Details

sample240.0ms

Algorithm

intervals

Results

82.0ms	53×	body	1280	valid
59.0ms	147×	body	80	valid
57.0ms	50×	body	640	valid
16.0ms	23×	body	320	valid
10.0ms	15×	body	160	valid

simplify94.0ms

Calls

1 calls:

Slowest

94.0ms

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

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize25.0ms

Local error

Found 3 expressions with local error:

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

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

3 calls:

Slowest

8.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
1.0ms	(/ 1 (sin B))
1.0ms	(/ x (tan B))

series254.0ms

Calls

3 calls:

Slowest

125.0ms	(/ x (tan B))
112.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
17.0ms	(/ 1 (sin B))

simplify265.0ms

Calls

24 calls:

Slowest

40.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
39.0ms	(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
34.0ms	(- (+ (* 1/6 B) (/ 1 B)) (/ x B))
28.0ms	(- (/ x B) (* 1/3 (* x B)))
27.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))

prune341.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-cube-cbrt`
8×	`*-un-lft-identity`
8×	`add-sqr-sqrt`
7×	`add-exp-log`
7×	`pow1`
6×	`add-log-exp`
6×	`add-cbrt-cube`
6×	`associate-/r*`
4×	`associate-l`
3×	`div-inv`
3×	`associate-*l/`
3×	`associate-r`
2×	`frac-2neg`
2×	`clear-num`
1×	`sub-div`
1×	`inv-pow`
1×	`flip--`
1×	`pow-flip`
1×	`cbrt-unprod`
1×	`frac-sub`
1×	`*-commutative`
1×	`prod-exp`
1×	`pow-prod-down`
1×	`diff-log`
1×	`flip3--`
1×	`sub-neg`
1×	`rec-exp`

Calls

4 calls:

Slowest

6.0ms	(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
4.0ms	(* (/ x (sin B)) (cos B))
1.0ms	(/ 1 (sin B))
0.0ms	(/ x (sin B))

series229.0ms

Calls

4 calls:

Slowest

90.0ms	(* (/ x (sin B)) (cos B))
77.0ms	(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
48.0ms	(/ x (sin B))
13.0ms	(/ 1 (sin B))

simplify489.0ms

Calls

33 calls:

Slowest

107.0ms	(- (* 1 (sin B)) (* (sin B) (* x (cos B))))
103.0ms	(* (* (* (/ x (sin B)) (/ x (sin B))) (/ x (sin B))) (* (* (cos B) (cos B)) (cos B)))
41.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
33.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
32.0ms	(- (+ (* 1/6 B) (/ 1 B)) (/ x B))

prune604.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 3 expressions with local error:

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

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-cube-cbrt`
12×	`*-un-lft-identity`
12×	`add-sqr-sqrt`
9×	`times-frac`
5×	`add-exp-log`
5×	`add-cbrt-cube`
3×	`add-log-exp`
3×	`associate-/l*`
3×	`associate-r`
3×	`associate-/r*`
3×	`pow1`
2×	`associate-/l/`
2×	`flip--`
2×	`flip3--`
1×	`div-inv`
1×	`*-commutative`
1×	`div-exp`
1×	`div-sub`
1×	`frac-2neg`
1×	`sub-neg`
1×	`clear-num`
1×	`cbrt-undiv`

Calls

3 calls:

Slowest

5.0ms	(/ (- 1 (* x (cos B))) (sin B))
2.0ms	(* x (cos B))
1.0ms	(- 1 (* x (cos B)))

series137.0ms

Calls

3 calls:

Slowest

62.0ms	(/ (- 1 (* x (cos B))) (sin B))
45.0ms	(- 1 (* x (cos B)))
30.0ms	(* x (cos B))

simplify895.0ms

Calls

40 calls:

Slowest

244.0ms	(- (pow 1 3) (pow (* x (cos B)) 3))
157.0ms	(/ (* (* (- 1 (* x (cos B))) (- 1 (* x (cos B)))) (- 1 (* x (cos B)))) (* (* (sin B) (sin B)) (sin B)))
53.0ms	(- (* 1 1) (* (* x (cos B)) (* x (cos B))))
53.0ms	(/ (- 1 (* x (cos B))) (cbrt (sin B)))
42.0ms	(/ (- 1 (* x (cos B))) (sin B))

prune472.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 (sin B)) (cos B))
0.2b	(* x (* (/ 1 (sin B)) (cos B)))
0.2b	(/ 1 (sin B))
0.2b	(/ 1 (sin B))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-exp-log`
8×	`add-cube-cbrt`
8×	`*-un-lft-identity`
8×	`pow1`
8×	`add-sqr-sqrt`
6×	`add-cbrt-cube`
6×	`associate-/r*`
4×	`add-log-exp`
4×	`associate-l`
4×	`associate-r`
3×	`div-inv`
3×	`rec-exp`
2×	`inv-pow`
2×	`pow-flip`
2×	`*-commutative`
2×	`prod-exp`
2×	`associate-*l/`
2×	`frac-2neg`
2×	`clear-num`
1×	`cbrt-unprod`
1×	`associate-*r/`
1×	`pow-prod-down`

Calls

4 calls:

Slowest

8.0ms	(* (/ 1 (sin B)) (cos B))
7.0ms	(* x (* (/ 1 (sin B)) (cos B)))
1.0ms	(/ 1 (sin B))
1.0ms	(/ 1 (sin B))

series176.0ms

Calls

4 calls:

Slowest

119.0ms	(* x (* (/ 1 (sin B)) (cos B)))
29.0ms	(* (/ 1 (sin B)) (cos B))
15.0ms	(/ 1 (sin B))
13.0ms	(/ 1 (sin B))

simplify791.0ms

Calls

32 calls:

Slowest

434.0ms	(* (* (* (/ 1 (sin B)) (/ 1 (sin B))) (/ 1 (sin B))) (* (* (cos B) (cos B)) (cos B)))
138.0ms	(- (/ 1 B) (+ (* 1/3 B) (* 1/45 (pow B 3))))
52.0ms	(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
30.0ms	(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
21.0ms	(- (/ x B) (* 1/3 (* x B)))

prune640.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.0b

regimes92.0ms

Accuracy

0% (0.2b remaining)

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

bsearch1.0ms

end0.0ms

sample8.9s

Algorithm

intervals

Results

3.7s	1648×	body	1280	valid
2.1s	1414×	body	640	valid
2.0s	4970×	body	80	valid
678.0ms	757×	body	320	valid
260.0ms	368×	body	160	valid