Details

sample359.0ms

Algorithm

intervals

Results

127.0ms	55×	body	1280	valid
65.0ms	165×	body	80	valid
62.0ms	50×	body	640	valid
19.0ms	21×	body	320	valid
8.0ms	14×	body	160	valid

simplify508.0ms

Calls

1 calls:

Slowest

507.0ms

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

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize35.0ms

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)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

20×	`prod-diff`
18×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
13×	`div-inv`
6×	`associate-/r*`
5×	`add-log-exp`
5×	`associate-/r/`
5×	`tan-quot`
4×	`add-exp-log`
4×	`fma-neg`
4×	`pow1`
3×	`log1p-expm1-u`
3×	`add-cbrt-cube`
3×	`expm1-log1p-u`
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×	`diff-log`
1×	`flip3--`
1×	`sub-neg`
1×	`rec-exp`

Calls

3 calls:

Slowest

12.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
3.0ms	(/ x (tan B))
2.0ms	(/ 1 (sin B))

series308.0ms

Calls

3 calls:

Slowest

147.0ms	(/ x (tan B))
138.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
23.0ms	(/ 1 (sin B))

simplify1.6s

Calls

66 calls:

Slowest

61.0ms	(fma 1 (/ 1 (sin B)) (- (* (/ 1 (tan B)) x)))
59.0ms	(fma (* (cbrt (/ 1 (sin B))) (cbrt (/ 1 (sin B)))) (cbrt (/ 1 (sin B))) (- (* (/ 1 (tan B)) x)))
59.0ms	(fma (sqrt (/ 1 (sin B))) (sqrt (/ 1 (sin B))) (- (* (cos B) (/ x (sin B)))))
58.0ms	(fma (sqrt (/ 1 (sin B))) (sqrt (/ 1 (sin B))) (- (* (/ 1 (tan B)) x)))
56.0ms	(fma 1 (/ 1 (sin B)) (- (* (/ x (tan B)) 1)))

prune742.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (/ (tan B) x))
0.1b	(/ 1 (sin B))
0.1b	(/ (tan B) x)
0.0b	(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
20×	`prod-diff`
19×	`add-sqr-sqrt`
18×	`div-inv`
17×	`add-cube-cbrt`
7×	`associate-/r*`
6×	`add-log-exp`
6×	`add-exp-log`
6×	`pow1`
5×	`associate-/r/`
4×	`distribute-lft-out--`
4×	`log1p-expm1-u`
4×	`fma-neg`
4×	`add-cbrt-cube`
4×	`expm1-log1p-u`
3×	`associate-/l*`
3×	`frac-2neg`
3×	`clear-num`
2×	`inv-pow`
2×	`pow-flip`
2×	`rec-exp`
1×	`associate-/l/`
1×	`difference-of-squares`
1×	`flip--`
1×	`frac-sub`
1×	`tan-quot`
1×	`diff-log`
1×	`flip3--`
1×	`sub-neg`

Calls

4 calls:

Slowest

11.0ms	(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
5.0ms	(/ (tan B) x)
2.0ms	(/ 1 (sin B))
1.0ms	(/ 1 (/ (tan B) x))

series287.0ms

Calls

4 calls:

Slowest

148.0ms	(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
81.0ms	(/ 1 (/ (tan B) x))
44.0ms	(/ (tan B) x)
13.0ms	(/ 1 (sin B))

simplify2.9s

Calls

75 calls:

Slowest

90.0ms	(fma (* (cbrt (/ 1 (sin B))) (cbrt (/ 1 (sin B)))) (cbrt (/ 1 (sin B))) (- (* x (/ 1 (tan B)))))
88.0ms	(fma (- (/ 1 (/ (tan B) x))) 1 (* (/ 1 (/ (tan B) x)) 1))
83.0ms	(fma (* (cbrt (/ 1 (sin B))) (cbrt (/ 1 (sin B)))) (cbrt (/ 1 (sin B))) (- (* (/ 1 (/ (tan B) x)) 1)))
83.0ms	(fma (- (/ 1 (/ (tan B) x))) 1 (* (/ 1 (/ (tan B) x)) 1))
80.0ms	(fma 1 (/ 1 (sin B)) (- (* (/ 1 (/ (tan B) x)) 1)))

