Details

sample231.0ms

Algorithm

intervals

Results

104.0ms	56×	body	1280	valid
47.0ms	41×	body	640	valid
41.0ms	170×	body	80	valid
19.0ms	22×	body	320	valid
3.0ms	5×	body	160	valid

simplify146.0ms

Calls

1 calls:

Slowest

145.0ms

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

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize444.0ms

Local error

Found 3 expressions with local error:

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

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

8×	`*-un-lft-identity`
7×	`add-sqr-sqrt`
6×	`associate-/r*`
5×	`add-cube-cbrt` `add-log-exp`
4×	`pow1` `add-exp-log`
3×	`add-cbrt-cube` `insert-posit16` `div-inv`
2×	`clear-num` `frac-2neg` `distribute-lft-out--`
1×	`rec-exp` `sub-neg` `flip3--` `diff-log` `tan-quot` `associate-/r/` `frac-sub` `pow-flip` `flip--` `inv-pow` `difference-of-squares`

Calls

3 calls:

Slowest

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

series317.0ms

Calls

3 calls:

Slowest

170.0ms	(/ x (tan B))
125.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
22.0ms	(/ 1 (sin B))

simplify705.0ms

Calls

24 calls:

Slowest

89.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
87.0ms	(- (+ (* 1/6 B) (/ 1 B)) (/ x B))
83.0ms	(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
80.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
60.0ms	(- (/ x B) (* 1/3 (* x B)))

prune600.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (/ (tan B) x))
0.2b	(/ (tan B) x)
0.1b	(/ 1 (sin B))
0.0b	(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity`
9×	`add-sqr-sqrt`
8×	`div-inv`
7×	`associate-/r*` `add-cube-cbrt`
6×	`pow1` `add-exp-log` `add-log-exp`
4×	`add-cbrt-cube` `insert-posit16` `distribute-lft-out--`
3×	`clear-num` `frac-2neg` `associate-/l*`
2×	`rec-exp` `pow-flip` `inv-pow`
1×	`sub-neg` `flip3--` `diff-log` `tan-quot` `associate-/r/` `frac-sub` `flip--` `difference-of-squares` `associate-/l/`

Calls

4 calls:

Slowest

9.0ms	(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
5.0ms	(/ (tan B) x)
2.0ms	(/ 1 (/ (tan B) x))
2.0ms	(/ 1 (sin B))

series321.0ms

Calls

4 calls:

Slowest

133.0ms	(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
108.0ms	(/ 1 (/ (tan B) x))
57.0ms	(/ (tan B) x)
23.0ms	(/ 1 (sin B))

simplify1.4s

Calls

33 calls:

Slowest

193.0ms	(+ (/ B x) (+ (* 1/3 (/ (pow B 3) x)) (* 2/15 (/ (pow B 5) x))))
108.0ms	(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
107.0ms	(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
100.0ms	(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
84.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))

prune866.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (tan B))
0.6b	(cbrt (tan B))
0.6b	(cbrt (tan B))
0.5b	(* (cbrt (tan B)) (cbrt (tan B)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`pow1`
7×	`cbrt-div` `pow1/3` `tan-quot`
6×	`associate-r` `associate-l` `add-exp-log`
4×	`add-cbrt-cube` `insert-posit16` `add-log-exp`
2×	`pow-prod-down` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod`

Calls

4 calls:

Slowest

10.0ms	(* (cbrt (tan B)) (cbrt (tan B)))
1.0ms	(cbrt (tan B))
1.0ms	(cbrt (tan B))
1.0ms	(cbrt (tan B))

series817.0ms

Calls

4 calls:

Slowest

220.0ms	(cbrt (tan B))
218.0ms	(cbrt (tan B))
194.0ms	(cbrt (tan B))
184.0ms	(* (cbrt (tan B)) (cbrt (tan B)))

simplify542.0ms

Calls

48 calls:

Slowest

68.0ms	(+ (pow B 1/3) (+ (* 1/9 (pow (pow B 7) 1/3)) (* 13/405 (pow (pow B 13) 1/3))))
64.0ms	(+ (pow B 1/3) (+ (* 1/9 (pow (pow B 7) 1/3)) (* 13/405 (pow (pow B 13) 1/3))))
62.0ms	(+ (pow B 2/3) (+ (* 31/405 (pow (pow B 14) 1/3)) (* 2/9 (pow (pow B 8) 1/3))))
54.0ms	(+ (pow B 1/3) (+ (* 1/9 (pow (pow B 7) 1/3)) (* 13/405 (pow (pow B 13) 1/3))))
48.0ms	(pow (/ (pow (sin B) 2) (pow (cos B) 2)) 1/3)

prune1.2s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (/ 1 (sin B))) (cbrt (/ 1 (sin B))))
0.4b	(cbrt (/ 1 (sin B)))
0.4b	(cbrt (/ 1 (sin B)))
0.4b	(cbrt (/ 1 (sin B)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

20×	`cbrt-prod`
11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`pow1`
7×	`cbrt-div` `pow1/3` `associate-r` `associate-l`
6×	`add-exp-log`
5×	`div-inv`
4×	`add-cbrt-cube` `insert-posit16` `add-log-exp`
2×	`pow-prod-down` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod`

Calls

4 calls:

Slowest

12.0ms	(* (cbrt (/ 1 (sin B))) (cbrt (/ 1 (sin B))))
2.0ms	(cbrt (/ 1 (sin B)))
2.0ms	(cbrt (/ 1 (sin B)))
2.0ms	(cbrt (/ 1 (sin B)))

series812.0ms

Calls

4 calls:

Slowest

214.0ms	(* (cbrt (/ 1 (sin B))) (cbrt (/ 1 (sin B))))
206.0ms	(cbrt (/ 1 (sin B)))
200.0ms	(cbrt (/ 1 (sin B)))
191.0ms	(cbrt (/ 1 (sin B)))

simplify922.0ms

Calls

53 calls:

Slowest

69.0ms	(+ (* 1/9 (pow (pow B 4) 1/3)) (+ (pow B -2/3) (* 4/405 (pow (pow B 10) 1/3))))
68.0ms	(+ (pow B -1/3) (+ (* 11/3240 (pow (pow B 11) 1/3)) (* 1/18 (pow (pow B 5) 1/3))))
64.0ms	(+ (pow B -1/3) (+ (* 11/3240 (pow (pow B 11) 1/3)) (* 1/18 (pow (pow B 5) 1/3))))
60.0ms	(+ (pow B -1/3) (+ (* 11/3240 (pow (pow B 11) 1/3)) (* 1/18 (pow (pow B 5) 1/3))))
35.0ms	(pow (/ 1 (pow (sin B) 2)) 1/3)

prune1.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes158.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch2.0ms

end0.0ms

sample10.2s

Algorithm

intervals

Results

3.8s	1678×	body	1280	valid
2.7s	4998×	body	80	valid
2.3s	1473×	body	640	valid
797.0ms	716×	body	320	valid
272.0ms	344×	body	160	valid