Details

sample119.0ms

Algorithm

intervals

Results

56.0ms	53×	body	1280	valid
20.0ms	39×	body	640	valid
18.0ms	157×	body	80	valid
9.0ms	24×	body	320	valid
2.0ms	10×	body	160	valid

simplify48.0ms

Counts: 1 → 1

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
0.1b	(/ 1.0 (tan B))
0.1b	(/ 1.0 (sin B))
0.3b	(* x (/ 1.0 (tan B)))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
28×	`add-cube-cbrt` `times-frac`
14×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
6×	`pow1` `associate-/r` `associate-/l`
3×	`cbrt-undiv` `div-exp` `associate-l` `div-inv`
2×	`tan-quot` `frac-2neg` `associate-*r/` `prod-exp` `clear-num` `sum-log` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `neg-sub0` `associate-+l-` `flip3-+` `pow-prod-down` `neg-log` `frac-add` `*-commutative` `flip-+` `distribute-neg-frac` `distribute-lft-out`

Counts

4 → 103

Calls

4 calls:

25.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
11.0ms	(/ 1.0 (tan B))
32.0ms	(/ 1.0 (sin B))
28.0ms	(* x (/ 1.0 (tan B)))

series349.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
46.0ms	(/ 1.0 (tan B))
31.0ms	(/ 1.0 (sin B))
150.0ms	(* x (/ 1.0 (tan B)))

simplify640.0ms

Counts: 115 → 115

prune435.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 3 expressions with local error:

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

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
13×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
7×	`add-log-exp`
6×	`associate-/r*`
4×	`associate-/l*`
3×	`pow1` `cbrt-undiv` `div-exp`
2×	`frac-2neg` `clear-num` `sum-log` `div-inv` `distribute-lft-out`
1×	`tan-quot` `+-commutative` `neg-sub0` `associate-+l-` `distribute-rgt-neg-in` `flip3-+` `neg-log` `frac-add` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+` `distribute-neg-frac`

Counts

3 → 65

Calls

3 calls:

87.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
9.0ms	(/ 1.0 (sin B))
18.0ms	(/ (* x 1.0) (tan B))

series268.0ms

Counts

3 → 9

Calls

3 calls:

125.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
22.0ms	(/ 1.0 (sin B))
121.0ms	(/ (* x 1.0) (tan B))

simplify476.0ms

Counts: 74 → 74

prune198.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-exp-log` `add-cbrt-cube`
19×	`add-sqr-sqrt` `*-un-lft-identity`
17×	`add-cube-cbrt`
15×	`times-frac`
8×	`add-log-exp`
7×	`associate-l`
6×	`pow1` `associate-/r*`
5×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
4×	`associate-/l*`
3×	`associate-r` `div-inv`
2×	`frac-2neg` `associate-*l/` `clear-num` `sum-log`
1×	`+-commutative` `neg-sub0` `associate-+l-` `flip3-+` `pow-prod-down` `neg-log` `frac-add` `*-commutative` `flip-+` `distribute-neg-frac` `distribute-lft-out` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

22.0ms	(+ (- (* (/ (* x 1.0) (sin B)) (cos B))) (/ 1.0 (sin B)))
6.0ms	(/ 1.0 (sin B))
11.0ms	(/ (* x 1.0) (sin B))
26.0ms	(* (/ (* x 1.0) (sin B)) (cos B))

series387.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(+ (- (* (/ (* x 1.0) (sin B)) (cos B))) (/ 1.0 (sin B)))
32.0ms	(/ 1.0 (sin B))
81.0ms	(/ (* x 1.0) (sin B))
136.0ms	(* (/ (* x 1.0) (sin B)) (cos B))

simplify971.0ms

Counts: 102 → 102

prune382.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
16×	`add-cube-cbrt`
15×	`add-exp-log` `times-frac`
13×	`add-cbrt-cube`
7×	`pow1` `div-inv`
6×	`associate-/r*` `add-log-exp`
4×	`div-exp` `associate-/l*`
3×	`cbrt-undiv` `distribute-rgt-out--` `associate-r` `associate-l` `difference-of-squares`
2×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `distribute-lft-out--`
1×	`sub-neg` `rec-exp` `flip3--` `pow-flip` `diff-log` `1-exp` `pow-prod-down` `*-commutative` `frac-sub` `flip--` `inv-pow` `sub-div` `unswap-sqr`

Counts

4 → 92

Calls

4 calls:

54.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
7.0ms	(/ 1 (sin B))
9.0ms	(* x (cos B))
19.0ms	(/ (* x (cos B)) (sin B))

series309.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
28.0ms	(/ 1 (sin B))
49.0ms	(* x (cos B))
126.0ms	(/ (* x (cos B)) (sin B))

simplify564.0ms

Counts: 104 → 104

prune341.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes78.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify5.2s

end0.0ms

sample6.7s

Algorithm

intervals

Results

3.1s	1741×	body	1280	valid
1.7s	1384×	body	640	valid
891.0ms	4950×	body	80	valid
441.0ms	713×	body	320	valid
157.0ms	351×	body	160	valid