Details

sample490.0ms

Algorithm

intervals

Results

144.0ms	158×	body	80	valid
131.0ms	57×	body	1280	valid
89.0ms	49×	body	640	valid
23.0ms	25×	body	320	valid
5.0ms	9×	body	160	valid

simplify130.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

129.0ms

(+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B)))

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 3 expressions with local error:

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

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
27×	`times-frac`
19×	`add-cube-cbrt`
9×	`add-exp-log`
7×	`add-cbrt-cube`
6×	`associate-/r` `associate-/l` `difference-of-squares`
5×	`add-log-exp`
4×	`pow1`
3×	`div-exp` `insert-posit16` `div-inv` `distribute-lft-out--`
2×	`cbrt-undiv` `clear-num` `frac-2neg`
1×	`rec-exp` `sub-neg` `flip3--` `diff-log` `1-exp` `tan-quot` `associate-/r/` `frac-sub` `pow-flip` `flip--` `inv-pow`

Counts

3 → 84

Calls

3 calls:

Slowest

19.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
15.0ms	(/ x (tan B))
5.0ms	(/ 1 (sin B))

series250.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

123.0ms	(/ x (tan B))
107.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
20.0ms	(/ 1 (sin B))

simplify2.0s

Counts

81 → 93

Calls

81 calls:

Slowest

385.0ms	(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
301.0ms	(/ (* (* x x) x) (* (* (tan B) (tan B)) (tan B)))
85.0ms	(/ (* (* 1 1) 1) (* (* (sin B) (sin B)) (sin B)))
79.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
74.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))

prune968.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 3 expressions with local error:

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

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
27×	`times-frac`
19×	`add-cube-cbrt`
9×	`add-exp-log`
7×	`add-cbrt-cube`
6×	`associate-/r` `associate-/l` `difference-of-squares`
5×	`add-log-exp`
4×	`pow1`
3×	`div-exp` `insert-posit16` `div-inv` `distribute-lft-out--`
2×	`cbrt-undiv` `clear-num` `frac-2neg`
1×	`rec-exp` `sub-neg` `flip3--` `diff-log` `1-exp` `tan-quot` `associate-/r/` `frac-sub` `pow-flip` `flip--` `inv-pow`

Counts

3 → 84

Calls

3 calls:

Slowest

19.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
10.0ms	(/ x (tan B))
8.0ms	(/ 1 (sin B))

series353.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

168.0ms	(/ x (tan B))
159.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
25.0ms	(/ 1 (sin B))

simplify2.3s

Counts

81 → 93

Calls

81 calls:

Slowest

427.0ms	(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
396.0ms	(/ (* (* x x) x) (* (* (tan B) (tan B)) (tan B)))
111.0ms	(/ (* (* 1 1) 1) (* (* (sin B) (sin B)) (sin B)))
96.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
93.0ms	(- (+ (* 1/6 B) (/ 1 B)) (/ x B))

prune956.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
16×	`add-cube-cbrt`
15×	`times-frac` `add-exp-log`
13×	`add-cbrt-cube`
7×	`pow1` `div-inv`
6×	`associate-/r*` `add-log-exp`
4×	`div-exp` `insert-posit16` `associate-/l*`
3×	`cbrt-undiv` `distribute-rgt-out--` `associate-r` `associate-l` `difference-of-squares`
2×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `distribute-lft-out--`
1×	`rec-exp` `sub-neg` `flip3--` `diff-log` `1-exp` `pow-prod-down` `*-commutative` `frac-sub` `pow-flip` `flip--` `inv-pow` `sub-div` `unswap-sqr`

Counts

4 → 96

Calls

4 calls:

Slowest

41.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
23.0ms	(/ (* x (cos B)) (sin B))
14.0ms	(* x (cos B))
10.0ms	(/ 1 (sin B))

series359.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

158.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
130.0ms	(/ (* x (cos B)) (sin B))
46.0ms	(* x (cos B))
25.0ms	(/ 1 (sin B))

simplify3.2s

Counts

81 → 108

Calls

81 calls:

Slowest

394.0ms	(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
372.0ms	(* (* (* x x) x) (* (* (cos B) (cos B)) (cos B)))
242.0ms	(- (* 1 (sin B)) (* (sin B) (* x (cos B))))
229.0ms	(/ (* (* (* x (cos B)) (* x (cos B))) (* x (cos B))) (* (* (sin B) (sin B)) (sin B)))
170.0ms	(/ (* (* (* x x) x) (* (* (cos B) (cos B)) (cos B))) (* (* (sin B) (sin B)) (sin B)))

prune1.6s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
16×	`add-cube-cbrt`
15×	`times-frac` `add-exp-log`
13×	`add-cbrt-cube`
7×	`pow1` `div-inv`
6×	`associate-/r*` `add-log-exp`
4×	`div-exp` `insert-posit16` `associate-/l*`
3×	`cbrt-undiv` `distribute-rgt-out--` `associate-r` `associate-l` `difference-of-squares`
2×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `distribute-lft-out--`
1×	`rec-exp` `sub-neg` `flip3--` `diff-log` `1-exp` `pow-prod-down` `*-commutative` `frac-sub` `pow-flip` `flip--` `inv-pow` `sub-div` `unswap-sqr`

Counts

4 → 96

Calls

4 calls:

Slowest

35.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
14.0ms	(/ (* x (cos B)) (sin B))
10.0ms	(/ 1 (sin B))
8.0ms	(* x (cos B))

series368.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

161.0ms	(/ (* x (cos B)) (sin B))
123.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
58.0ms	(* x (cos B))
25.0ms	(/ 1 (sin B))

simplify3.0s

Counts

81 → 108

Calls

81 calls:

Slowest

431.0ms	(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
308.0ms	(* (* (* x x) x) (* (* (cos B) (cos B)) (cos B)))
177.0ms	(- (* 1 (sin B)) (* (sin B) (* x (cos B))))
172.0ms	(/ (* (* (* x (cos B)) (* x (cos B))) (* x (cos B))) (* (* (sin B) (sin B)) (sin B)))
171.0ms	(/ (* (* (* x x) x) (* (* (cos B) (cos B)) (cos B))) (* (* (sin B) (sin B)) (sin B)))

prune1.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes120.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch2.0ms

end0.0ms

sample9.0s

Algorithm

intervals

Results

3.8s	1701×	body	1280	valid
2.1s	4890×	body	80	valid
2.0s	1462×	body	640	valid
609.0ms	729×	body	320	valid
207.0ms	361×	body	160	valid