Details

sample167.0ms

Algorithm

intervals

Results

68.0ms	240×	body	80	nan
48.0ms	126×	body	160	valid
24.0ms	130×	body	80	valid

simplify1.6s

Counts: 1 → 1

prune30.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 7.5b

localize59.0ms

Local error

Found 4 expressions with local error:

6.5b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (/ 2 (* (/ l t) (/ l t))))))
0.6b	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (/ 2 (* (/ l t) (/ l t)))))))
0.3b	(/ 2 (* (/ l t) (/ l t)))
0.3b	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (/ 2 (* (/ l t) (/ l t)))))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

58×	`*-un-lft-identity`
44×	`times-frac`
39×	`add-sqr-sqrt`
27×	`add-cube-cbrt`
26×	`sqrt-prod`
24×	`add-cbrt-cube` `add-exp-log`
18×	`difference-of-squares`
11×	`distribute-lft-out`
10×	`cbrt-undiv` `div-exp`
8×	`associate-/l*`
7×	`associate-/r/`
5×	`pow1` `associate-/r*`
4×	`prod-exp` `cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`div-inv`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `flip3-+` `flip-+` `associate-/l/`
1×	`frac-times` `asin-acos` `sqrt-pow1` `flip3--` `pow1/2` `sqrt-div` `div-sub` `associate-l/` `associate-r/` `flip--`

Counts

4 → 126

Calls

4 calls:

Slowest

28.0ms	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (/ 2 (* (/ l t) (/ l t)))))
25.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (/ 2 (* (/ l t) (/ l t))))))
18.0ms	(/ 2 (* (/ l t) (/ l t)))
1.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (/ 2 (* (/ l t) (/ l t)))))))

series301.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

149.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (/ 2 (* (/ l t) (/ l t))))))
103.0ms	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (/ 2 (* (/ l t) (/ l t)))))
39.0ms	(/ 2 (* (/ l t) (/ l t)))
11.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (/ 2 (* (/ l t) (/ l t)))))))

simplify2.7s

Counts: 138 → 138

prune2.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.5b

localize45.0ms

Local error

Found 4 expressions with local error:

6.5b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
0.6b	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
0.3b	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
0.3b	(* (/ Om Omc) (/ Om Omc))

rewrite77.0ms

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:

Slowest

30.0ms	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
25.0ms	(* (/ Om Omc) (/ Om Omc))
15.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
1.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))

series324.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

178.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
96.0ms	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
30.0ms	(* (/ Om Omc) (/ Om Omc))
20.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))

simplify984.0ms

Counts: 164 → 164

prune2.9s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 7.5b

localize45.0ms

Local error

Found 4 expressions with local error:

6.6b	(sqrt (+ 1 (/ 2 (* (/ l t) (/ l t)))))
0.6b	(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (/ 2 (* (/ l t) (/ l t)))))))
0.4b	(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (/ 2 (* (/ l t) (/ l t))))))
0.3b	(/ 2 (* (/ l t) (/ l t)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

80×	`sqrt-prod`
69×	`*-un-lft-identity`
59×	`times-frac`
50×	`add-sqr-sqrt`
41×	`add-cube-cbrt`
24×	`add-cbrt-cube` `add-exp-log`
16×	`difference-of-squares`
11×	`associate-/l*`
10×	`cbrt-undiv` `div-exp` `distribute-lft-out`
8×	`associate-/r*`
6×	`sqrt-div`
5×	`pow1` `associate-/r/`
4×	`prod-exp` `cbrt-unprod` `insert-posit16` `add-log-exp`
2×	`clear-num` `frac-2neg` `flip3-+` `flip-+` `div-inv` `associate-/l/`
1×	`frac-times` `rem-sqrt-square` `asin-acos` `sqrt-undiv` `sqrt-pow1` `flip3--` `pow1/2` `associate-l/` `associate-r/` `flip--`

Counts

4 → 146

Calls

4 calls:

Slowest

18.0ms	(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (/ 2 (* (/ l t) (/ l t))))))
13.0ms	(/ 2 (* (/ l t) (/ l t)))
9.0ms	(sqrt (+ 1 (/ 2 (* (/ l t) (/ l t)))))
1.0ms	(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (/ 2 (* (/ l t) (/ l t)))))))

series261.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

148.0ms	(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (/ 2 (* (/ l t) (/ l t))))))
52.0ms	(/ 2 (* (/ l t) (/ l t)))
49.0ms	(sqrt (+ 1 (/ 2 (* (/ l t) (/ l t)))))
11.0ms	(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (/ 2 (* (/ l t) (/ l t)))))))

simplify1.7s

Counts: 158 → 158

prune2.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.1b

localize44.0ms

Local error

Found 4 expressions with local error:

10.4b	(sqrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (/ 2 (* (/ l t) (/ l t))))))))
10.4b	(sqrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (/ 2 (* (/ l t) (/ l t))))))))
6.5b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (/ 2 (* (/ l t) (/ l t))))))
6.5b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (/ 2 (* (/ l t) (/ l t))))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

58×	`sqrt-prod`
54×	`*-un-lft-identity`
42×	`add-sqr-sqrt` `times-frac`
26×	`add-cube-cbrt`
16×	`difference-of-squares`
10×	`distribute-lft-out`
8×	`pow1`
6×	`rem-sqrt-square`
4×	`sqrt-pow1` `add-cbrt-cube` `pow1/2` `add-exp-log` `associate-/r/` `insert-posit16` `add-log-exp`
2×	`flip3-+` `sqrt-div` `flip-+` `div-inv`

Counts

4 → 106

Calls

4 calls:

Slowest

15.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (/ 2 (* (/ l t) (/ l t))))))
13.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (/ 2 (* (/ l t) (/ l t))))))
1.0ms	(sqrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (/ 2 (* (/ l t) (/ l t))))))))
1.0ms	(sqrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (/ 2 (* (/ l t) (/ l t))))))))

series365.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

162.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (/ 2 (* (/ l t) (/ l t))))))
144.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (/ 2 (* (/ l t) (/ l t))))))
31.0ms	(sqrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (/ 2 (* (/ l t) (/ l t))))))))
28.0ms	(sqrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (/ 2 (* (/ l t) (/ l t))))))))

simplify2.8s

Counts: 118 → 118

prune1.7s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.0b

regimes521.0ms

Accuracy

98.1% (0.1b remaining)

Error of 5.8b against oracle of 5.8b and baseline of 10.3b

bsearch7.0ms

end0.0ms

sample4.6s

Algorithm

intervals

Results

1.4s	3807×	body	160	valid
1.4s	8025×	body	80	nan
1.1s	4193×	body	80	valid