Details

sample88.0ms

Algorithm

intervals

Results

38.0ms	61×	body	1280	valid
19.0ms	56×	body	640	valid
11.0ms	149×	body	80	valid
5.0ms	20×	body	320	valid
1.0ms	9×	body	160	valid

simplify12.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	18	7
1	33	6
2	43	6
3	54	6
4	60	6
5	62	6
6	62	6
done	62	6

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma (- x) (/ 1.0 (tan B)) (/ 1.0 (sin B)))
0.1b	(/ 1.0 (sin B))
0.1b	(/ 1.0 (tan B))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r` `associate-/l`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`
1×	`tan-quot` `associate-/r/` `fma-udef`

Counts

3 → 69

Calls

3 calls:

0.0ms	(fma (- x) (/ 1.0 (tan B)) (/ 1.0 (sin B)))
6.0ms	(/ 1.0 (sin B))
6.0ms	(/ 1.0 (tan B))

series162.0ms

Counts

3 → 9

Calls

3 calls:

102.0ms	(fma (- x) (/ 1.0 (tan B)) (/ 1.0 (sin B)))
23.0ms	(/ 1.0 (sin B))
36.0ms	(/ 1.0 (tan B))

simplify55.0ms

Counts

78 → 78

Iterations

Useful iterations: 3 (51.0ms)

Iter	Nodes	Cost
0	246	416
1	694	382
2	2127	382
3	5002	377
done	5002	377

prune245.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1.0 (sin B))
0.1b	(* x (cos B))
0.1b	(* (/ 1.0 (sin B)) (- 1 (* x (cos B))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
23×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
16×	`associate-l`
12×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`associate-r` `prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in`
3×	`expm1-log1p-u` `prod-exp` `associate-/r` `cbrt-unprod` `log1p-expm1-u` `associate-/l` `add-log-exp` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `sub-neg` `flip3--` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `flip--` `div-inv`
1×	`frac-2neg` `associate-*l/` `clear-num`

Counts

3 → 97

Calls

3 calls:

5.0ms	(/ 1.0 (sin B))
8.0ms	(* x (cos B))
32.0ms	(* (/ 1.0 (sin B)) (- 1 (* x (cos B))))

series134.0ms

Counts

3 → 9

Calls

3 calls:

19.0ms	(/ 1.0 (sin B))
36.0ms	(* x (cos B))
80.0ms	(* (/ 1.0 (sin B)) (- 1 (* x (cos B))))

simplify52.0ms

Counts

106 → 106

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	415	714
1	2101	633
2	5001	629
done	5001	629

prune241.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 2 expressions with local error:

0.1b	(* x (cos B))
0.2b	(/ (* 1.0 (- 1 (* x (cos B)))) (sin B))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 45

Calls

2 calls:

8.0ms	(* x (cos B))
18.0ms	(/ (* 1.0 (- 1 (* x (cos B)))) (sin B))

series123.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(* x (cos B))
81.0ms	(/ (* 1.0 (- 1 (* x (cos B)))) (sin B))

simplify35.0ms

Counts

51 → 51

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	248	316
1	1125	266
2	5001	263
done	5001	263

prune128.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (cos B)) (cbrt (cos B)))
0.4b	(cbrt (cos B))
0.4b	(cbrt (cos B))
0.4b	(cbrt (cos B))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `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 → 81

Calls

4 calls:

13.0ms	(* (cbrt (cos B)) (cbrt (cos B)))
1.0ms	(cbrt (cos B))
1.0ms	(cbrt (cos B))
1.0ms	(cbrt (cos B))

series457.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(* (cbrt (cos B)) (cbrt (cos B)))
97.0ms	(cbrt (cos B))
97.0ms	(cbrt (cos B))
103.0ms	(cbrt (cos B))

simplify99.0ms

Counts

93 → 93

Iterations

Useful iterations: 3 (94.0ms)

Iter	Nodes	Cost
0	128	471
1	498	419
2	3230	387
3	5002	381
done	5002	381

prune255.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes65.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	6
1	14	6
done	14	6

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.0s	1753×	body	1280	valid
518.0ms	1484×	body	640	valid
386.0ms	4893×	body	80	valid
176.0ms	713×	body	320	valid
56.0ms	343×	body	160	valid