Details

sample380.0ms

Algorithm

intervals

Results

144.0ms	59×	body	1280	valid
111.0ms	57×	body	640	valid
55.0ms	190×	body	80	valid
34.0ms	30×	body	320	valid
9.0ms	14×	body	160	valid

simplify1.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	2003
4	2003
3	1174
2	189
1	54
0	19

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 17.8b

localize48.0ms

Local error

Found 4 expressions with local error:

1.8b	(* (/ t (* (/ l t) (/ l t))) (sin k))
2.4b	(/ t (* (/ l t) (/ l t)))
2.5b	(* (* (/ t (* (/ l t) (/ l t))) (sin k)) (tan k))
11.7b	(* (* (* (/ t (* (/ l t) (/ l t))) (sin k)) (tan k)) (fma (/ k t) (/ k t) 2))

rewrite853.0ms

Algorithm

rewrite-expression-head

Rules

122×	`add-cbrt-cube` `add-exp-log`
56×	`prod-exp` `cbrt-unprod`
36×	`cbrt-undiv` `div-exp`
20×	`pow1`
15×	`add-sqr-sqrt`
12×	`associate-l` `associate-*l/`
11×	`*-un-lft-identity` `add-cube-cbrt`
10×	`pow-prod-down`
9×	`associate-r`
7×	`times-frac`
6×	`associate-/r/`
4×	`expm1-log1p-u` `frac-times` `tan-quot` `associate-*r/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`-commutative` `associate-/l`
2×	`fma-udef` `div-inv` `unswap-sqr`
1×	`distribute-rgt-in` `clear-num` `associate-/r*` `frac-2neg` `distribute-lft-in`

Counts

4 → 146

Calls

4 calls:

43.0ms	(* (/ t (* (/ l t) (/ l t))) (sin k))
15.0ms	(/ t (* (/ l t) (/ l t)))
187.0ms	(* (* (/ t (* (/ l t) (/ l t))) (sin k)) (tan k))
602.0ms	(* (* (* (/ t (* (/ l t) (/ l t))) (sin k)) (tan k)) (fma (/ k t) (/ k t) 2))

series879.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(* (/ t (* (/ l t) (/ l t))) (sin k))
47.0ms	(/ t (* (/ l t) (/ l t)))
209.0ms	(* (* (/ t (* (/ l t) (/ l t))) (sin k)) (tan k))
503.0ms	(* (* (* (/ t (* (/ l t) (/ l t))) (sin k)) (tan k)) (fma (/ k t) (/ k t) 2))

simplify1.1s

Counts

158 → 158

Iterations

Iter	Nodes
done	2003
2	2003
1	672
0	235

prune2.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.3b

localize67.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt t)
2.5b	(* (* (/ (* (cbrt t) (cbrt t)) (/ l t)) (* (/ (cbrt t) (/ l t)) (sin k))) (tan k))
3.3b	(* (/ (cbrt t) (/ l t)) (sin k))
11.7b	(* (* (* (/ (* (cbrt t) (cbrt t)) (/ l t)) (* (/ (cbrt t) (/ l t)) (sin k))) (tan k)) (fma (/ k t) (/ k t) 2))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

284×	`add-exp-log`
230×	`add-cbrt-cube`
153×	`prod-exp` `cbrt-unprod`
138×	`times-frac`
93×	`add-sqr-sqrt`
85×	`associate-l`
81×	`cbrt-undiv` `div-exp`
77×	`*-un-lft-identity` `add-cube-cbrt`
44×	`cbrt-prod`
29×	`pow1`
26×	`associate-*l/`
17×	`pow-prod-down`
10×	`frac-times`
9×	`associate-r`
8×	`tan-quot`
7×	`div-inv`
6×	`associate-*r/`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`fma-udef`
1×	`distribute-rgt-in` `distribute-lft-in` `pow1/3` `associate-/r/`

Counts

4 → 263

Calls

4 calls:

