Details

sample162.0ms

Algorithm

intervals

Results

76.0ms	50×	body	1280	valid
27.0ms	173×	body	80	valid
25.0ms	39×	body	640	valid
10.0ms	26×	body	320	valid
3.0ms	10×	body	160	valid

simplify63.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	62
6	62
5	60
4	54
3	43
2	33
1	18
0	10

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize309.0ms

Local error

Found 3 expressions with local error:

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

rewrite53.0ms

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` `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 → 188

Calls

3 calls:

31.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
4.0ms	(/ 1.0 (sin B))
10.0ms	(/ (* x 1.0) (tan B))

series279.0ms

Counts

3 → 9

Calls

3 calls:

132.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
20.0ms	(/ 1.0 (sin B))
127.0ms	(/ (* x 1.0) (tan B))

simplify1.6s

Counts

197 → 197

Iterations

Iter	Nodes
done	5000
2	2707
1	680
0	285

prune1.2s

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

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 115

Calls

4 calls:

23.0ms	(- (/ 1.0 (sin B)) (* 1.0 (/ (* x (cos B)) (sin B))))
13.0ms	(/ 1.0 (sin B))
10.0ms	(/ (* x (cos B)) (sin B))
6.0ms	(* x (cos B))

series311.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(- (/ 1.0 (sin B)) (* 1.0 (/ (* x (cos B)) (sin B))))
26.0ms	(/ 1.0 (sin B))
119.0ms	(/ (* x (cos B)) (sin B))
39.0ms	(* x (cos B))

simplify1.1s

Counts

127 → 127

Iterations

Iter	Nodes
done	5001
2	1736
1	421
0	175

prune796.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 2 expressions with local error:

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

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 52

Calls

2 calls:

24.0ms	(/ (- 1.0 (* 1.0 (* x (cos B)))) (sin B))
13.0ms	(* x (cos B))

series183.0ms

Counts

2 → 6

Calls

2 calls:

127.0ms	(/ (- 1.0 (* 1.0 (* x (cos B)))) (sin B))
56.0ms	(* x (cos B))

simplify876.0ms

Counts

58 → 58

Iterations

Iter	Nodes
done	5000
2	957
1	246
0	107

prune306.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize81.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (/ 1.0 (sin B)))
0.5b	(cbrt (/ 1.0 (sin B)))
0.5b	(* (cbrt (/ 1.0 (sin B))) (cbrt (/ 1.0 (sin B))))
32.2b	(fma (- (cos B)) (/ (* x 1.0) (sin B)) (* (cos B) (/ (* x 1.0) (sin B))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

90×	`cbrt-prod`
74×	`add-sqr-sqrt`
60×	`times-frac`
50×	`*-un-lft-identity` `add-cube-cbrt`
16×	`swap-sqr` `associate-r` `associate-l`
11×	`pow1`
9×	`unswap-sqr`
8×	`pow1/3`
6×	`cbrt-div` `add-exp-log` `div-inv`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 138

Calls

4 calls:

2.0ms	(cbrt (/ 1.0 (sin B)))
2.0ms	(cbrt (/ 1.0 (sin B)))
39.0ms	(* (cbrt (/ 1.0 (sin B))) (cbrt (/ 1.0 (sin B))))
1.0ms	(fma (- (cos B)) (/ (* x 1.0) (sin B)) (* (cos B) (/ (* x 1.0) (sin B))))

series736.0ms

Counts

4 → 12

Calls

4 calls:

201.0ms	(cbrt (/ 1.0 (sin B)))
206.0ms	(cbrt (/ 1.0 (sin B)))
250.0ms	(* (cbrt (/ 1.0 (sin B))) (cbrt (/ 1.0 (sin B))))
79.0ms	(fma (- (cos B)) (/ (* x 1.0) (sin B)) (* (cos B) (/ (* x 1.0) (sin B))))

simplify1.4s

Counts

150 → 150

Iterations

Iter	Nodes
done	5000
2	1648
1	380
0	195

prune1.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes173.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	11
1	11
0	9

end0.0ms

sample6.0s

Algorithm

intervals

Results

2.0s	1734×	body	1280	valid
1.6s	1499×	body	640	valid
1.5s	4856×	body	80	valid
370.0ms	681×	body	320	valid
149.0ms	379×	body	160	valid