Details

sample415.0ms

Algorithm

intervals

Results

150.0ms	46×	body	1280	valid
73.0ms	53×	body	640	valid
48.0ms	152×	body	80	valid
20.0ms	20×	body	320	valid
11.0ms	15×	body	160	valid

simplify1.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	2000
15	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

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize31.0ms

Local error

Found 3 expressions with local error:

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

rewrite102.0ms

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:

64.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
12.0ms	(/ 1 (sin B))
14.0ms	(/ x (tan B))

series375.0ms

Counts

3 → 9

Calls

3 calls:

165.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
19.0ms	(/ 1 (sin B))
189.0ms	(/ x (tan B))

simplify1.3s

Counts

294 → 294

Iterations

Iter	Nodes
done	2011
3	2011
2	1990
1	848
0	381

prune3.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

1390×	`times-frac`
881×	`add-sqr-sqrt`
855×	`*-un-lft-identity`
834×	`add-cube-cbrt`
572×	`prod-diff`
108×	`div-inv`
21×	`add-exp-log`
19×	`associate-/r*`
15×	`difference-of-squares`
14×	`associate-/r/`
13×	`add-cbrt-cube` `fma-neg`
10×	`div-exp`
9×	`associate-/l*`
7×	`distribute-lft-out--`
6×	`pow1` `add-log-exp`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`rec-exp` `clear-num` `frac-2neg` `1-exp`
2×	`pow-flip` `inv-pow`
1×	`sub-neg` `flip3--` `diff-log` `tan-quot` `frac-sub` `flip--` `associate-/l/`

Counts

4 → 767

Calls

4 calls:

50.0ms	(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
7.0ms	(/ (tan B) x)
6.0ms	(/ 1 (sin B))
7.0ms	(/ 1 (/ (tan B) x))

series370.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
71.0ms	(/ (tan B) x)
26.0ms	(/ 1 (sin B))
141.0ms	(/ 1 (/ (tan B) x))

simplify1.5s

Counts

779 → 779

Iterations

Iter	Nodes
done	2000
1	2000
0	961

prune12.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt x) (cbrt x))
0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 85

Calls

4 calls:

13.0ms	(* (cbrt x) (cbrt x))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series1.1s

Counts

4 → 12

Calls

4 calls:

249.0ms	(* (cbrt x) (cbrt x))
282.0ms	(cbrt x)
283.0ms	(cbrt x)
324.0ms	(cbrt x)

simplify1.0s

Counts

97 → 97

Iterations

Iter	Nodes
done	2002
4	2002
3	1106
2	364
1	141
0	67

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize56.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (sin B))
0.7b	(cbrt (sin B))
0.7b	(cbrt (sin B))
35.0b	(fma (- (cos B)) (/ x (sin B)) (* (cos B) (/ x (sin B))))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 53

Calls

4 calls:

1.0ms	(cbrt (sin B))
1.0ms	(cbrt (sin B))
2.0ms	(cbrt (sin B))
0.0ms	(fma (- (cos B)) (/ x (sin B)) (* (cos B) (/ x (sin B))))

series554.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(cbrt (sin B))
142.0ms	(cbrt (sin B))
167.0ms	(cbrt (sin B))
100.0ms	(fma (- (cos B)) (/ x (sin B)) (* (cos B) (/ x (sin B))))

simplify1.1s

Counts

65 → 65

Iterations

Iter	Nodes
done	2000
4	2000
3	594
2	214
1	95
0	51

prune1.1s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes155.0ms

Accuracy

0% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 0.6b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	14
1	14
0	11

end0.0ms

sample8.0s

Algorithm

intervals

Results

3.4s	1688×	body	1280	valid
1.8s	1462×	body	640	valid
1.8s	4846×	body	80	valid
604.0ms	729×	body	320	valid
172.0ms	336×	body	160	valid