Details

sample192.0ms

Algorithm

intervals

Results

67.0ms	55×	body	640	valid
57.0ms	44×	body	1280	valid
33.0ms	158×	body	80	valid
12.0ms	19×	body	320	valid
11.0ms	14×	body	160	valid

simplify97.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

97.0ms

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

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

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)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 84

Calls

3 calls:

Slowest

31.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
5.0ms	(/ 1 (sin B))
5.0ms	(/ x (tan B))

series295.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

148.0ms	(/ x (tan B))
126.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
21.0ms	(/ 1 (sin B))

simplify2.1s

Counts

81 → 93

Calls

81 calls:

Slowest

401.0ms	(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
378.0ms	(/ (* (* x x) x) (* (* (tan B) (tan B)) (tan B)))
129.0ms	(/ (* (* 1 1) 1) (* (* (sin B) (sin B)) (sin B)))
68.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
61.0ms	(- (/ x B) (* 1/3 (* x B)))

prune801.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
16×	`add-cube-cbrt`
15×	`times-frac` `add-exp-log`
13×	`add-cbrt-cube`
7×	`pow1` `div-inv`
6×	`associate-/r*` `add-log-exp`
4×	`div-exp` `insert-posit16` `associate-/l*`
3×	`cbrt-undiv` `distribute-rgt-out--` `associate-r` `associate-l` `difference-of-squares`
2×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `distribute-lft-out--`
1×	`rec-exp` `sub-neg` `flip3--` `diff-log` `1-exp` `pow-prod-down` `*-commutative` `frac-sub` `pow-flip` `flip--` `inv-pow` `sub-div` `unswap-sqr`

Counts

4 → 96

Calls

4 calls:

Slowest

25.0ms	(/ (* x (cos B)) (sin B))
18.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
12.0ms	(* x (cos B))
9.0ms	(/ 1 (sin B))

series315.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

139.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
122.0ms	(/ (* x (cos B)) (sin B))
40.0ms	(* x (cos B))
14.0ms	(/ 1 (sin B))

simplify3.1s

Counts

81 → 108

Calls

81 calls:

Slowest

386.0ms	(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
321.0ms	(* (* (* x x) x) (* (* (cos B) (cos B)) (cos B)))
183.0ms	(- (* 1 (sin B)) (* (sin B) (* x (cos B))))
182.0ms	(/ (* (* (* x (cos B)) (* x (cos B))) (* x (cos B))) (* (* (sin B) (sin B)) (sin B)))
139.0ms	(/ (* (* (* x x) x) (* (* (cos B) (cos B)) (cos B))) (* (* (sin B) (sin B)) (sin B)))

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (cos B))
0.3b	(cbrt (cos B))
0.3b	(cbrt (cos B))
0.2b	(* (cbrt (cos B)) (cbrt (cos B)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`add-cbrt-cube` `insert-posit16` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 77

Calls

4 calls:

Slowest

19.0ms	(* (cbrt (cos B)) (cbrt (cos B)))
2.0ms	(cbrt (cos B))
2.0ms	(cbrt (cos B))
2.0ms	(cbrt (cos B))

series631.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

212.0ms	(* (cbrt (cos B)) (cbrt (cos B)))
157.0ms	(cbrt (cos B))
133.0ms	(cbrt (cos B))
129.0ms	(cbrt (cos B))

simplify1.4s

Counts

65 → 89

Calls

65 calls:

Slowest

424.0ms	(- 1 (+ (* 1/405 (pow B 6)) (* 1/3 (pow B 2))))
194.0ms	(- 1 (+ (* 1/72 (pow B 4)) (* 1/6 (pow B 2))))
162.0ms	(- 1 (+ (* 1/72 (pow B 4)) (* 1/6 (pow B 2))))
137.0ms	(- 1 (+ (* 1/72 (pow B 4)) (* 1/6 (pow B 2))))
103.0ms	(* (* (cbrt (cbrt (cos B))) (cbrt (cbrt (cos B)))) (* (cbrt (cbrt (cos B))) (cbrt (cbrt (cos B)))))

prune1.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

10.8b	(/ (- (sin B) (* (sin B) (* x (cos B)))) (* (sin B) (sin B)))
0.3b	(* (sin B) (sin B))
0.2b	(* (sin B) (* x (cos B)))
0.1b	(* x (cos B))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

18×	`pow1` `add-cbrt-cube` `add-exp-log`
17×	`add-sqr-sqrt`
13×	`*-un-lft-identity` `add-cube-cbrt`
9×	`associate-l`
7×	`associate-r`
6×	`prod-exp` `cbrt-unprod`
5×	`pow-prod-down`
4×	`insert-posit16` `add-log-exp`
3×	`times-frac` `swap-sqr` `-commutative` `associate-/l`
2×	`cbrt-undiv` `div-exp` `sin-mult` `unswap-sqr` `associate-/l/`
1×	`pow2` `clear-num` `associate-/r*` `frac-2neg` `pow-plus` `flip3--` `div-sub` `associate-/r/` `pow-sqr` `pow-prod-up` `sqr-sin` `div-inv` `flip--`

Counts

4 → 92

Calls

4 calls:

Slowest

43.0ms	(* (sin B) (* x (cos B)))
21.0ms	(* (sin B) (sin B))
20.0ms	(/ (- (sin B) (* (sin B) (* x (cos B)))) (* (sin B) (sin B)))
14.0ms	(* x (cos B))

series382.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

197.0ms	(/ (- (sin B) (* (sin B) (* x (cos B)))) (* (sin B) (sin B)))
87.0ms	(* (sin B) (* x (cos B)))
64.0ms	(* x (cos B))
33.0ms	(* (sin B) (sin B))

simplify4.3s

Counts

70 → 104

Calls

70 calls:

Slowest

490.0ms	(* (* (* (sin B) (sin B)) (sin B)) (* (* (* x (cos B)) (* x (cos B))) (* x (cos B))))
462.0ms	(* (* (* (sin B) (sin B)) (sin B)) (* (* (* x x) x) (* (* (cos B) (cos B)) (cos B))))
347.0ms	(- (* (sin B) (sin B)) (* (* (sin B) (* x (cos B))) (* (sin B) (* x (cos B)))))
274.0ms	(* (* (* x x) x) (* (* (cos B) (cos B)) (cos B)))
251.0ms	(/ (- (sin B) (* (sin B) (* x (cos B)))) (sin B))

prune1.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes110.0ms

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

3.6s	1653×	body	1280	valid
2.3s	1413×	body	640	valid
1.9s	4982×	body	80	valid
618.0ms	762×	body	320	valid
324.0ms	342×	body	160	valid