Details

sample151.0ms

Algorithm

intervals

Results

60.0ms	225×	body	80	nan
43.0ms	114×	body	160	valid
26.0ms	142×	body	80	valid

simplify1.3s

Counts

1 → 1

Iterations

Iter	Nodes
6	3286
5	888
4	311
3	124
2	59
1	30
0	16

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.4b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ Om Omc) (/ Om Omc))
0.4b	(/ (- 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))))
10.2b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

73×	`add-sqr-sqrt`
71×	`times-frac`
58×	`*-un-lft-identity`
51×	`add-cube-cbrt`
19×	`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×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`associate-/r*`
2×	`rem-sqrt-square` `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 → 156

Calls

4 calls:

27.0ms	(* (/ Om Omc) (/ Om Omc))
26.0ms	(/ (- 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))))
7.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

series337.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (/ Om Omc) (/ Om Omc))
117.0ms	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
17.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
172.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

simplify7.8s

Counts

168 → 168

Iterations

Iter	Nodes
3	6581
2	1847
1	641
0	257

prune2.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 11.4b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ Om Omc) (/ Om Omc))
0.4b	(/ (- 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))))
10.2b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

73×	`add-sqr-sqrt`
71×	`times-frac`
58×	`*-un-lft-identity`
51×	`add-cube-cbrt`
19×	`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×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`associate-/r*`
2×	`rem-sqrt-square` `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 → 156

Calls

4 calls:

12.0ms	(* (/ Om Omc) (/ Om Omc))
13.0ms	(/ (- 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))))
10.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

series277.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (/ Om Omc) (/ Om Omc))
90.0ms	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
14.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
132.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

simplify6.4s

Counts

168 → 168

Iterations

Iter	Nodes
3	6581
2	1847
1	641
0	257

prune2.3s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 11.4b

localize71.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ t l) (/ t l))
0.4b	(/ (- 1 (/ Om Omc)) (fma (* (/ t l) (/ t l)) 2 1))
0.7b	(asin (sqrt (* (+ (/ Om Omc) 1) (/ (- 1 (/ Om Omc)) (fma (* (/ t l) (/ t l)) 2 1)))))
10.2b	(sqrt (* (+ (/ Om Omc) 1) (/ (- 1 (/ Om Omc)) (fma (* (/ t l) (/ t l)) 2 1))))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

89×	`add-sqr-sqrt`
72×	`times-frac`
61×	`*-un-lft-identity`
45×	`add-cube-cbrt`
18×	`add-cbrt-cube` `add-exp-log`
16×	`difference-of-squares`
14×	`pow1`
13×	`swap-sqr` `associate-r` `associate-l`
8×	`associate-/l*`
5×	`cbrt-undiv` `sqrt-div` `div-exp` `div-inv`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `unswap-sqr`
3×	`frac-times` `associate-/r` `associate-l/`
2×	`sqrt-pow1` `flip3-+` `pow-prod-down` `associate-*r/` `flip-+` `associate-/l/`
1×	`pow2` `asin-acos` `clear-num` `frac-2neg` `pow-plus` `flip3--` `pow1/2` `div-sub` `pow-sqr` `*-commutative` `pow-prod-up` `sqrt-prod` `flip--`

Counts

4 → 153

Calls

4 calls:

28.0ms	(* (/ t l) (/ t l))
28.0ms	(/ (- 1 (/ Om Omc)) (fma (* (/ t l) (/ t l)) 2 1))
1.0ms	(asin (sqrt (* (+ (/ Om Omc) 1) (/ (- 1 (/ Om Omc)) (fma (* (/ t l) (/ t l)) 2 1)))))
14.0ms	(sqrt (* (+ (/ Om Omc) 1) (/ (- 1 (/ Om Omc)) (fma (* (/ t l) (/ t l)) 2 1))))

series271.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (/ t l) (/ t l))
83.0ms	(/ (- 1 (/ Om Omc)) (fma (* (/ t l) (/ t l)) 2 1))
13.0ms	(asin (sqrt (* (+ (/ Om Omc) 1) (/ (- 1 (/ Om Omc)) (fma (* (/ t l) (/ t l)) 2 1)))))
136.0ms	(sqrt (* (+ (/ Om Omc) 1) (/ (- 1 (/ Om Omc)) (fma (* (/ t l) (/ t l)) 2 1))))

simplify1.1s

Counts

165 → 165

Iterations

Iter	Nodes
2	2060
1	709
0	274

prune3.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 11.4b

localize52.0ms

Local error

Found 4 expressions with local error:

10.7b	(sqrt (* (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))))
17.1b	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
17.1b	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
17.1b	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

57×	`cbrt-prod`
45×	`times-frac`
40×	`add-sqr-sqrt` `*-un-lft-identity`
31×	`add-cube-cbrt`
18×	`difference-of-squares`
12×	`pow1`
9×	`sqrt-pow1` `pow1/3`
7×	`cbrt-div`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-div` `div-inv`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `rem-sqrt-square` `pow-plus` `pow1/2` `associate-l/` `associate-r/` `sqrt-prod`

Counts

4 → 118

Calls

4 calls:

9.0ms	(sqrt (* (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))))
3.0ms	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
3.0ms	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
3.0ms	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

series1.1s

Counts

4 → 12

Calls

4 calls:

270.0ms	(sqrt (* (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))))
249.0ms	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
260.0ms	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
277.0ms	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

simplify3.1s

Counts

130 → 130

Iterations

Iter	Nodes
4	4856
3	1426
2	563
1	295
0	166

prune2.5s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 11.4b

regimes533.0ms

Accuracy

0% (0.1b remaining)

Error of 10.7b against oracle of 10.6b and baseline of 10.7b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	20
1	20
0	18

end0.0ms

sample5.3s

Algorithm

intervals

Results

1.7s	3730×	body	160	valid
1.6s	8006×	body	80	nan
1.4s	4270×	body	80	valid