Details

sample282.0ms

Algorithm

intervals

Results

72.0ms	53×	body	1280	valid
58.0ms	147×	body	80	valid
47.0ms	50×	body	640	valid
14.0ms	23×	body	320	valid
9.0ms	15×	body	160	valid

simplify80.0ms

Calls

1 calls:

Slowest

79.0ms

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

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

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)))

rewrite10.0ms

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

5.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
2.0ms	(/ 1 (sin B))
0.0ms	(/ x (tan B))

series223.0ms

Calls

3 calls:

Slowest

109.0ms	(/ x (tan B))
89.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
25.0ms	(/ 1 (sin B))

simplify323.0ms

Calls

24 calls:

Slowest

49.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
48.0ms	(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
44.0ms	(- (+ (* 1/6 B) (/ 1 B)) (/ x B))
44.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
25.0ms	(/ (exp (/ 1 (sin B))) (exp (/ x (tan B))))

prune491.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

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)))

rewrite16.0ms

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

7.0ms	(* (/ x (sin B)) (cos B))
6.0ms	(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
1.0ms	(/ 1 (sin B))
1.0ms	(/ x (sin B))

series353.0ms

Calls

4 calls:

Slowest

135.0ms	(* (/ x (sin B)) (cos B))
113.0ms	(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
81.0ms	(/ x (sin B))
24.0ms	(/ 1 (sin B))

simplify653.0ms

Calls

33 calls:

Slowest

172.0ms	(* (* (* (/ x (sin B)) (/ x (sin B))) (/ x (sin B))) (* (* (cos B) (cos B)) (cos B)))
147.0ms	(- (* 1 (sin B)) (* (sin B) (* x (cos B))))
56.0ms	(/ (exp (/ 1 (sin B))) (exp (* (/ x (sin B)) (cos B))))
40.0ms	(- (/ x B) (* 1/3 (* x B)))
34.0ms	(+ (log (/ x (sin B))) (log (cos B)))

prune637.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

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)))

rewrite11.0ms

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

6.0ms	(/ (- 1 (* x (cos B))) (sin B))
2.0ms	(* x (cos B))
1.0ms	(- 1 (* x (cos B)))

series143.0ms

Calls

3 calls:

Slowest

72.0ms	(/ (- 1 (* x (cos B))) (sin B))
42.0ms	(- 1 (* x (cos B)))
29.0ms	(* x (cos B))

simplify981.0ms

Calls

40 calls:

Slowest

301.0ms	(- (pow 1 3) (pow (* x (cos B)) 3))
189.0ms	(/ (* (* (- 1 (* x (cos B))) (- 1 (* x (cos B)))) (- 1 (* x (cos B)))) (* (* (sin B) (sin B)) (sin B)))
48.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
47.0ms	(/ (- 1 (* x (cos B))) (sin B))
45.0ms	(/ (- 1 (* x (cos B))) (cbrt (sin B)))

prune585.0ms

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

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

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

series207.0ms

Calls

4 calls:

Slowest

100.0ms	(* (* x (/ 1 (sin B))) (cos B))
61.0ms	(* x (/ 1 (sin B)))
23.0ms	(/ 1 (sin B))
22.0ms	(/ 1 (sin B))

simplify607.0ms

Calls

34 calls:

Slowest

325.0ms	(* (* (* (* x (/ 1 (sin B))) (* x (/ 1 (sin B)))) (* x (/ 1 (sin B)))) (* (* (cos B) (cos B)) (cos B)))
56.0ms	(+ (log (* x (/ 1 (sin B)))) (log (cos B)))
50.0ms	(* (* x (/ 1 (sin B))) (cos B))
33.0ms	(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
31.0ms	(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))

prune635.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.0b

regimes107.0ms

Accuracy

0% (0.2b remaining)

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

bsearch2.0ms

end0.0ms

sample8.8s

Algorithm

intervals

Results

3.3s	1648×	body	1280	valid
2.7s	1414×	body	640	valid
1.6s	4970×	body	80	valid
761.0ms	757×	body	320	valid
238.0ms	368×	body	160	valid