Details

sample360.0ms

Algorithm

intervals

Results

187.0ms	68×	body	1280	valid
54.0ms	49×	body	640	valid
33.0ms	113×	body	80	valid
18.0ms	26×	body	320	valid
9.0ms	17×	body	160	valid

simplify478.0ms

Calls

1 calls:

Slowest

477.0ms

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

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize25.0ms

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)))

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)))
3.0ms	(/ x (tan B))
1.0ms	(/ 1 (sin B))

series335.0ms

Calls

3 calls:

Slowest

168.0ms	(/ x (tan B))
144.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
24.0ms	(/ 1 (sin B))

simplify235.0ms

Calls

24 calls:

Slowest

38.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
36.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
33.0ms	(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
26.0ms	(- (/ x B) (* 1/3 (* x B)))
21.0ms	(/ (exp (/ 1 (sin B))) (exp (/ x (tan B))))

prune522.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize1.0ms

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)))

rewrite13.0ms

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

10.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
2.0ms	(/ 1 (sin B))
1.0ms	(/ x (tan B))

series263.0ms

Calls

3 calls:

Slowest

136.0ms	(/ x (tan B))
105.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
22.0ms	(/ 1 (sin B))

simplify247.0ms

Calls

24 calls:

Slowest

36.0ms	(- (/ x B) (* 1/3 (* x B)))
28.0ms	(- (+ (* 1/6 B) (/ 1 B)) (/ x B))
27.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
26.0ms	(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
24.0ms	(/ (exp (/ 1 (sin B))) (exp (/ x (tan B))))

prune514.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite19.0ms

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

12.0ms	(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
4.0ms	(* (/ x (sin B)) (cos B))
1.0ms	(/ 1 (sin B))
1.0ms	(/ x (sin B))

series337.0ms

Calls

4 calls:

Slowest

145.0ms	(* (/ x (sin B)) (cos B))
102.0ms	(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
66.0ms	(/ x (sin B))
23.0ms	(/ 1 (sin B))

simplify679.0ms

Calls

33 calls:

Slowest

164.0ms	(* (* (* (/ x (sin B)) (/ x (sin B))) (/ x (sin B))) (* (* (cos B) (cos B)) (cos B)))
149.0ms	(- (* 1 (sin B)) (* (sin B) (* x (cos B))))
54.0ms	(/ (exp (/ 1 (sin B))) (exp (* (/ x (sin B)) (cos B))))
49.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
47.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))

prune690.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (- (/ 1 (sin B)) (/ x (tan B)))) (cbrt (- (/ 1 (sin B)) (/ x (tan B)))))
0.5b	(cbrt (- (/ 1 (sin B)) (/ x (tan B))))
0.5b	(cbrt (- (/ 1 (sin B)) (/ x (tan B))))
0.5b	(cbrt (- (/ 1 (sin B)) (/ x (tan B))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

33×	`cbrt-div`
30×	`cbrt-prod`
26×	`*-un-lft-identity`
21×	`add-sqr-sqrt`
11×	`flip--`
11×	`add-cube-cbrt`
11×	`frac-sub`
11×	`flip3--`
10×	`distribute-lft-out--`
9×	`associate-l`
9×	`associate-r`
9×	`pow1`
9×	`frac-times`
7×	`pow1/3`
6×	`add-exp-log`
5×	`difference-of-squares`
5×	`div-inv`
4×	`add-log-exp`
4×	`add-cbrt-cube`
3×	`associate-*r/`
3×	`associate-*l/`
2×	`pow-prod-up`
2×	`pow-prod-down`
1×	`cbrt-unprod`
1×	`*-commutative`
1×	`prod-exp`
1×	`pow-plus`
1×	`pow2`

Calls

4 calls:

Slowest

15.0ms	(* (cbrt (- (/ 1 (sin B)) (/ x (tan B)))) (cbrt (- (/ 1 (sin B)) (/ x (tan B)))))
4.0ms	(cbrt (- (/ 1 (sin B)) (/ x (tan B))))
3.0ms	(cbrt (- (/ 1 (sin B)) (/ x (tan B))))
3.0ms	(cbrt (- (/ 1 (sin B)) (/ x (tan B))))

series576.0ms

Calls

4 calls:

Slowest

161.0ms	(* (cbrt (- (/ 1 (sin B)) (/ x (tan B)))) (cbrt (- (/ 1 (sin B)) (/ x (tan B)))))
150.0ms	(cbrt (- (/ 1 (sin B)) (/ x (tan B))))
138.0ms	(cbrt (- (/ 1 (sin B)) (/ x (tan B))))
127.0ms	(cbrt (- (/ 1 (sin B)) (/ x (tan B))))

simplify8.0s

Calls

89 calls:

Slowest

359.0ms	(* (cbrt (- (* 1 (tan B)) (* (sin B) x))) (cbrt (- (pow (/ 1 (sin B)) 3) (pow (/ x (tan B)) 3))))
325.0ms	(* (cbrt (+ (/ 1 (sin B)) (/ x (tan B)))) (cbrt (+ (* (/ 1 (sin B)) (/ 1 (sin B))) (+ (* (/ x (tan B)) (/ x (tan B))) (* (/ 1 (sin B)) (/ x (tan B)))))))
309.0ms	(* (cbrt (- (pow (/ 1 (sin B)) 3) (pow (/ x (tan B)) 3))) (cbrt (- (* 1 (tan B)) (* (sin B) x))))
296.0ms	(- (exp (* 1/3 (- (log (/ (pow (cos B) 2) (pow (sin B) 2))) (* 2 (log (/ -1 x)))))) (+ (* 2/3 (/ (exp (* 1/3 (- (log (/ (pow (cos B) 2) (pow (sin B) 2))) (* 2 (log (/ -1 x)))))) (* x (cos B)))) (* 1/9 (/ (exp (* 1/3 (- (log (/ (pow (cos B) 2) (pow (sin B) 2))) (* 2 (log (/ -1 x)))))) (* (pow x 2) (pow (cos B) 2))))))
278.0ms	(cbrt (- (* (/ 1 (sin B)) (/ 1 (sin B))) (* (/ x (tan B)) (/ x (tan B)))))

prune1.3s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0b

regimes161.0ms

Accuracy

0% (0.1b remaining)

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

bsearch1.0ms

end0.0ms

sample8.6s

Algorithm

intervals

Results

3.4s	1752×	body	1280	valid
2.7s	1426×	body	640	valid
1.5s	4898×	body	80	valid
701.0ms	742×	body	320	valid
183.0ms	347×	body	160	valid