Details

sample207.0ms

Algorithm

intervals

Results

66.0ms	306×	body	80	nan
54.0ms	126×	body	160	valid
52.0ms	130×	body	80	valid

simplify1.5s

Counts: 1 → 1

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.2b

localize55.0ms

Local error

Found 4 expressions with local error:

11.3b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
0.6b	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))))
0.3b	(* (/ Om Omc) (/ Om Omc))
0.2b	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))

rewrite182.0ms

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:

Slowest

87.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
67.0ms	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))
24.0ms	(* (/ Om Omc) (/ Om Omc))
1.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))))

series269.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

148.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
79.0ms	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))
27.0ms	(* (/ Om Omc) (/ Om Omc))
15.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))))

simplify976.0ms

Counts: 175 → 175

prune2.4s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 12.1b

localize70.0ms

Local error

Found 4 expressions with local error:

11.3b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
11.3b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
7.5b	(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))))
7.5b	(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))))

rewrite245.0ms

Algorithm

rewrite-expression-head

Rules

166×	`sqrt-prod`
102×	`*-un-lft-identity`
84×	`times-frac`
76×	`add-sqr-sqrt`
46×	`add-cube-cbrt`
32×	`difference-of-squares`
20×	`distribute-lft-out`
10×	`pow1` `rem-sqrt-square` `sqrt-pow1`
8×	`associate-/r/`
6×	`pow1/2` `sqrt-div`
4×	`flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `insert-posit16` `div-inv` `add-log-exp`

Counts

4 → 168

Calls

4 calls:

Slowest

74.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
62.0ms	(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))))
59.0ms	(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))))
45.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))

series913.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

287.0ms	(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))))
251.0ms	(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))))
194.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
180.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))

simplify1.2s

Counts: 180 → 180

prune2.9s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 12.1b

localize86.0ms

Local error

Found 4 expressions with local error:

18.2b	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
18.2b	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
18.2b	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
11.3b	(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))))))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))))

rewrite282.0ms

Algorithm

rewrite-expression-head

Rules

78×	`cbrt-prod`
76×	`*-un-lft-identity`
60×	`times-frac`
46×	`add-sqr-sqrt`
34×	`add-cube-cbrt`
24×	`pow1` `difference-of-squares`
15×	`cbrt-div` `sqrt-pow1` `distribute-lft-out`
12×	`pow1/3`
9×	`pow-prod-up`
7×	`sqrt-div`
6×	`pow-plus` `associate-/r/`
5×	`frac-times` `pow-prod-down` `associate-*l/`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`flip3-+` `associate-*r/` `pow-sqr` `flip-+` `div-inv`
2×	`pow2`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 140

Calls

4 calls:

Slowest

204.0ms	(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))))))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))))
29.0ms	(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))))))
22.0ms	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))

series1.0s

Counts

4 → 12

Calls

4 calls:

Slowest

485.0ms	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
218.0ms	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
209.0ms	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
130.0ms	(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))))))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))))

simplify1.4s

Counts: 152 → 152

prune2.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 12.1b

localize106.0ms

Local error

Found 4 expressions with local error:

18.2b	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
18.2b	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
18.2b	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
11.9b	(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))))))))

rewrite128.0ms

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

44.0ms	(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))))))))
31.0ms	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
26.0ms	(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))))))

series1.2s

Counts

4 → 12

Calls

4 calls:

Slowest

299.0ms	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
297.0ms	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
293.0ms	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
286.0ms	(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))))))))

simplify1.4s

Counts: 143 → 143

prune3.1s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 12.1b

regimes542.0ms

Accuracy

0% (0.0b remaining)

Error of 10.2b against oracle of 10.2b and baseline of 10.2b

bsearch3.0ms

end0.0ms

sample5.4s

Algorithm

intervals

Results

1.7s	3792×	body	160	valid
1.6s	7856×	body	80	nan
832.0ms	4208×	body	80	valid