
IterNodes
done5022
64794
51100
4363
3142
261
132
016

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.7b

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ Om Omc) (/ Om Omc))
0.3b
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))
0.4b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))))
7.9b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))

rewrite171.0ms

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:
21.0ms
(* (/ Om Omc) (/ Om Omc))
86.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))
1.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))))
59.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))

series276.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(* (/ Om Omc) (/ Om Omc))
98.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))
11.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))))
126.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))

simplify2.0s

Counts
175 → 175
Iterations
IterNodes
done5000
22231
1727
0267

prune863.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.6b

localize37.0ms

Local error

Found 4 expressions with local error:

0.4b
(asin (sqrt (* (/ (+ 1 (/ Om Omc)) (sqrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))) (/ (- 1 (/ Om Omc)) (sqrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))))))
7.9b
(sqrt (* (/ (+ 1 (/ Om Omc)) (sqrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))) (/ (- 1 (/ Om Omc)) (sqrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))))
8.0b
(sqrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))
8.0b
(sqrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))

rewrite127.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
9×pow1 sqrt-prod
8×add-sqr-sqrt
7×sqrt-div
6×add-cube-cbrt
4×sqrt-pow1 add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×pow1/2
2×rem-sqrt-square flip3-+ flip-+ distribute-lft-out
1×frac-times asin-acos pow-prod-down associate-*l/ associate-*r/
Counts
4 → 58
Calls
4 calls:
1.0ms
(asin (sqrt (* (/ (+ 1 (/ Om Omc)) (sqrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))) (/ (- 1 (/ Om Omc)) (sqrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))))))
49.0ms
(sqrt (* (/ (+ 1 (/ Om Omc)) (sqrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))) (/ (- 1 (/ Om Omc)) (sqrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))))
37.0ms
(sqrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))
40.0ms
(sqrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))

series350.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(asin (sqrt (* (/ (+ 1 (/ Om Omc)) (sqrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))) (/ (- 1 (/ Om Omc)) (sqrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))))))
177.0ms
(sqrt (* (/ (+ 1 (/ Om Omc)) (sqrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))) (/ (- 1 (/ Om Omc)) (sqrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))))
97.0ms
(sqrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))
64.0ms
(sqrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))

simplify2.2s

Counts
70 → 70
Iterations
IterNodes
done5000
32161
2488
1180
090

prune446.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.6b

localize50.0ms

Local error

Found 4 expressions with local error:

7.9b
(sqrt (* (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (* (cbrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))) (cbrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))) (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))))
12.2b
(cbrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))
12.2b
(cbrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))
12.2b
(cbrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))

rewrite280.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
12×cbrt-prod
7×add-sqr-sqrt pow1 add-cube-cbrt
6×cbrt-div
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×flip3-+ pow1/3 sqrt-div flip-+ distribute-lft-out
2×sqrt-pow1
1×frac-times pow1/2 pow-prod-down associate-*l/ associate-*r/ sqrt-prod
Counts
4 → 60
Calls
4 calls:
223.0ms
(sqrt (* (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (* (cbrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))) (cbrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))) (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))))
19.0ms
(cbrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))
18.0ms
(cbrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))
18.0ms
(cbrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))

series650.0ms

Counts
4 → 12
Calls
4 calls:
131.0ms
(sqrt (* (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (* (cbrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))) (cbrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))) (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))))
162.0ms
(cbrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))
179.0ms
(cbrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))
178.0ms
(cbrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))

simplify2.8s

Counts
72 → 72
Iterations
IterNodes
done5000
44858
31596
2527
1186
089

prune480.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 8.6b

localize52.0ms

Local error

Found 4 expressions with local error:

7.1b
(sqrt (* (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))))
11.9b
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
11.9b
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
11.9b
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))

rewrite121.0ms

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:
57.0ms
(sqrt (* (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))))
21.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
20.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
20.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))

series895.0ms

Counts
4 → 12
Calls
4 calls:
195.0ms
(sqrt (* (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))))
198.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
247.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
255.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))

simplify2.4s

Counts
143 → 143
Iterations
IterNodes
done5006
32881
2802
1351
0180

prune1.0s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 8.6b

regimes370.0ms

Accuracy

0% (0.1b remaining)

Error of 10.5b against oracle of 10.3b and baseline of 10.5b

bsearch0.0ms

simplify4.0ms

Iterations
IterNodes
done23
123
018

end0.0ms

sample3.1s

Algorithm
intervals
Results
932.0ms7763×body80nan
882.0ms3818×body160valid
847.0ms4182×body80valid