Details

Time bar (total: 25.1s)

sample173.0ms

Algorithm
intervals
Results
65.0ms128×body160valid
46.0ms242×body80nan
27.0ms128×body80valid

simplify3.2s

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

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.7b

localize56.0ms

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))))))

rewrite162.0ms

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))
73.0ms
(/ (- 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)))))))
73.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))

series330.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(* (/ Om Omc) (/ Om Omc))
102.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))
12.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))))
187.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))

simplify2.1s

Counts
175 → 175
Iterations
IterNodes
done5000
22231
1727
0267

prune933.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.6b

localize52.0ms

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)))))

rewrite187.0ms

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)))))))))
76.0ms
(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))))))))
54.0ms
(sqrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))
54.0ms
(sqrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))

series360.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(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)))))))))
167.0ms
(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))))))))
87.0ms
(sqrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))
90.0ms
(sqrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))

simplify2.1s

Counts
70 → 70
Iterations
IterNodes
done5000
32161
2488
1180
090

prune424.0ms

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)))))

rewrite278.0ms

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:
194.0ms
(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))))))))
26.0ms
(cbrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))
25.0ms
(cbrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))
31.0ms
(cbrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))

series642.0ms

Counts
4 → 12
Calls
4 calls:
168.0ms
(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))))))))
154.0ms
(cbrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))
140.0ms
(cbrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))
180.0ms
(cbrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))

simplify3.3s

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

prune423.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 8.6b

localize49.0ms

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))))))

rewrite109.0ms

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:
42.0ms
(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))))))))
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))))))
25.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))

series1.0s

Counts
4 → 12
Calls
4 calls:
279.0ms
(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))))))))
275.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
268.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
196.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))

simplify2.3s

Counts
143 → 143
Iterations
IterNodes
done5006
32881
2802
1351
0180

prune1.2s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 8.6b

regimes374.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations
IterNodes
done23
123
018

end0.0ms

sample5.2s

Algorithm
intervals
Results
2.3s3818×body160valid
1.5s7763×body80nan
813.0ms4182×body80valid