1.0ms	(cbrt t)
244.0ms	(* (* (/ (* (cbrt t) (cbrt t)) (/ l t)) (* (/ (cbrt t) (/ l t)) (sin k))) (tan k))
19.0ms	(* (/ (cbrt t) (/ l t)) (sin k))
874.0ms	(* (* (* (/ (* (cbrt t) (cbrt t)) (/ l t)) (* (/ (cbrt t) (/ l t)) (sin k))) (tan k)) (fma (/ k t) (/ k t) 2))

series1.3s

Counts

4 → 12

Calls

4 calls:

276.0ms	(cbrt t)
244.0ms	(* (* (/ (* (cbrt t) (cbrt t)) (/ l t)) (* (/ (cbrt t) (/ l t)) (sin k))) (tan k))
226.0ms	(* (/ (cbrt t) (/ l t)) (sin k))
534.0ms	(* (* (* (/ (* (cbrt t) (cbrt t)) (/ l t)) (* (/ (cbrt t) (/ l t)) (sin k))) (tan k)) (fma (/ k t) (/ k t) 2))

simplify2.0s

Counts

275 → 275

Iterations

Iter	Nodes
done	2000
2	2000
1	1350
0	453

prune4.9s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 1.0b

localize42.0ms

Local error

Found 4 expressions with local error:

3.3b	(* (/ (cbrt t) (/ l t)) (sin k))
3.5b	(* (* (* (cbrt t) (cbrt t)) (* (/ (cbrt t) (/ l t)) (sin k))) (tan k))
4.4b	(/ (* (* (* (* (cbrt t) (cbrt t)) (* (/ (cbrt t) (/ l t)) (sin k))) (tan k)) (fma (/ k t) (/ k t) 2)) (/ l t))
9.5b	(* (* (* (* (cbrt t) (cbrt t)) (* (/ (cbrt t) (/ l t)) (sin k))) (tan k)) (fma (/ k t) (/ k t) 2))

rewrite1.7s

Algorithm

rewrite-expression-head

Rules

249×	`add-exp-log`
199×	`add-cbrt-cube`
169×	`times-frac`
141×	`prod-exp` `cbrt-unprod`
106×	`add-sqr-sqrt`
90×	`*-un-lft-identity` `add-cube-cbrt`
85×	`associate-l`
60×	`cbrt-undiv` `div-exp`
49×	`pow1`
41×	`cbrt-prod`
33×	`pow-prod-down`
16×	`associate-*l/`
13×	`associate-/r*`
10×	`div-inv`
9×	`associate-r` `associate-*r/`
6×	`tan-quot`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`frac-times` `*-commutative` `associate-/l/`
2×	`associate-/r/` `fma-udef`
1×	`distribute-rgt-in` `clear-num` `frac-2neg` `distribute-lft-in` `associate-/l*`

Counts

4 → 285

Calls

4 calls:

36.0ms	(* (/ (cbrt t) (/ l t)) (sin k))
218.0ms	(* (* (* (cbrt t) (cbrt t)) (* (/ (cbrt t) (/ l t)) (sin k))) (tan k))
676.0ms	(/ (* (* (* (* (cbrt t) (cbrt t)) (* (/ (cbrt t) (/ l t)) (sin k))) (tan k)) (fma (/ k t) (/ k t) 2)) (/ l t))
736.0ms	(* (* (* (* (cbrt t) (cbrt t)) (* (/ (cbrt t) (/ l t)) (sin k))) (tan k)) (fma (/ k t) (/ k t) 2))

series1.5s

Counts

4 → 12

Calls

4 calls:

206.0ms	(* (/ (cbrt t) (/ l t)) (sin k))
276.0ms	(* (* (* (cbrt t) (cbrt t)) (* (/ (cbrt t) (/ l t)) (sin k))) (tan k))
459.0ms	(/ (* (* (* (* (cbrt t) (cbrt t)) (* (/ (cbrt t) (/ l t)) (sin k))) (tan k)) (fma (/ k t) (/ k t) 2)) (/ l t))
538.0ms	(* (* (* (* (cbrt t) (cbrt t)) (* (/ (cbrt t) (/ l t)) (sin k))) (tan k)) (fma (/ k t) (/ k t) 2))

simplify1.7s

Counts

297 → 297

Iterations

Iter	Nodes
done	2010
2	2010
1	1390
0	465

prune5.0s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.7b

localize80.0ms

Local error

Found 4 expressions with local error:

