Details

sample157.0ms

Algorithm

intervals

Results

57.0ms	265×	body	80	nan
44.0ms	113×	body	160	valid
27.0ms	143×	body	80	valid

simplify350.0ms

Counts: 1 → 1

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.1b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite37.0ms

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

16.0ms	(* (/ Om Omc) (/ Om Omc))
12.0ms	(* (/ t l) (/ t l))
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))))

series231.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

152.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
34.0ms	(* (/ t l) (/ t l))
32.0ms	(* (/ Om Omc) (/ Om Omc))
13.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))

simplify420.0ms

Counts: 247 → 197

prune2.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.0b

localize38.0ms

Local error

Found 4 expressions with local error:

7.2b	(sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma (* (/ t l) (/ t l)) 2 1)))
3.7b	(log (exp (* (/ Om Omc) (/ Om Omc))))
0.8b	(asin (sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma (* (/ t l) (/ t l)) 2 1))))
0.3b	(* (/ t l) (/ t l))

rewrite37.0ms

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

18.0ms	(sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma (* (/ t l) (/ t l)) 2 1)))
13.0ms	(* (/ t l) (/ t l))
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))))

series296.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

189.0ms	(sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma (* (/ t l) (/ t l)) 2 1)))
45.0ms	(* (/ t l) (/ t l))
45.0ms	(log (exp (* (/ Om Omc) (/ Om Omc))))
17.0ms	(asin (sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma (* (/ t l) (/ t l)) 2 1))))

simplify325.0ms

Counts: 192 → 150

prune2.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.0b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite55.0ms

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

21.0ms	(* (/ t l) (/ t l))
18.0ms	(* (/ Om Omc) (/ Om Omc))
11.0ms	(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))))

series252.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

160.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
38.0ms	(* (/ Om Omc) (/ Om Omc))
37.0ms	(* (/ t l) (/ t l))
17.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))

simplify433.0ms

Counts: 247 → 197

prune3.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 8.0b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

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×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
2×	`pow2` `frac-times` `pow-plus` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`rem-sqrt-square` `asin-acos` `sqrt-pow1` `pow1/2`

Counts

4 → 167

Calls

4 calls:

Slowest

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

series146.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

67.0ms	(sqrt (fma (* (/ t l) (/ t l)) 2 1))
42.0ms	(* (/ Om Omc) (/ Om Omc))
27.0ms	(* (/ t l) (/ t l))
9.0ms	(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))

simplify327.0ms

Counts: 213 → 179

prune3.2s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.0b

regimes667.0ms

Accuracy

98.6% (0.1b remaining)

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

bsearch15.0ms

end0.0ms

sample5.5s

Algorithm

intervals

Results

2.3s	7947×	body	80	nan
1.6s	3769×	body	160	valid
938.0ms	4231×	body	80	valid