Details

sample327.0ms

Algorithm

intervals

Results

144.0ms	63×	body	1280	valid
39.0ms	165×	body	80	valid
33.0ms	32×	body	640	valid
20.0ms	23×	body	320	valid
7.0ms	14×	body	160	valid

simplify1.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	2000
14	1959
13	1787
12	1570
11	1347
10	1172
9	1050
8	909
7	752
6	541
5	310
4	185
3	85
2	45
1	20
0	10

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (/ 1 (sin B)) (/ x (tan B)))
0.1b	(/ 1 (sin B))
0.1b	(/ x (tan B))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

279×	`times-frac`
232×	`add-sqr-sqrt`
224×	`*-un-lft-identity`
215×	`add-cube-cbrt`
182×	`prod-diff`
31×	`div-inv`
14×	`tan-quot` `associate-/r/`
13×	`fma-neg`
9×	`add-exp-log`
7×	`add-cbrt-cube`
6×	`associate-/r` `associate-/l` `difference-of-squares`
5×	`add-log-exp`
4×	`pow1`
3×	`expm1-log1p-u` `div-exp` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--`
2×	`cbrt-undiv` `clear-num` `frac-2neg`
1×	`rec-exp` `sub-neg` `flip3--` `diff-log` `1-exp` `frac-sub` `pow-flip` `flip--` `inv-pow`

Counts

3 → 285

Calls

3 calls:

30.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
5.0ms	(/ 1 (sin B))
13.0ms	(/ x (tan B))

series358.0ms

Counts

3 → 9

Calls

3 calls:

185.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
26.0ms	(/ 1 (sin B))
147.0ms	(/ x (tan B))

simplify936.0ms

Counts

294 → 294

Iterations

Iter	Nodes
done	2000
2	1990
1	848
0	381

prune933.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
0.1b	(* x (cos B))
0.1b	(/ 1 (sin B))
0.2b	(/ (* x (cos B)) (sin B))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

126×	`times-frac`
107×	`add-sqr-sqrt`
105×	`*-un-lft-identity`
98×	`add-cube-cbrt`
91×	`prod-diff`
28×	`div-inv`
15×	`add-exp-log`
13×	`add-cbrt-cube` `fma-neg`
7×	`pow1`
6×	`associate-/r*` `add-log-exp`
4×	`expm1-log1p-u` `div-exp` `insert-posit16` `log1p-expm1-u` `associate-/l*`
3×	`cbrt-undiv` `distribute-rgt-out--` `associate-r` `associate-l` `difference-of-squares`
2×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `distribute-lft-out--`
1×	`rec-exp` `sub-neg` `flip3--` `diff-log` `1-exp` `pow-prod-down` `*-commutative` `frac-sub` `pow-flip` `flip--` `inv-pow` `sub-div` `unswap-sqr`

Counts

4 → 208

Calls

4 calls:

24.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
11.0ms	(* x (cos B))
5.0ms	(/ 1 (sin B))
22.0ms	(/ (* x (cos B)) (sin B))

series391.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
66.0ms	(* x (cos B))
14.0ms	(/ 1 (sin B))
162.0ms	(/ (* x (cos B)) (sin B))

simplify1.3s

Counts

220 → 220

Iterations

Iter	Nodes
done	2000
2	1634
1	613
0	269

prune809.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (/ 1 (cbrt (sin B))) (/ 1 (cbrt (sin B))))
0.6b	(cbrt (sin B))
0.6b	(cbrt (sin B))
0.6b	(cbrt (sin B))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

129×	`add-sqr-sqrt`
112×	`times-frac`
81×	`*-un-lft-identity`
65×	`cbrt-prod`
59×	`add-cube-cbrt`
44×	`add-exp-log`
25×	`unswap-sqr`
24×	`swap-sqr`
22×	`associate-r` `associate-l`
19×	`pow1`
16×	`div-exp` `prod-exp`
14×	`pow-flip`
12×	`add-cbrt-cube`
9×	`pow1/3`
8×	`rec-exp` `1-exp` `inv-pow`
6×	`pow-prod-up` `div-inv`
4×	`expm1-log1p-u` `cbrt-undiv` `pow-prod-down` `pow-sqr` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`pow2` `frac-times` `pow-plus` `associate-l/` `associate-r/` `un-div-inv` `*-commutative`

Counts

4 → 186

Calls

4 calls:

39.0ms	(* (/ 1 (cbrt (sin B))) (/ 1 (cbrt (sin B))))
1.0ms	(cbrt (sin B))
1.0ms	(cbrt (sin B))
1.0ms	(cbrt (sin B))

series593.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(* (/ 1 (cbrt (sin B))) (/ 1 (cbrt (sin B))))
144.0ms	(cbrt (sin B))
140.0ms	(cbrt (sin B))
118.0ms	(cbrt (sin B))

simplify865.0ms

Counts

198 → 198

Iterations

Iter	Nodes
done	2006
2	1281
1	676
0	219

prune1.1s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (tan B) (* (sin B) x))
0.1b	(* (sin B) x)
0.2b	(* (sin B) (tan B))
12.7b	(/ (- (tan B) (* (sin B) x)) (* (sin B) (tan B)))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
13×	`add-cbrt-cube` `add-exp-log`
12×	`*-un-lft-identity` `add-cube-cbrt`
8×	`pow1`
6×	`associate-r` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`times-frac` `fma-neg` `prod-diff` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`cbrt-undiv` `flip3--` `div-exp` `pow-prod-down` `tan-quot` `associate-r/` `-commutative` `flip--` `unswap-sqr` `associate-/l/`
1×	`clear-num` `associate-/r*` `sub-neg` `frac-2neg` `diff-log` `div-sub` `associate-/r/` `div-inv`

Counts

4 → 92

Calls

4 calls:

11.0ms	(- (tan B) (* (sin B) x))
9.0ms	(* (sin B) x)
22.0ms	(* (sin B) (tan B))
52.0ms	(/ (- (tan B) (* (sin B) x)) (* (sin B) (tan B)))

series450.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(- (tan B) (* (sin B) x))
37.0ms	(* (sin B) x)
79.0ms	(* (sin B) (tan B))
231.0ms	(/ (- (tan B) (* (sin B) x)) (* (sin B) (tan B)))

simplify739.0ms

Counts

104 → 104

Iterations

Iter	Nodes
done	2015
2	1374
1	374
0	153

prune398.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes94.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	12
1	12
0	9

end0.0ms

sample8.4s

Algorithm

intervals

Results

3.4s	1718×	body	1280	valid
2.6s	1427×	body	640	valid
1.4s	4963×	body	80	valid
640.0ms	696×	body	320	valid
215.0ms	352×	body	160	valid