4.4b	(/ (* (* (* (* (* (cbrt t) (cbrt t)) (* (/ (cbrt t) (/ l t)) (sin k))) (tan k)) (sqrt (fma (/ k t) (/ k t) 2))) (sqrt (fma (/ k t) (/ k t) 2))) (/ l t))
8.4b	(sqrt (fma (/ k t) (/ k t) 2))
8.4b	(sqrt (fma (/ k t) (/ k t) 2))
9.9b	(* (* (* (* (cbrt t) (cbrt t)) (* (/ (cbrt t) (/ l t)) (sin k))) (tan k)) (sqrt (fma (/ k t) (/ k t) 2)))

rewrite3.1s

Algorithm

rewrite-expression-head

Rules

225×	`add-exp-log`
189×	`add-cbrt-cube`
133×	`prod-exp` `cbrt-unprod`
54×	`cbrt-undiv` `div-exp`
31×	`pow1` `times-frac`
24×	`add-sqr-sqrt`
22×	`*-un-lft-identity` `add-cube-cbrt`
19×	`pow-prod-down`
15×	`associate-*l/`
13×	`associate-/r*`
9×	`sqrt-prod`
6×	`associate-r` `associate-*r/`
4×	`expm1-log1p-u` `tan-quot` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`div-inv` `associate-/l/`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`clear-num` `frac-2neg` `associate-l` `associate-/r/` `-commutative` `associate-/l`

Counts

4 → 171

Calls

4 calls:

2.3s	(/ (* (* (* (* (* (cbrt t) (cbrt t)) (* (/ (cbrt t) (/ l t)) (sin k))) (tan k)) (sqrt (fma (/ k t) (/ k t) 2))) (sqrt (fma (/ k t) (/ k t) 2))) (/ l t))
2.0ms	(sqrt (fma (/ k t) (/ k t) 2))
2.0ms	(sqrt (fma (/ k t) (/ k t) 2))
800.0ms	(* (* (* (* (cbrt t) (cbrt t)) (* (/ (cbrt t) (/ l t)) (sin k))) (tan k)) (sqrt (fma (/ k t) (/ k t) 2)))

series1.1s

Counts

4 → 12

Calls

4 calls:

539.0ms	(/ (* (* (* (* (* (cbrt t) (cbrt t)) (* (/ (cbrt t) (/ l t)) (sin k))) (tan k)) (sqrt (fma (/ k t) (/ k t) 2))) (sqrt (fma (/ k t) (/ k t) 2))) (/ l t))
55.0ms	(sqrt (fma (/ k t) (/ k t) 2))
49.0ms	(sqrt (fma (/ k t) (/ k t) 2))
450.0ms	(* (* (* (* (cbrt t) (cbrt t)) (* (/ (cbrt t) (/ l t)) (sin k))) (tan k)) (sqrt (fma (/ k t) (/ k t) 2)))

simplify1.5s

Counts

183 → 183

Iterations

Iter	Nodes
done	2002
2	2002
1	1108
0	341

prune3.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.7b

regimes609.0ms

Accuracy

42.3% (7.1b remaining)

Error of 9.4b against oracle of 2.3b and baseline of 14.6b

bsearch717.0ms

Steps

Iters	Range		Point
10	4.100102368803987e+30	5.944168512074441e+44	1.1156366225410403e+35
8	-32298.533864343164	-7.368438279267977	-9.958705001521343

simplify13.0ms

Iterations

Iter	Nodes
done	53
1	53
0	42

end0.0ms

sample14.8s

Algorithm

intervals

Results

6.5s	1983×	body	1280	valid
3.5s	1723×	body	640	valid
2.6s	5912×	body	80	valid
1.5s	848×	body	320	valid
342.0ms	437×	body	160	valid