Details

sample198.0ms

Algorithm

intervals

Results

52.0ms	26×	body	320	valid
44.0ms	59×	body	1280	valid
27.0ms	51×	body	640	valid
16.0ms	139×	body	80	valid
3.0ms	15×	body	160	valid

simplify8.0ms

Counts: 1 → 1

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
0.1b	(/ 1.0 (sin B))
0.2b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))

rewrite74.0ms

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:

33.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
6.0ms	(/ 1.0 (sin B))
6.0ms	(/ 1.0 (tan B))
21.0ms	(* x (/ 1.0 (tan B)))

series337.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
21.0ms	(/ 1.0 (sin B))
46.0ms	(/ 1.0 (tan B))
140.0ms	(* x (/ 1.0 (tan B)))

simplify45.0ms

Counts: 115 → 115

prune324.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 3 expressions with local error:

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

rewrite73.0ms

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:

54.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
11.0ms	(/ (* x 1.0) (tan B))
6.0ms	(/ 1.0 (sin B))

series281.0ms

Counts

3 → 9

Calls

3 calls:

136.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
123.0ms	(/ (* x 1.0) (tan B))
22.0ms	(/ 1.0 (sin B))

simplify33.0ms

Counts: 74 → 74

prune195.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

16.0ms	(+ (- (* 1.0 (/ (* x (cos B)) (sin B)))) (/ 1.0 (sin B)))
9.0ms	(* x (cos B))
6.0ms	(/ 1.0 (sin B))
17.0ms	(/ (* x (cos B)) (sin B))

series291.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(+ (- (* 1.0 (/ (* x (cos B)) (sin B)))) (/ 1.0 (sin B)))
45.0ms	(* x (cos B))
21.0ms	(/ 1.0 (sin B))
107.0ms	(/ (* x (cos B)) (sin B))

simplify39.0ms

Counts: 94 → 94

prune247.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (- (/ 1 (/ (tan B) (* x 1.0)))) (/ 1.0 (sin B)))
0.1b	(/ 1.0 (sin B))
0.2b	(/ (tan B) (* x 1.0))
0.3b	(/ 1 (/ (tan B) (* x 1.0)))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

47×	`times-frac`
39×	`*-un-lft-identity`
32×	`add-exp-log`
30×	`add-sqr-sqrt` `add-cube-cbrt`
20×	`add-cbrt-cube`
15×	`div-exp`
11×	`associate-/r*`
9×	`associate-/l*`
8×	`cbrt-undiv` `div-inv` `add-log-exp`
5×	`pow1`
4×	`prod-exp` `distribute-lft-out`
3×	`rec-exp` `distribute-rgt-neg-in` `frac-2neg` `1-exp` `clear-num`
2×	`sum-log` `cbrt-unprod`
1×	`tan-quot` `+-commutative` `neg-sub0` `associate-+l-` `pow-flip` `flip3-+` `neg-log` `frac-add` `associate-/r/` `flip-+` `associate-/l/` `distribute-neg-frac` `inv-pow`

Counts

4 → 123

Calls

4 calls:

96.0ms	(+ (- (/ 1 (/ (tan B) (* x 1.0)))) (/ 1.0 (sin B)))
6.0ms	(/ 1.0 (sin B))
9.0ms	(/ (tan B) (* x 1.0))
16.0ms	(/ 1 (/ (tan B) (* x 1.0)))

series320.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(+ (- (/ 1 (/ (tan B) (* x 1.0)))) (/ 1.0 (sin B)))
26.0ms	(/ 1.0 (sin B))
57.0ms	(/ (tan B) (* x 1.0))
98.0ms	(/ 1 (/ (tan B) (* x 1.0)))

simplify52.0ms

Counts: 135 → 135

prune285.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes58.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.8s	1758×	body	1280	valid
1.1s	1463×	body	640	valid
829.0ms	4847×	body	80	valid
370.0ms	728×	body	320	valid
88.0ms	391×	body	160	valid