Details

sample139.0ms

Algorithm

intervals

Results

43.0ms	265×	body	80	nan
41.0ms	113×	body	160	valid
25.0ms	143×	body	80	valid

simplify855.0ms

Counts: 1 → 1

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.1b

localize42.0ms

Local error

Found 4 expressions with local error:

7.2b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
0.8b	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
0.3b	(* (/ t l) (/ t l))
0.2b	(* (/ Om Omc) (/ Om Omc))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-sqr-sqrt`
96×	`times-frac`
72×	`*-un-lft-identity`
69×	`add-cube-cbrt`
28×	`add-cbrt-cube` `add-exp-log`
26×	`swap-sqr` `associate-r` `associate-l`
21×	`sqrt-prod`
19×	`pow1`
9×	`div-inv`
8×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `unswap-sqr`
6×	`difference-of-squares`
4×	`insert-posit16` `add-log-exp`
2×	`pow2` `frac-times` `rem-sqrt-square` `pow-plus` `pow-prod-down` `associate-l/` `associate-r/` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`asin-acos` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `flip-+`

Counts

4 → 179

Calls

4 calls:

Slowest

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

series273.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

169.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
48.0ms	(* (/ t l) (/ t l))
44.0ms	(* (/ Om Omc) (/ Om Omc))
11.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))

simplify531.0ms

Counts: 243 → 191

prune2.7s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 8.0b

localize31.0ms

Local error

Found 4 expressions with local error:

7.3b	(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
0.8b	(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
0.3b	(* (/ t l) (/ t l))
0.2b	(* (/ Om Omc) (/ Om Omc))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

86×	`add-sqr-sqrt`
80×	`times-frac`
61×	`*-un-lft-identity` `add-cube-cbrt`
28×	`add-cbrt-cube` `add-exp-log`
26×	`swap-sqr` `associate-r` `associate-l`
19×	`pow1`
8×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
4×	`insert-posit16` `add-log-exp`
3×	`sqrt-prod`
2×	`pow2` `frac-times` `pow-plus` `sqrt-div` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`rem-sqrt-square` `asin-acos` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 161

Calls

4 calls:

Slowest

18.0ms	(* (/ t l) (/ t l))
14.0ms	(* (/ Om Omc) (/ Om Omc))
6.0ms	(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
4.0ms	(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

series148.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

75.0ms	(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
32.0ms	(* (/ Om Omc) (/ Om Omc))
30.0ms	(* (/ t l) (/ t l))
11.0ms	(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))

simplify341.0ms

Counts: 209 → 173

prune2.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.0b

localize55.0ms

Local error

Found 4 expressions with local error:

7.3b	(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
3.7b	(log (exp (* (/ Om Omc) (/ Om Omc))))
0.8b	(asin (/ (sqrt (- 1 (log (exp (* (/ Om Omc) (/ Om Omc)))))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
0.3b	(* (/ t l) (/ t l))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
40×	`times-frac`
34×	`*-un-lft-identity` `add-cube-cbrt`
16×	`add-cbrt-cube` `add-exp-log`
13×	`pow1` `swap-sqr` `associate-r` `associate-l`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `insert-posit16` `div-inv` `unswap-sqr`
3×	`log-prod` `log-pow` `sqrt-prod`
2×	`sqrt-div`
1×	`pow2` `frac-times` `rem-sqrt-square` `asin-acos` `exp-prod` `sqrt-pow1` `flip3-+` `pow-plus` `exp-to-pow` `pow1/2` `rem-log-exp` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `flip-+`

Counts

4 → 108

Calls

4 calls:

Slowest

14.0ms	(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
13.0ms	(* (/ t l) (/ t l))
7.0ms	(log (exp (* (/ Om Omc) (/ Om Omc))))
1.0ms	(asin (/ (sqrt (- 1 (log (exp (* (/ Om Omc) (/ Om Omc)))))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))

series156.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

72.0ms	(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
41.0ms	(* (/ t l) (/ t l))
27.0ms	(log (exp (* (/ Om Omc) (/ Om Omc))))
15.0ms	(asin (/ (sqrt (- 1 (log (exp (* (/ Om Omc) (/ Om Omc)))))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))

simplify563.0ms

Counts: 142 → 120

prune1.8s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.0b

localize81.0ms

Local error

Found 4 expressions with local error:

7.3b	(sqrt (+ 1 (* 2 (* (* (/ t l) (* (/ (cbrt t) (cbrt l)) (/ (cbrt t) (cbrt l)))) (/ (cbrt t) (cbrt l))))))
0.8b	(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (* (/ t l) (* (/ (cbrt t) (cbrt l)) (/ (cbrt t) (cbrt l)))) (/ (cbrt t) (cbrt l))))))))
0.6b	(cbrt t)
0.6b	(cbrt t)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-prod`
5×	`pow1`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`sqrt-prod`
2×	`pow1/3` `sqrt-div`
1×	`rem-sqrt-square` `asin-acos` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 49

Calls

4 calls:

Slowest

12.0ms	(sqrt (+ 1 (* 2 (* (* (/ t l) (* (/ (cbrt t) (cbrt l)) (/ (cbrt t) (cbrt l)))) (/ (cbrt t) (cbrt l))))))
1.0ms	(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (* (/ t l) (* (/ (cbrt t) (cbrt l)) (/ (cbrt t) (cbrt l)))) (/ (cbrt t) (cbrt l))))))))
1.0ms	(cbrt t)
1.0ms	(cbrt t)

series586.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

251.0ms	(cbrt t)
242.0ms	(cbrt t)
81.0ms	(sqrt (+ 1 (* 2 (* (* (/ t l) (* (/ (cbrt t) (cbrt l)) (/ (cbrt t) (cbrt l)))) (/ (cbrt t) (cbrt l))))))
11.0ms	(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (* (/ t l) (* (/ (cbrt t) (cbrt l)) (/ (cbrt t) (cbrt l)))) (/ (cbrt t) (cbrt l))))))))

simplify1.2s

Counts: 69 → 61

prune931.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 4.0b

regimes688.0ms

Accuracy

98.2% (0.1b remaining)

Error of 5.8b against oracle of 5.7b and baseline of 10.5b

bsearch9.0ms

end0.0ms

sample4.8s

Algorithm

intervals

Results

1.8s	3769×	body	160	valid
1.5s	7947×	body	80	nan
872.0ms	4231×	body	80	valid