Details

sample149.0ms

Algorithm

intervals

Results

54.0ms	117×	body	160	valid
39.0ms	252×	body	80	nan
20.0ms	139×	body	80	valid

simplify2.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	4967
5	1097
4	396
3	153
2	63
1	32
0	16

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.7b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ Om Omc) (/ Om Omc))
0.3b	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1))
0.5b	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1))))
8.8b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1)))

rewrite70.0ms

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:

31.0ms	(* (/ Om Omc) (/ Om Omc))
24.0ms	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1))
1.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1))))
9.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1)))

series325.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (/ Om Omc) (/ Om Omc))
109.0ms	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1))
15.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1))))
166.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1)))

simplify1.9s

Counts

168 → 168

Iterations

Iter	Nodes
done	5000
2	1951
1	655
0	257

prune905.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 9.6b

localize46.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma 2 (* (/ t l) (/ t l)) 1))
0.5b	(asin (sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma 2 (* (/ t l) (/ t l)) 1))))
2.7b	(log (exp (* (/ Om Omc) (/ Om Omc))))
8.8b	(sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma 2 (* (/ t l) (/ t l)) 1)))

rewrite87.0ms

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:

43.0ms	(/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma 2 (* (/ t l) (/ t l)) 1))
1.0ms	(asin (sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma 2 (* (/ t l) (/ t l)) 1))))
6.0ms	(log (exp (* (/ Om Omc) (/ Om Omc))))
32.0ms	(sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma 2 (* (/ t l) (/ t l)) 1)))

series298.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma 2 (* (/ t l) (/ t l)) 1))
16.0ms	(asin (sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma 2 (* (/ t l) (/ t l)) 1))))
33.0ms	(log (exp (* (/ Om Omc) (/ Om Omc))))
149.0ms	(sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma 2 (* (/ t l) (/ t l)) 1)))

simplify1.9s

Counts

129 → 129

Iterations

Iter	Nodes
done	5001
3	2460
2	726
1	307
0	177

prune672.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 9.6b

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (sqrt (- 1 (log (exp (* (/ Om Omc) (/ Om Omc)))))) (sqrt (fma 2 (* (/ t l) (/ t l)) 1)))
0.5b	(asin (fabs (/ (sqrt (- 1 (log (exp (* (/ Om Omc) (/ Om Omc)))))) (sqrt (fma 2 (* (/ t l) (/ t l)) 1)))))
2.7b	(log (exp (* (/ Om Omc) (/ Om Omc))))
8.9b	(sqrt (fma 2 (* (/ t l) (/ t l)) 1))

rewrite43.0ms

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:

28.0ms	(/ (sqrt (- 1 (log (exp (* (/ Om Omc) (/ Om Omc)))))) (sqrt (fma 2 (* (/ t l) (/ t l)) 1)))
1.0ms	(asin (fabs (/ (sqrt (- 1 (log (exp (* (/ Om Omc) (/ Om Omc)))))) (sqrt (fma 2 (* (/ t l) (/ t l)) 1)))))
4.0ms	(log (exp (* (/ Om Omc) (/ Om Omc))))
2.0ms	(sqrt (fma 2 (* (/ t l) (/ t l)) 1))

series297.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(/ (sqrt (- 1 (log (exp (* (/ Om Omc) (/ Om Omc)))))) (sqrt (fma 2 (* (/ t l) (/ t l)) 1)))
16.0ms	(asin (fabs (/ (sqrt (- 1 (log (exp (* (/ Om Omc) (/ Om Omc)))))) (sqrt (fma 2 (* (/ t l) (/ t l)) 1)))))
41.0ms	(log (exp (* (/ Om Omc) (/ Om Omc))))
65.0ms	(sqrt (fma 2 (* (/ t l) (/ t l)) 1))

simplify1.8s

Counts

150 → 150

Iterations

Iter	Nodes
done	5003
3	1534
2	579
1	304
0	193

prune880.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.8b

localize79.0ms

Local error

Found 4 expressions with local error:

9.0b	(sqrt (* (cbrt (fma 2 (* (/ t l) (/ t l)) 1)) (cbrt (fma 2 (* (/ t l) (/ t l)) 1))))
15.3b	(cbrt (fma 2 (* (/ t l) (/ t l)) 1))
15.3b	(cbrt (fma 2 (* (/ t l) (/ t l)) 1))
15.3b	(cbrt (fma 2 (* (/ t l) (/ t l)) 1))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

12×	`pow1`
9×	`cbrt-prod` `sqrt-pow1` `pow1/3`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `rem-sqrt-square` `pow-plus` `pow1/2` `sqrt-prod`

Counts

4 → 64

Calls

4 calls:

10.0ms	(sqrt (* (cbrt (fma 2 (* (/ t l) (/ t l)) 1)) (cbrt (fma 2 (* (/ t l) (/ t l)) 1))))
1.0ms	(cbrt (fma 2 (* (/ t l) (/ t l)) 1))
1.0ms	(cbrt (fma 2 (* (/ t l) (/ t l)) 1))
2.0ms	(cbrt (fma 2 (* (/ t l) (/ t l)) 1))

series760.0ms

Counts

4 → 12

Calls

4 calls:

192.0ms	(sqrt (* (cbrt (fma 2 (* (/ t l) (/ t l)) 1)) (cbrt (fma 2 (* (/ t l) (/ t l)) 1))))
183.0ms	(cbrt (fma 2 (* (/ t l) (/ t l)) 1))
185.0ms	(cbrt (fma 2 (* (/ t l) (/ t l)) 1))
200.0ms	(cbrt (fma 2 (* (/ t l) (/ t l)) 1))

simplify2.2s

Counts

76 → 76

Iterations

Iter	Nodes
done	5001
4	2217
3	784
2	266
1	116
0	67

prune624.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.8b

regimes673.0ms

Accuracy

96.2% (0.3b remaining)

Error of 1.3b against oracle of 0.9b and baseline of 10.1b

bsearch3.0ms

simplify10.0ms

Iterations

Iter	Nodes
done	36
1	36
0	30

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.3s	7980×	body	80	nan
876.0ms	3824×	body	160	valid
540.0ms	4176×	body	80	valid