Details

sample309.0ms

Algorithm

intervals

Results

113.0ms	48×	body	640	valid
58.0ms	41×	body	1280	valid
37.0ms	174×	body	80	valid
19.0ms	30×	body	320	valid
5.0ms	11×	body	160	valid

simplify75.0ms

Counts: 1 → 1

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
0.1b	(/ 1.0 (sin B))
0.2b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
28×	`add-cube-cbrt` `times-frac`
14×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
6×	`pow1` `associate-/r` `associate-/l`
3×	`cbrt-undiv` `div-exp` `associate-l` `div-inv`
2×	`tan-quot` `frac-2neg` `associate-*r/` `prod-exp` `clear-num` `sum-log` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `neg-sub0` `associate-+l-` `flip3-+` `pow-prod-down` `neg-log` `frac-add` `*-commutative` `flip-+` `distribute-neg-frac` `distribute-lft-out`

Counts

4 → 103

Calls

4 calls:

21.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
11.0ms	(/ 1.0 (sin B))
14.0ms	(/ 1.0 (tan B))
67.0ms	(* x (/ 1.0 (tan B)))

series402.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
21.0ms	(/ 1.0 (sin B))
47.0ms	(/ 1.0 (tan B))
168.0ms	(* x (/ 1.0 (tan B)))

simplify802.0ms

Counts: 115 → 115

prune460.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
0.1b	(/ 1.0 (sin B))
0.1b	(/ (* x 1.0) (tan B))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
13×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
7×	`add-log-exp`
6×	`associate-/r*`
4×	`associate-/l*`
3×	`pow1` `cbrt-undiv` `div-exp`
2×	`frac-2neg` `clear-num` `sum-log` `div-inv` `distribute-lft-out`
1×	`tan-quot` `+-commutative` `neg-sub0` `associate-+l-` `distribute-rgt-neg-in` `flip3-+` `neg-log` `frac-add` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+` `distribute-neg-frac`

Counts

3 → 65

Calls

3 calls:

82.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
10.0ms	(/ 1.0 (sin B))
22.0ms	(/ (* x 1.0) (tan B))

series393.0ms

Counts

3 → 9

Calls

3 calls:

168.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
38.0ms	(/ 1.0 (sin B))
188.0ms	(/ (* x 1.0) (tan B))

simplify692.0ms

Counts: 74 → 74

prune313.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (- (* (/ (* x 1.0) (sin B)) (cos B))) (/ 1.0 (sin B)))
0.1b	(/ 1.0 (sin B))
0.1b	(/ (* x 1.0) (sin B))
0.2b	(* (/ (* x 1.0) (sin B)) (cos B))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-exp-log` `add-cbrt-cube`
19×	`add-sqr-sqrt` `*-un-lft-identity`
17×	`add-cube-cbrt`
15×	`times-frac`
8×	`add-log-exp`
7×	`associate-l`
6×	`pow1` `associate-/r*`
5×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
4×	`associate-/l*`
3×	`associate-r` `div-inv`
2×	`frac-2neg` `associate-*l/` `clear-num` `sum-log`
1×	`+-commutative` `neg-sub0` `associate-+l-` `flip3-+` `pow-prod-down` `neg-log` `frac-add` `*-commutative` `flip-+` `distribute-neg-frac` `distribute-lft-out` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

23.0ms	(+ (- (* (/ (* x 1.0) (sin B)) (cos B))) (/ 1.0 (sin B)))
6.0ms	(/ 1.0 (sin B))
11.0ms	(/ (* x 1.0) (sin B))
42.0ms	(* (/ (* x 1.0) (sin B)) (cos B))

series438.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(+ (- (* (/ (* x 1.0) (sin B)) (cos B))) (/ 1.0 (sin B)))
21.0ms	(/ 1.0 (sin B))
103.0ms	(/ (* x 1.0) (sin B))
130.0ms	(* (/ (* x 1.0) (sin B)) (cos B))

simplify941.0ms

Counts: 102 → 102

prune421.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (cbrt x) (cbrt x))
0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `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 → 73

Calls

4 calls:

24.0ms	(* (cbrt x) (cbrt x))
2.0ms	(cbrt x)
2.0ms	(cbrt x)
2.0ms	(cbrt x)

series1.2s

Counts

4 → 12

Calls

4 calls:

370.0ms	(* (cbrt x) (cbrt x))
275.0ms	(cbrt x)
271.0ms	(cbrt x)
303.0ms	(cbrt x)

simplify908.0ms

Counts: 85 → 85

prune344.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes75.0ms

Accuracy

-37.2% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.7s

end0.0ms

sample6.6s

Algorithm

intervals

Results

2.3s	1722×	body	1280	valid
1.5s	4855×	body	80	valid
1.2s	1411×	body	640	valid
889.0ms	751×	body	320	valid
286.0ms	396×	body	160	valid