Details

sample151.0ms

Algorithm

intervals

Results

68.0ms	62×	body	1280	valid
23.0ms	174×	body	80	valid
18.0ms	33×	body	640	valid
9.0ms	21×	body	320	valid
3.0ms	11×	body	160	valid

simplify168.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	56
6	56
5	54
4	48
3	41
2	33
1	18
0	10

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize70.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
0.1b	(/ (* x 1.0) (tan B))
0.2b	(/ 1.0 (sin B))

rewrite220.0ms

Algorithm

rewrite-expression-head

Rules

133×	`times-frac`
107×	`add-sqr-sqrt`
104×	`*-un-lft-identity` `prod-diff`
102×	`add-cube-cbrt`
24×	`div-inv`
14×	`tan-quot` `associate-/r/`
13×	`fma-neg`
10×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r*`
5×	`add-log-exp`
4×	`associate-/l*`
3×	`expm1-log1p-u` `pow1` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u`
2×	`clear-num` `frac-2neg` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `prod-exp` `frac-sub` `cbrt-unprod` `flip--` `distribute-lft-out--`

Counts

3 → 191

Calls

3 calls:

135.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
43.0ms	(/ (* x 1.0) (tan B))
15.0ms	(/ 1.0 (sin B))

series629.0ms

Counts

3 → 9

Calls

3 calls:

337.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
242.0ms	(/ (* x 1.0) (tan B))
49.0ms	(/ 1.0 (sin B))

simplify3.9s

Counts

200 → 200

Iterations

Iter	Nodes
done	5002
2	1895
1	682
0	288

prune2.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize156.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 (sin B)) (* (* (/ x (sin B)) (cos B)) 1.0))
0.1b	(/ x (sin B))
0.2b	(/ 1.0 (sin B))
0.2b	(* (/ x (sin B)) (cos B))

rewrite328.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 138

Calls

4 calls:

177.0ms	(- (/ 1.0 (sin B)) (* (* (/ x (sin B)) (cos B)) 1.0))
30.0ms	(/ x (sin B))
24.0ms	(/ 1.0 (sin B))
77.0ms	(* (/ x (sin B)) (cos B))

series699.0ms

Counts

4 → 12

Calls

4 calls:

277.0ms	(- (/ 1.0 (sin B)) (* (* (/ x (sin B)) (cos B)) 1.0))
127.0ms	(/ x (sin B))
47.0ms	(/ 1.0 (sin B))
248.0ms	(* (/ x (sin B)) (cos B))

simplify5.1s

Counts

150 → 150

Iterations

Iter	Nodes
done	5000
2	1597
1	483
0	201

prune2.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize244.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.2b	(* (/ 1.0 (tan B)) (/ x 1))
0.2b	(* (/ 1.0 (tan B)) (/ x 1))
61.2b	(fma (- (/ 1.0 (tan B))) (/ x 1) (* (/ 1.0 (tan B)) (/ x 1)))

rewrite201.0ms

Algorithm

rewrite-expression-head

Rules

74×	`add-sqr-sqrt`
59×	`times-frac`
44×	`*-un-lft-identity`
40×	`add-exp-log` `add-cube-cbrt`
30×	`add-cbrt-cube`
28×	`associate-l`
26×	`associate-r`
15×	`div-exp`
12×	`prod-exp` `unswap-sqr`
9×	`cbrt-undiv`
8×	`pow1` `cbrt-unprod`
5×	`div-inv`
4×	`expm1-log1p-u` `1-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `tan-quot` `associate-/r/` `associate-/l`
2×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`
1×	`clear-num` `frac-2neg` `fma-udef`

Counts

4 → 158

Calls

4 calls:

13.0ms	(/ 1.0 (tan B))
86.0ms	(* (/ 1.0 (tan B)) (/ x 1))
86.0ms	(* (/ 1.0 (tan B)) (/ x 1))
3.0ms	(fma (- (/ 1.0 (tan B))) (/ x 1) (* (/ 1.0 (tan B)) (/ x 1)))

series899.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(/ 1.0 (tan B))
260.0ms	(* (/ 1.0 (tan B)) (/ x 1))
241.0ms	(* (/ 1.0 (tan B)) (/ x 1))
253.0ms	(fma (- (/ 1.0 (tan B))) (/ x 1) (* (/ 1.0 (tan B)) (/ x 1)))

simplify4.2s

Counts

170 → 170

Iterations

Iter	Nodes
done	5000
2	1468
1	477
0	176

prune2.5s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize78.0ms

Local error

Found 3 expressions with local error:

0.0b	(- 1.0 (* (* x (cos B)) 1.0))
0.1b	(* x (cos B))
0.2b	(/ (- 1.0 (* (* x (cos B)) 1.0)) (sin B))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 80

Calls

3 calls:

24.0ms	(- 1.0 (* (* x (cos B)) 1.0))
39.0ms	(* x (cos B))
45.0ms	(/ (- 1.0 (* (* x (cos B)) 1.0)) (sin B))

series395.0ms

Counts

3 → 9

Calls

3 calls:

91.0ms	(- 1.0 (* (* x (cos B)) 1.0))
81.0ms	(* x (cos B))
223.0ms	(/ (- 1.0 (* (* x (cos B)) 1.0)) (sin B))

simplify11.0s

Counts

89 → 89

Iterations

Iter	Nodes
done	5000
3	4465
2	1004
1	340
0	143

prune1.2s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.0b

regimes495.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	12
1	12
0	10

end0.0ms

sample6.6s

Algorithm

intervals

Results

3.2s	1760×	body	1280	valid
1.3s	1476×	body	640	valid
1.1s	4936×	body	80	valid
445.0ms	656×	body	320	valid
213.0ms	364×	body	160	valid