Details

sample194.0ms

Algorithm

intervals

Results

65.0ms	286×	body	80	nan
61.0ms	122×	body	160	valid
31.0ms	134×	body	80	valid

simplify1.9s

Counts: 1 → 1

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.3b

localize55.0ms

Local error

Found 4 expressions with local error:

7.4b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
0.7b	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))))
0.2b	(* (/ Om Omc) (/ Om Omc))
0.2b	(* (/ t l) (/ t l))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

101×	`add-sqr-sqrt` `times-frac`
84×	`*-un-lft-identity`
70×	`add-cube-cbrt`
28×	`add-cbrt-cube` `add-exp-log`
26×	`swap-sqr` `associate-r` `associate-l` `sqrt-prod`
19×	`pow1`
9×	`div-inv`
8×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `difference-of-squares` `unswap-sqr`
5×	`distribute-lft-out`
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 → 184

Calls

4 calls:

Slowest

71.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
27.0ms	(* (/ t l) (/ t l))
25.0ms	(* (/ Om Omc) (/ Om Omc))
1.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))))

series262.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

173.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
38.0ms	(* (/ t l) (/ t l))
36.0ms	(* (/ Om Omc) (/ Om Omc))
14.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))))

simplify1.3s

Counts: 196 → 196

prune3.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.3b

localize29.0ms

Local error

Found 4 expressions with local error:

7.1b	(sqrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))
0.7b	(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))))
0.6b	(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
0.2b	(* (/ Om Omc) (/ Om Omc))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

96×	`times-frac`
95×	`*-un-lft-identity`
88×	`add-sqr-sqrt`
80×	`sqrt-prod`
67×	`add-cube-cbrt`
18×	`add-cbrt-cube` `add-exp-log`
16×	`difference-of-squares`
13×	`swap-sqr` `associate-r` `associate-l`
12×	`pow1`
10×	`distribute-lft-out`
8×	`associate-/l*`
7×	`associate-/r*`
6×	`sqrt-div`
5×	`cbrt-undiv` `div-exp` `div-inv`
4×	`prod-exp` `cbrt-unprod` `insert-posit16` `add-log-exp` `unswap-sqr`
2×	`flip3-+` `associate-/r/` `flip-+` `associate-/l/`
1×	`pow2` `frac-times` `rem-sqrt-square` `asin-acos` `sqrt-undiv` `clear-num` `frac-2neg` `sqrt-pow1` `pow-plus` `flip3--` `pow1/2` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `flip--`

Counts

4 → 183

Calls

4 calls:

Slowest

55.0ms	(sqrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))
55.0ms	(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
24.0ms	(* (/ Om Omc) (/ Om Omc))
2.0ms	(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))))

series293.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

147.0ms	(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
99.0ms	(sqrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))
30.0ms	(* (/ Om Omc) (/ Om Omc))
16.0ms	(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))))

simplify888.0ms

Counts: 195 → 195

prune2.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.5b

localize37.0ms

Local error

Found 4 expressions with local error:

7.1b	(sqrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))
3.0b	(log (exp (* (/ Om Omc) (/ Om Omc))))
0.7b	(asin (/ (sqrt (- 1 (log (exp (* (/ Om Omc) (/ Om Omc)))))) (sqrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))))
0.6b	(/ (sqrt (- 1 (log (exp (* (/ Om Omc) (/ Om Omc)))))) (sqrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))

rewrite149.0ms

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:

Slowest

79.0ms	(/ (sqrt (- 1 (log (exp (* (/ Om Omc) (/ Om Omc)))))) (sqrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
63.0ms	(sqrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))
3.0ms	(log (exp (* (/ Om Omc) (/ Om Omc))))
1.0ms	(asin (/ (sqrt (- 1 (log (exp (* (/ Om Omc) (/ Om Omc)))))) (sqrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))))

series303.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

173.0ms	(/ (sqrt (- 1 (log (exp (* (/ Om Omc) (/ Om Omc)))))) (sqrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
77.0ms	(sqrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))
41.0ms	(log (exp (* (/ Om Omc) (/ Om Omc))))
12.0ms	(asin (/ (sqrt (- 1 (log (exp (* (/ Om Omc) (/ Om Omc)))))) (sqrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))))

simplify931.0ms

Counts: 158 → 158

prune2.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.5b

localize89.0ms

Local error

Found 4 expressions with local error:

7.4b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) (* (/ (cbrt t) (cbrt l)) (/ t l)))))))
0.7b	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) (* (/ (cbrt t) (cbrt l)) (/ t l))))))))
0.6b	(cbrt l)
0.6b	(cbrt l)

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

30×	`*-un-lft-identity`
26×	`sqrt-prod`
23×	`add-sqr-sqrt`
21×	`times-frac`
16×	`add-cube-cbrt`
8×	`difference-of-squares`
6×	`cbrt-prod`
5×	`pow1` `distribute-lft-out`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
2×	`rem-sqrt-square` `pow1/3` `associate-/r/`
1×	`asin-acos` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `flip-+` `div-inv`

Counts

4 → 72

Calls

4 calls:

Slowest

61.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) (* (/ (cbrt t) (cbrt l)) (/ t l)))))))
1.0ms	(cbrt l)
1.0ms	(cbrt l)
1.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) (* (/ (cbrt t) (cbrt l)) (/ t l))))))))

series723.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

291.0ms	(cbrt l)
258.0ms	(cbrt l)
163.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) (* (/ (cbrt t) (cbrt l)) (/ t l)))))))
11.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) (* (/ (cbrt t) (cbrt l)) (/ t l))))))))

simplify1.8s

Counts: 84 → 84

prune1.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.4b

regimes512.0ms

Accuracy

98.4% (0.1b remaining)

Error of 5.7b against oracle of 5.6b and baseline of 10.1b

bsearch10.0ms

end0.0ms

sample4.8s

Algorithm

intervals

Results

1.9s	8004×	body	80	nan
1.4s	3777×	body	160	valid
790.0ms	4223×	body	80	valid