Details

sample149.0ms

Algorithm

intervals

Results

48.0ms	126×	body	160	valid
44.0ms	240×	body	80	nan
24.0ms	130×	body	80	valid

simplify1.5s

Counts: 1 → 1

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.6b

localize37.0ms

Local error

Found 4 expressions with local error:

6.5b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
0.6b	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
0.3b	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
0.3b	(* (/ Om Omc) (/ Om Omc))

rewrite56.0ms

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:

Slowest

24.0ms	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
19.0ms	(* (/ Om Omc) (/ Om Omc))
8.0ms	(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))))

series288.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

161.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
84.0ms	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
31.0ms	(* (/ Om Omc) (/ Om Omc))
13.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))

simplify793.0ms

Counts: 168 → 168

prune2.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.5b

localize47.0ms

Local error

Found 4 expressions with local error:

6.5b	(sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma (* (/ t l) (/ t l)) 2 1)))
2.8b	(log (exp (* (/ Om Omc) (/ Om Omc))))
0.6b	(asin (sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma (* (/ t l) (/ t l)) 2 1))))
0.3b	(/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma (* (/ t l) (/ t l)) 2 1))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

56×	`*-un-lft-identity`
52×	`add-sqr-sqrt`
43×	`times-frac`
28×	`add-cube-cbrt`
25×	`sqrt-prod`
14×	`distribute-lft-out--` `difference-of-squares`
13×	`pow1`
10×	`log-pow`
7×	`associate-/l*`
6×	`add-cbrt-cube` `add-exp-log`
5×	`add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`log-prod` `associate-/r*`
2×	`rem-sqrt-square` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `asin-acos` `exp-prod` `clear-num` `frac-2neg` `sqrt-pow1` `flip3--` `exp-to-pow` `pow1/2` `sqrt-div` `div-sub` `div-exp` `rem-log-exp` `flip--`

Counts

4 → 117

Calls

4 calls:

Slowest

28.0ms	(/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma (* (/ t l) (/ t l)) 2 1))
11.0ms	(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))))

series311.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

183.0ms	(sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma (* (/ t l) (/ t l)) 2 1)))
89.0ms	(/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma (* (/ t l) (/ t l)) 2 1))
31.0ms	(log (exp (* (/ Om Omc) (/ Om Omc))))
9.0ms	(asin (sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma (* (/ t l) (/ t l)) 2 1))))

simplify867.0ms

Counts: 129 → 129

prune1.7s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.5b

localize48.0ms

Local error

Found 4 expressions with local error:

6.6b	(sqrt (fma (* (/ t l) (/ t l)) 2 1))
2.8b	(log (exp (* (/ Om Omc) (/ Om Omc))))
0.6b	(asin (fabs (/ (sqrt (- 1 (log (exp (* (/ Om Omc) (/ Om Omc)))))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))))
0.4b	(/ (sqrt (- 1 (log (exp (* (/ Om Omc) (/ Om Omc)))))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))

rewrite38.0ms

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)))))

series351.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

173.0ms	(/ (sqrt (- 1 (log (exp (* (/ Om Omc) (/ Om Omc)))))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
111.0ms	(sqrt (fma (* (/ t l) (/ t l)) 2 1))
47.0ms	(log (exp (* (/ Om Omc) (/ Om Omc))))
20.0ms	(asin (fabs (/ (sqrt (- 1 (log (exp (* (/ Om Omc) (/ Om Omc)))))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))))

simplify1.3s

Counts: 150 → 150

prune2.8s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 1.0b

localize97.0ms

Local error

Found 4 expressions with local error:

10.5b	(sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
10.5b	(sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
6.6b	(sqrt (fma (* (/ t l) (/ t l)) 2 1))
6.6b	(sqrt (fma (* (/ t l) (/ t l)) 2 1))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

26×	`sqrt-prod`
16×	`add-sqr-sqrt`
10×	`pow1` `*-un-lft-identity` `sqrt-pow1` `add-cube-cbrt`
6×	`rem-sqrt-square` `pow1/2`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

4 → 76

Calls

4 calls:

Slowest

4.0ms	(sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
4.0ms	(sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
2.0ms	(sqrt (fma (* (/ t l) (/ t l)) 2 1))
2.0ms	(sqrt (fma (* (/ t l) (/ t l)) 2 1))

series521.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

187.0ms	(sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
160.0ms	(sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
94.0ms	(sqrt (fma (* (/ t l) (/ t l)) 2 1))
79.0ms	(sqrt (fma (* (/ t l) (/ t l)) 2 1))

simplify2.0s

Counts: 88 → 88

prune1.9s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 1.0b

regimes716.0ms

Accuracy

99.1% (0.1b remaining)

Error of 1.1b against oracle of 1.0b and baseline of 10.3b

bsearch18.0ms

end0.0ms

sample5.3s

Algorithm

intervals

Results

1.7s	3807×	body	160	valid
1.6s	8025×	body	80	nan
1.3s	4193×	body	80	valid