Details

Time bar (total: 21.7s)

sample108.0ms

Algorithm
intervals
Results
42.0ms117×body160valid
27.0ms252×body80nan
14.0ms139×body80valid

simplify3.1s

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.7b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ Om Omc) (/ Om Omc))
0.3b
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))
0.5b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))))
8.8b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))

rewrite218.0ms

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:
28.0ms
(* (/ Om Omc) (/ Om Omc))
102.0ms
(/ (- 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)))))))
81.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))

series370.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (/ Om Omc) (/ Om Omc))
124.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))
22.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))))
176.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))

simplify2.2s

Counts
175 → 175
Iterations
IterNodes
done5000
22231
1727
0267

prune921.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 9.6b

localize50.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))
0.5b
(asin (sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))))
2.7b
(log (exp (* (/ Om Omc) (/ Om Omc))))
8.8b
(sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))

rewrite222.0ms

Algorithm
rewrite-expression-head
Rules
96×*-un-lft-identity
60×add-sqr-sqrt
57×times-frac
34×sqrt-prod
30×add-cube-cbrt
18×distribute-lft-out-- difference-of-squares
15×pow1 distribute-lft-out
12×log-pow
7×associate-/l*
6×add-cbrt-cube add-exp-log
5×add-log-exp
4×associate-/r* associate-/r/ insert-posit16
3×log-prod
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 → 128
Calls
4 calls:
104.0ms
(/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))
1.0ms
(asin (sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))))
5.0ms
(log (exp (* (/ Om Omc) (/ Om Omc))))
109.0ms
(sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))

series305.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))
17.0ms
(asin (sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))))
30.0ms
(log (exp (* (/ Om Omc) (/ Om Omc))))
141.0ms
(sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))

simplify3.0s

Counts
140 → 140
Iterations
IterNodes
done5000
34693
21064
1379
0187

prune627.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 9.6b

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (sqrt (- 1 (log (exp (* (/ Om Omc) (/ Om Omc)))))) (sqrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
0.5b
(asin (fabs (/ (sqrt (- 1 (log (exp (* (/ Om Omc) (/ Om Omc)))))) (sqrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))))
2.7b
(log (exp (* (/ Om Omc) (/ Om Omc))))
8.9b
(sqrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))

rewrite180.0ms

Algorithm
rewrite-expression-head
Rules
104×sqrt-prod
100×*-un-lft-identity
70×times-frac
69×add-sqr-sqrt
44×add-cube-cbrt
16×distribute-lft-out-- difference-of-squares
14×pow1
12×distribute-lft-out
11×log-pow
10×associate-/l*
7×associate-/r*
6×add-cbrt-cube sqrt-div add-exp-log
5×add-log-exp
4×insert-posit16
3×log-prod
2×flip3-+ associate-/r/ flip-+ associate-/l/
1×cbrt-undiv rem-sqrt-square asin-acos sqrt-undiv exp-prod clear-num frac-2neg sqrt-pow1 flip3-- exp-to-pow pow1/2 div-exp rem-log-exp div-inv flip--
Counts
4 → 146
Calls
4 calls:
108.0ms
(/ (sqrt (- 1 (log (exp (* (/ Om Omc) (/ Om Omc)))))) (sqrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
1.0ms
(asin (fabs (/ (sqrt (- 1 (log (exp (* (/ Om Omc) (/ Om Omc)))))) (sqrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))))
4.0ms
(log (exp (* (/ Om Omc) (/ Om Omc))))
61.0ms
(sqrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))

series320.0ms

Counts
4 → 12
Calls
4 calls:
176.0ms
(/ (sqrt (- 1 (log (exp (* (/ Om Omc) (/ Om Omc)))))) (sqrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
19.0ms
(asin (fabs (/ (sqrt (- 1 (log (exp (* (/ Om Omc) (/ Om Omc)))))) (sqrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))))
39.0ms
(log (exp (* (/ Om Omc) (/ Om Omc))))
87.0ms
(sqrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))

simplify2.0s

Counts
158 → 158
Iterations
IterNodes
done5001
32474
2756
1350
0203

prune770.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.8b

localize53.0ms

Local error

Found 4 expressions with local error:

2.0b
(sqrt (cbrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
2.7b
(log (exp (* (/ Om Omc) (/ Om Omc))))
15.3b
(cbrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))
15.3b
(cbrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))

rewrite149.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
13×cbrt-prod
11×add-sqr-sqrt
9×add-cube-cbrt
7×sqrt-prod
6×pow1 cbrt-div
5×add-log-exp
4×add-cbrt-cube add-exp-log insert-posit16
3×log-prod flip3-+ pow1/3 log-pow flip-+ distribute-lft-out
2×rem-sqrt-square sqrt-pow1 sqrt-div
1×exp-prod exp-to-pow pow1/2 rem-log-exp
Counts
4 → 67
Calls
4 calls:
75.0ms
(sqrt (cbrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
5.0ms
(log (exp (* (/ Om Omc) (/ Om Omc))))
40.0ms
(cbrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))
27.0ms
(cbrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))

series565.0ms

Counts
4 → 12
Calls
4 calls:
158.0ms
(sqrt (cbrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
34.0ms
(log (exp (* (/ Om Omc) (/ Om Omc))))
183.0ms
(cbrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))
190.0ms
(cbrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))

simplify1.8s

Counts
79 → 79
Iterations
IterNodes
done5001
31935
2553
1209
0110

prune623.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.8b

regimes607.0ms

Accuracy

96.2% (0.4b remaining)

Error of 1.3b against oracle of 0.9b and baseline of 10.1b

bsearch3.0ms

simplify12.0ms

Iterations
IterNodes
done38
138
031

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.3s7980×body80nan
960.0ms3824×body160valid
553.0ms4176×body80valid