Details

sample133.0ms

Algorithm

intervals

Results

45.0ms	130×	body	160	valid
44.0ms	222×	body	80	nan
22.0ms	126×	body	80	valid

simplify405.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

405.0ms

(asin (sqrt (/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (pow (/ t l) 2))))))

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.5b

localize36.0ms

Local error

Found 4 expressions with local error:

8.7b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
0.5b	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
0.2b	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
0.2b	(* (/ t l) (/ t l))

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:

Slowest

28.0ms	(* (/ t l) (/ t l))
27.0ms	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
6.0ms	(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))))

series355.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

198.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
117.0ms	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
28.0ms	(* (/ t l) (/ t l))
12.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))

simplify15.0s

Counts

152 → 168

Calls

152 calls:

Slowest

668.0ms	(/ (* (* (- 1 (* (/ Om Omc) (/ Om Omc))) (- 1 (* (/ Om Omc) (/ Om Omc)))) (- 1 (* (/ Om Omc) (/ Om Omc)))) (* (* (fma (* (/ t l) (/ t l)) 2 1) (fma (* (/ t l) (/ t l)) 2 1)) (fma (* (/ t l) (/ t l)) 2 1)))
589.0ms	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
562.0ms	(- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3))
392.0ms	(* (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))))
299.0ms	(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)))))

prune2.5s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 9.5b

localize61.0ms

Local error

Found 4 expressions with local error:

8.7b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
0.5b	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
0.2b	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
0.2b	(* (/ t l) (/ t l))

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

30.0ms	(* (/ t l) (/ t l))
15.0ms	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
6.0ms	(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))))

series360.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

167.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
135.0ms	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
48.0ms	(* (/ t l) (/ t l))
10.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))

simplify14.9s

Counts

152 → 168

Calls

152 calls:

Slowest

673.0ms	(/ (* (* (- 1 (* (/ Om Omc) (/ Om Omc))) (- 1 (* (/ Om Omc) (/ Om Omc)))) (- 1 (* (/ Om Omc) (/ Om Omc)))) (* (* (fma (* (/ t l) (/ t l)) 2 1) (fma (* (/ t l) (/ t l)) 2 1)) (fma (* (/ t l) (/ t l)) 2 1)))
467.0ms	(* (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))))
455.0ms	(- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3))
325.0ms	(/ (- (sqrt 1) (/ Om Omc)) (fma (* (/ t l) (/ t l)) 2 1))
295.0ms	(/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))

prune3.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 9.5b

localize59.0ms

Local error

Found 4 expressions with local error:

8.9b	(sqrt (fma (* (/ t l) (/ t l)) 2 1))
0.5b	(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
0.2b	(* (/ t l) (/ t l))
0.2b	(* (/ Om Omc) (/ Om Omc))

rewrite57.0ms

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

27.0ms	(* (/ t l) (/ t l))
22.0ms	(* (/ Om Omc) (/ Om Omc))
3.0ms	(sqrt (fma (* (/ t l) (/ t l)) 2 1))
2.0ms	(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))

series196.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

93.0ms	(sqrt (fma (* (/ t l) (/ t l)) 2 1))
53.0ms	(* (/ t l) (/ t l))
32.0ms	(* (/ Om Omc) (/ Om Omc))
19.0ms	(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))

simplify6.7s

Counts

167 → 179

Calls

167 calls:

Slowest

392.0ms	(* (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))))
378.0ms	(* (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))) (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))))
255.0ms	(asin (sqrt (/ (- 1 (/ (pow Om 2) (pow Omc 2))) (fma (/ (pow t 2) (pow l 2)) 2 1))))
244.0ms	(asin (sqrt (/ (- 1 (/ (pow Om 2) (pow Omc 2))) (fma (/ (pow t 2) (pow l 2)) 2 1))))
230.0ms	(asin (sqrt (/ (- 1 (/ (pow Om 2) (pow Omc 2))) (fma (/ (pow t 2) (pow l 2)) 2 1))))

prune3.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.8b

localize66.0ms

Local error

Found 4 expressions with local error:

14.8b	(cbrt (fma (* (/ t l) (/ t l)) 2 1))
14.8b	(cbrt (fma (* (/ t l) (/ t l)) 2 1))
14.8b	(cbrt (fma (* (/ t l) (/ t l)) 2 1))
8.7b	(sqrt (* (/ 1 (* (cbrt (fma (* (/ t l) (/ t l)) 2 1)) (cbrt (fma (* (/ t l) (/ t l)) 2 1)))) (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (cbrt (fma (* (/ t l) (/ t l)) 2 1)))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `sqrt-div`
2×	`sqrt-pow1`
1×	`frac-times` `pow1/2` `pow-prod-down` `associate-l/` `associate-r/` `sqrt-prod`

Counts

4 → 59

Calls

4 calls:

Slowest

33.0ms	(sqrt (* (/ 1 (* (cbrt (fma (* (/ t l) (/ t l)) 2 1)) (cbrt (fma (* (/ t l) (/ t l)) 2 1)))) (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (cbrt (fma (* (/ t l) (/ t l)) 2 1)))))
8.0ms	(cbrt (fma (* (/ t l) (/ t l)) 2 1))
2.0ms	(cbrt (fma (* (/ t l) (/ t l)) 2 1))
1.0ms	(cbrt (fma (* (/ t l) (/ t l)) 2 1))

series1.0s

Counts

4 → 12

Calls

4 calls:

Slowest

459.0ms	(sqrt (* (/ 1 (* (cbrt (fma (* (/ t l) (/ t l)) 2 1)) (cbrt (fma (* (/ t l) (/ t l)) 2 1)))) (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (cbrt (fma (* (/ t l) (/ t l)) 2 1)))))
225.0ms	(cbrt (fma (* (/ t l) (/ t l)) 2 1))
185.0ms	(cbrt (fma (* (/ t l) (/ t l)) 2 1))
174.0ms	(cbrt (fma (* (/ t l) (/ t l)) 2 1))

simplify3.8s

Counts

27 → 71

Calls

27 calls:

Slowest

378.0ms	(* (/ 1 (* (cbrt (fma (* (/ t l) (/ t l)) 2 1)) (cbrt (fma (* (/ t l) (/ t l)) 2 1)))) (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (cbrt (fma (* (/ t l) (/ t l)) 2 1))))
370.0ms	(sqrt (* 1 (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (cbrt (fma (* (/ t l) (/ t l)) 2 1)))))
349.0ms	(* (/ 1 (* (cbrt (fma (* (/ t l) (/ t l)) 2 1)) (cbrt (fma (* (/ t l) (/ t l)) 2 1)))) (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (cbrt (fma (* (/ t l) (/ t l)) 2 1))))
272.0ms	(exp (* 1/3 (- (+ (log 2) (* 2 (log (/ -1 l)))) (* 2 (log (/ -1 t))))))
233.0ms	(sqrt (* (/ 1 (* (cbrt (fma (* (/ t l) (/ t l)) 2 1)) (cbrt (fma (* (/ t l) (/ t l)) 2 1)))) (- 1 (* (/ Om Omc) (/ Om Omc)))))

prune1.3s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 4.8b

regimes673.0ms

Accuracy

98.6% (0.1b remaining)

Error of 5.4b against oracle of 5.4b and baseline of 10.3b

bsearch7.0ms

end0.0ms

sample5.3s

Algorithm

intervals

Results

2.2s	3923×	body	160	valid
1.6s	7688×	body	80	nan
940.0ms	4077×	body	80	valid