Details

sample144.0ms

Algorithm

intervals

Results

58.0ms	286×	body	80	nan
39.0ms	122×	body	160	valid
20.0ms	134×	body	80	valid

simplify1.3s

Counts: 1 → 1

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.3b

localize29.0ms

Local error

Found 4 expressions with local error:

7.4b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
0.7b	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
0.2b	(* (/ Om Omc) (/ Om Omc))
0.2b	(* (/ t l) (/ t l))

rewrite38.0ms

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`
19×	`pow1` `sqrt-prod`
9×	`div-inv`
8×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `unswap-sqr`
6×	`difference-of-squares`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow2` `frac-times` `rem-sqrt-square` `pow-plus` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`asin-acos` `sqrt-pow1` `pow1/2` `sqrt-div`

Counts

4 → 185

Calls

4 calls:

Slowest

17.0ms	(* (/ t l) (/ t l))
12.0ms	(* (/ Om Omc) (/ Om Omc))
5.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
1.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))

series197.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

126.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
31.0ms	(* (/ Om Omc) (/ Om Omc))
31.0ms	(* (/ t l) (/ t l))
9.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))

simplify951.0ms

Counts: 197 → 197

prune2.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.3b

localize51.0ms

Local error

Found 4 expressions with local error:

7.4b	(sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma (* (/ t l) (/ t l)) 2 1)))
3.0b	(log (exp (* (/ Om Omc) (/ Om Omc))))
0.7b	(asin (sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma (* (/ t l) (/ t l)) 2 1))))
0.2b	(* (/ Om Omc) (/ Om Omc))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

68×	`add-sqr-sqrt`
62×	`times-frac`
56×	`*-un-lft-identity`
44×	`add-cube-cbrt`
25×	`sqrt-prod`
16×	`pow1` `add-cbrt-cube` `add-exp-log`
13×	`swap-sqr` `associate-r` `associate-l`
6×	`log-pow` `distribute-lft-out--` `difference-of-squares`
5×	`div-inv` `add-log-exp`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
3×	`log-prod`
2×	`rem-sqrt-square`
1×	`pow2` `frac-times` `asin-acos` `exp-prod` `sqrt-pow1` `pow-plus` `exp-to-pow` `pow1/2` `sqrt-div` `rem-log-exp` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 138

Calls

4 calls:

Slowest

13.0ms	(* (/ Om Omc) (/ Om Omc))
10.0ms	(sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma (* (/ t l) (/ t l)) 2 1)))
4.0ms	(log (exp (* (/ Om Omc) (/ Om Omc))))
1.0ms	(asin (sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma (* (/ t l) (/ t l)) 2 1))))

series234.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

165.0ms	(sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma (* (/ t l) (/ t l)) 2 1)))
32.0ms	(* (/ Om Omc) (/ Om Omc))
28.0ms	(log (exp (* (/ Om Omc) (/ Om Omc))))
10.0ms	(asin (sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma (* (/ t l) (/ t l)) 2 1))))

simplify1.9s

Counts: 150 → 150

prune2.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.3b

localize40.0ms

Local error

Found 4 expressions with local error:

7.1b	(sqrt (fma (* (/ t l) (/ t l)) 2 1))
3.0b	(log (exp (* (/ Om Omc) (/ Om Omc))))
0.7b	(asin (fabs (/ (sqrt (- 1 (log (exp (* (/ Om Omc) (/ Om Omc)))))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))))
0.6b	(/ (sqrt (- 1 (log (exp (* (/ Om Omc) (/ Om Omc)))))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

85×	`sqrt-prod`
70×	`*-un-lft-identity`
64×	`add-sqr-sqrt`
60×	`times-frac`
42×	`add-cube-cbrt`
14×	`distribute-lft-out--` `difference-of-squares`
13×	`pow1`
10×	`log-pow` `associate-/l*`
6×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
5×	`add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`log-prod`
2×	`sqrt-div` `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 → 138

Calls

4 calls:

Slowest

28.0ms	(/ (sqrt (- 1 (log (exp (* (/ Om Omc) (/ Om Omc)))))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
4.0ms	(log (exp (* (/ Om Omc) (/ Om Omc))))
1.0ms	(sqrt (fma (* (/ t l) (/ t l)) 2 1))
1.0ms	(asin (fabs (/ (sqrt (- 1 (log (exp (* (/ Om Omc) (/ Om Omc)))))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))))

series287.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

153.0ms	(/ (sqrt (- 1 (log (exp (* (/ Om Omc) (/ Om Omc)))))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
77.0ms	(sqrt (fma (* (/ t l) (/ t l)) 2 1))
39.0ms	(log (exp (* (/ Om Omc) (/ Om Omc))))
19.0ms	(asin (fabs (/ (sqrt (- 1 (log (exp (* (/ Om Omc) (/ Om Omc)))))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))))

simplify1.5s

Counts: 150 → 150

prune2.9s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.3b

localize51.0ms

Local error

Found 4 expressions with local error:

10.4b	(cbrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))))
10.4b	(cbrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))))
10.4b	(cbrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))))
7.4b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
19×	`*-un-lft-identity` `sqrt-prod`
16×	`times-frac` `add-cube-cbrt`
9×	`cbrt-prod`
6×	`difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
2×	`rem-sqrt-square`
1×	`sqrt-pow1` `pow1/2` `sqrt-div` `div-inv`

Counts

4 → 76

Calls

4 calls:

Slowest

10.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
1.0ms	(cbrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))))
1.0ms	(cbrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))))
1.0ms	(cbrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))))

series461.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

154.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
113.0ms	(cbrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))))
112.0ms	(cbrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))))
82.0ms	(cbrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))))

simplify1.7s

Counts: 88 → 88

prune1.6s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 1.3b

regimes771.0ms

Accuracy

91.3% (0.8b remaining)

Error of 1.7b against oracle of 0.9b and baseline of 10.1b

bsearch19.0ms

end0.0ms

sample5.5s

Algorithm

intervals

Results

1.7s	8004×	body	80	nan
1.7s	3777×	body	160	valid
944.0ms	4223×	body	80	valid