Details

sample253.0ms

Algorithm

intervals

Results

121.0ms	68×	body	1280	valid
57.0ms	49×	body	640	valid
30.0ms	113×	body	80	valid
22.0ms	26×	body	320	valid
10.0ms	17×	body	160	valid

simplify83.0ms

Calls

1 calls:

Slowest

83.0ms

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

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize31.0ms

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)))

rewrite12.0ms

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

9.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
1.0ms	(/ 1 (sin B))
1.0ms	(/ x (tan B))

series227.0ms

Calls

3 calls:

Slowest

128.0ms	(/ x (tan B))
86.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
13.0ms	(/ 1 (sin B))

simplify211.0ms

Calls

24 calls:

Slowest

31.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
29.0ms	(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
26.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
26.0ms	(- (+ (* 1/6 B) (/ 1 B)) (/ x B))
20.0ms	(- (/ x B) (* 1/3 (* x B)))

prune457.0ms

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)))

rewrite12.0ms

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

9.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
1.0ms	(/ 1 (sin B))
1.0ms	(/ x (tan B))

series241.0ms

Calls

3 calls:

Slowest

120.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
106.0ms	(/ x (tan B))
14.0ms	(/ 1 (sin B))

simplify215.0ms

Calls

24 calls:

Slowest

31.0ms	(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
26.0ms	(- (/ x B) (* 1/3 (* x B)))
25.0ms	(/ (exp (/ 1 (sin B))) (exp (/ x (tan B))))
24.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
22.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))

prune425.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

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)))

rewrite24.0ms

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

14.0ms	(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
7.0ms	(* (/ x (sin B)) (cos B))
1.0ms	(/ 1 (sin B))
1.0ms	(/ x (sin B))

series298.0ms

Calls

4 calls:

Slowest

117.0ms	(* (/ x (sin B)) (cos B))
113.0ms	(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
55.0ms	(/ x (sin B))
13.0ms	(/ 1 (sin B))

simplify522.0ms

Calls

33 calls:

Slowest

146.0ms	(- (* 1 (sin B)) (* (sin B) (* x (cos B))))
122.0ms	(* (* (* (/ x (sin B)) (/ x (sin B))) (/ x (sin B))) (* (* (cos B) (cos B)) (cos B)))
40.0ms	(/ (exp (/ 1 (sin B))) (exp (* (/ x (sin B)) (cos B))))
32.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
31.0ms	(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))

prune558.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (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

14.0ms	(* (cbrt (- (/ 1 (sin B)) (/ x (tan B)))) (cbrt (- (/ 1 (sin B)) (/ x (tan B)))))
4.0ms	(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))))

series410.0ms

Calls

4 calls:

Slowest

108.0ms	(* (cbrt (- (/ 1 (sin B)) (/ x (tan B)))) (cbrt (- (/ 1 (sin B)) (/ x (tan B)))))
105.0ms	(cbrt (- (/ 1 (sin B)) (/ x (tan B))))
103.0ms	(cbrt (- (/ 1 (sin B)) (/ x (tan B))))
93.0ms	(cbrt (- (/ 1 (sin B)) (/ x (tan B))))

simplify7.8s

Calls

89 calls:

Slowest

340.0ms	(* (cbrt (- (* (/ 1 (sin B)) (/ 1 (sin B))) (* (/ x (tan B)) (/ x (tan B))))) (cbrt (- (* 1 (tan B)) (* (sin B) x))))
330.0ms	(* (cbrt (- (* 1 (tan B)) (* (sin B) x))) (cbrt (- (pow (/ 1 (sin B)) 3) (pow (/ x (tan B)) 3))))
311.0ms	(* (cbrt (- (pow (/ 1 (sin B)) 3) (pow (/ x (tan B)) 3))) (cbrt (- (* 1 (tan B)) (* (sin B) x))))
302.0ms	(cbrt (- (* (/ 1 (sin B)) (/ 1 (sin B))) (* (/ x (tan B)) (/ x (tan B)))))
301.0ms	(cbrt (- (* (/ 1 (sin B)) (/ 1 (sin B))) (* (/ x (tan B)) (/ x (tan B)))))

prune1.4s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0b

regimes129.0ms

Accuracy

0% (0.1b remaining)

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

bsearch1.0ms

end0.0ms

sample8.7s

Algorithm

intervals

Results

3.5s	1752×	body	1280	valid
2.2s	1426×	body	640	valid
1.5s	4898×	body	80	valid
1.1s	742×	body	320	valid
217.0ms	347×	body	160	valid