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

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)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-cube-cbrt`
10×	`*-un-lft-identity`
10×	`add-sqr-sqrt`
7×	`add-exp-log`
7×	`pow1`
6×	`add-log-exp`
6×	`add-cbrt-cube`
6×	`associate-/r*`
5×	`div-inv`
4×	`log1p-expm1-u`
4×	`prod-diff`
4×	`associate-l`
4×	`fma-neg`
4×	`expm1-log1p-u`
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)))
8.0ms	(* (/ x (sin B)) (cos B))
1.0ms	(/ 1 (sin B))
1.0ms	(/ x (sin B))

series292.0ms

Calls

4 calls:

Slowest

106.0ms	(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
103.0ms	(* (/ x (sin B)) (cos B))
70.0ms	(/ x (sin B))
13.0ms	(/ 1 (sin B))

simplify1.0s

Calls

43 calls:

Slowest

150.0ms	(- (* 1 (sin B)) (* (sin B) (* x (cos B))))
146.0ms	(* (* (* (/ x (sin B)) (/ x (sin B))) (/ x (sin B))) (* (* (cos B) (cos B)) (cos B)))
75.0ms	(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
52.0ms	(fma (- (cos B)) (/ x (sin B)) (* (cos B) (/ x (sin B))))
52.0ms	(fma (- (cos B)) (/ x (sin B)) (* (cos B) (/ x (sin B))))

prune884.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan B) (/ 1 x))
0.3b	(/ 1 (* (tan B) (/ 1 x)))
0.1b	(/ 1 (sin B))
0.0b	(- (/ 1 (sin B)) (/ 1 (* (tan B) (/ 1 x))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

32×	`prod-diff`
24×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
20×	`div-inv`
20×	`add-cube-cbrt`
20×	`associate-/r/`
12×	`tan-quot`
10×	`add-exp-log`
10×	`pow1`
6×	`add-log-exp`
6×	`un-div-inv`
6×	`associate-*r/`
6×	`associate-*l/`
6×	`add-cbrt-cube`
6×	`frac-times`
4×	`distribute-lft-out--`
4×	`log1p-expm1-u`
4×	`associate-r`
4×	`fma-neg`
4×	`associate-/r*`
4×	`expm1-log1p-u`
3×	`pow-flip`
3×	`associate-l`
3×	`rec-exp`
2×	`inv-pow`
2×	`prod-exp`
2×	`pow-prod-down`
2×	`frac-2neg`
2×	`clear-num`
1×	`difference-of-squares`
1×	`flip--`
1×	`cbrt-unprod`
1×	`frac-sub`
1×	`*-commutative`
1×	`diff-log`
1×	`flip3--`
1×	`sub-neg`

Calls

4 calls:

Slowest

11.0ms	(- (/ 1 (sin B)) (/ 1 (* (tan B) (/ 1 x))))
7.0ms	(* (tan B) (/ 1 x))
6.0ms	(/ 1 (* (tan B) (/ 1 x)))
2.0ms	(/ 1 (sin B))

series222.0ms

Calls

4 calls:

Slowest

85.0ms	(- (/ 1 (sin B)) (/ 1 (* (tan B) (/ 1 x))))
68.0ms	(/ 1 (* (tan B) (/ 1 x)))
49.0ms	(* (tan B) (/ 1 x))
19.0ms	(/ 1 (sin B))

simplify11.6s

Calls

108 calls:

Slowest

607.0ms	(fma 1 (/ 1 (sin B)) (- (* (cos B) (/ 1 (* (sin B) (/ 1 x))))))
567.0ms	(fma 1 (/ 1 (sin B)) (- (* (cos B) (/ 1 (* (sin B) (/ 1 x))))))
565.0ms	(fma (* (cbrt (/ 1 (sin B))) (cbrt (/ 1 (sin B)))) (cbrt (/ 1 (sin B))) (- (* (* (cos B) x) (/ 1 (* (sin B) 1)))))
515.0ms	(fma (- (* (cos B) x)) (/ 1 (* (sin B) 1)) (* (* (cos B) x) (/ 1 (* (sin B) 1))))
444.0ms	(fma (- (* (cos B) x)) (/ 1 (* (sin B) 1)) (* (* (cos B) x) (/ 1 (* (sin B) 1))))

prune1.3s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes119.0ms

Accuracy

0% (0.2b remaining)

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

bsearch2.0ms

end0.0ms

sample9.0s

Algorithm

intervals

Results

3.2s	1688×	body	1280	valid
3.2s	1453×	body	640	valid
1.5s	4931×	body	80	valid
734.0ms	756×	body	320	valid
198.0ms	355×	body	160	valid