Details

sample535.0ms

Algorithm

intervals

Results

129.0ms	68×	body	1280	valid
103.0ms	49×	body	640	valid
39.0ms	113×	body	80	valid
23.0ms	26×	body	320	valid
11.0ms	17×	body	160	valid

simplify113.0ms

Calls

1 calls:

Slowest

113.0ms

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

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize32.0ms

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)))

rewrite28.0ms

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

11.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
3.0ms	(/ x (tan B))
2.0ms	(/ 1 (sin B))

series309.0ms

Calls

3 calls:

Slowest

164.0ms	(/ x (tan B))
120.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
24.0ms	(/ 1 (sin B))

simplify1.9s

Calls

66 calls:

Slowest

90.0ms	(fma 1 (/ 1 (sin B)) (- (* (/ 1 (tan B)) x)))
90.0ms	(fma 1 (/ 1 (sin B)) (- (* (/ 1 (tan B)) x)))
72.0ms	(fma (sqrt (/ 1 (sin B))) (sqrt (/ 1 (sin B))) (- (* (/ 1 (tan B)) x)))
65.0ms	(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
60.0ms	(fma (* (cbrt (/ 1 (sin B))) (cbrt (/ 1 (sin B)))) (cbrt (/ 1 (sin B))) (- (* (/ 1 (tan B)) x)))

prune867.0ms

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

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

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

series273.0ms

Calls

3 calls:

Slowest

138.0ms	(/ x (tan B))
115.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
20.0ms	(/ 1 (sin B))

simplify1.7s

Calls

66 calls:

Slowest

91.0ms	(fma (* (cbrt (/ 1 (sin B))) (cbrt (/ 1 (sin B)))) (cbrt (/ 1 (sin B))) (- (* (/ 1 (tan B)) x)))
91.0ms	(fma 1 (/ 1 (sin B)) (- (* (/ 1 (tan B)) x)))
82.0ms	(fma (sqrt (/ 1 (sin B))) (sqrt (/ 1 (sin B))) (- (* (/ 1 (tan B)) x)))
70.0ms	(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
53.0ms	(fma 1 (/ 1 (sin B)) (- (* (/ 1 (tan B)) x)))

prune678.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 3 expressions with local error:

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

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-cube-cbrt`
13×	`*-un-lft-identity`
13×	`add-sqr-sqrt`
12×	`times-frac`
6×	`add-exp-log`
6×	`associate-/r*`
5×	`add-cbrt-cube`
4×	`associate-/l*`
4×	`neg-mul-1`
4×	`pow1`
3×	`add-log-exp`
3×	`log1p-expm1-u`
3×	`expm1-log1p-u`
2×	`div-inv`
2×	`frac-2neg`
2×	`clear-num`
1×	`inv-pow`
1×	`pow-flip`
1×	`fma-udef`
1×	`distribute-frac-neg`
1×	`div-exp`
1×	`div-sub`
1×	`rec-exp`
1×	`cbrt-undiv`
1×	`neg-sub0`

Calls

3 calls:

Slowest

3.0ms	(/ (- x) (sin B))
1.0ms	(/ 1 (sin B))
0.0ms	(fma (cos B) (/ (- x) (sin B)) (/ 1 (sin B)))

series179.0ms

Calls

3 calls:

Slowest

95.0ms	(fma (cos B) (/ (- x) (sin B)) (/ 1 (sin B)))
62.0ms	(/ (- x) (sin B))
22.0ms	(/ 1 (sin B))

simplify545.0ms

Calls

46 calls:

Slowest

207.0ms	(/ (* (* (- x) (- x)) (- x)) (* (* (sin B) (sin B)) (sin B)))
57.0ms	(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
46.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
38.0ms	(- (+ (* 1/6 B) (/ 1 B)) (/ x B))
32.0ms	(- (+ (/ x B) (* 1/6 (* x B))))

prune800.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ -1 (/ (sin B) x))
0.2b	(/ (sin B) x)
0.1b	(/ 1 (sin B))
0.1b	(fma (cos B) (/ -1 (/ (sin B) x)) (/ 1 (sin B)))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-cube-cbrt`
7×	`*-un-lft-identity`
7×	`associate-/r*`
7×	`add-sqr-sqrt`
5×	`add-exp-log`
5×	`pow1`
4×	`add-log-exp`
4×	`div-inv`
4×	`log1p-expm1-u`
4×	`add-cbrt-cube`
4×	`expm1-log1p-u`
3×	`associate-/l*`
3×	`frac-2neg`
3×	`clear-num`
1×	`inv-pow`
1×	`pow-flip`
1×	`fma-udef`
1×	`associate-/r/`
1×	`rec-exp`

Calls

4 calls:

Slowest

2.0ms	(/ (sin B) x)
1.0ms	(/ 1 (sin B))
1.0ms	(/ -1 (/ (sin B) x))
0.0ms	(fma (cos B) (/ -1 (/ (sin B) x)) (/ 1 (sin B)))

series173.0ms

Calls

4 calls:

Slowest

84.0ms	(fma (cos B) (/ -1 (/ (sin B) x)) (/ 1 (sin B)))
46.0ms	(/ -1 (/ (sin B) x))
25.0ms	(/ (sin B) x)
18.0ms	(/ 1 (sin B))

simplify459.0ms

Calls

22 calls:

Slowest

228.0ms	(- (+ (/ B x) (* 1/120 (/ (pow B 5) x))) (* 1/6 (/ (pow B 3) x)))
54.0ms	(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
38.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
37.0ms	(- (+ (* 1/6 B) (/ 1 B)) (/ x B))
33.0ms	(- (+ (/ x B) (* 1/6 (* x B))))

prune745.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes100.0ms

Accuracy

0% (0.1b remaining)

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

bsearch1.0ms

end0.0ms

sample8.9s

Algorithm

intervals

Results

4.2s	1752×	body	1280	valid
2.2s	1426×	body	640	valid
1.4s	4898×	body	80	valid
730.0ms	742×	body	320	valid
191.0ms	347×	body	160	valid