Details

sample421.0ms

Algorithm

intervals

Results

38.0ms	56×	body	640	valid
35.0ms	61×	body	1280	valid
13.0ms	149×	body	80	valid
5.0ms	20×	body	320	valid
1.0ms	9×	body	160	valid

simplify15.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	18	7
1	33	6
2	43	6
3	54	6
4	60	6
5	62	6
6	62	6
done	62	6

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize14.0ms

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))
0.1b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
29×	`add-cube-cbrt`
28×	`times-frac`
14×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
6×	`pow1` `fma-def` `associate-/r` `associate-/l`
4×	`expm1-log1p-u` `log1p-expm1-u`
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` `distribute-lft-neg-in` `associate-+l-` `neg-mul-1` `distribute-rgt-neg-in` `flip3-+` `pow-prod-down` `neg-log` `frac-add` `*-commutative` `flip-+` `distribute-neg-frac` `distribute-lft-out`

Counts

4 → 117

Calls

4 calls:

22.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
6.0ms	(/ 1.0 (sin B))
6.0ms	(/ 1.0 (tan B))
22.0ms	(* x (/ 1.0 (tan B)))

series308.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
22.0ms	(/ 1.0 (sin B))
39.0ms	(/ 1.0 (tan B))
126.0ms	(* x (/ 1.0 (tan B)))

simplify51.0ms

Counts

129 → 129

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	438	696
1	1724	639
2	5002	635
done	5002	635

prune345.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

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))
0.2b	(/ (* x 1.0) (tan B))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
20×	`fma-def`
18×	`add-sqr-sqrt` `add-cube-cbrt` `times-frac`
10×	`add-exp-log` `add-cbrt-cube`
9×	`distribute-rgt-neg-in`
8×	`distribute-lft-neg-in`
7×	`add-log-exp`
6×	`associate-/r*`
4×	`div-inv` `associate-/l*`
3×	`tan-quot` `pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `associate-/r/` `log1p-expm1-u`
2×	`frac-2neg` `clear-num` `sum-log` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `flip3-+` `neg-log` `frac-add` `prod-exp` `cbrt-unprod` `flip-+` `distribute-neg-frac`

Counts

3 → 91

Calls

3 calls:

55.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
5.0ms	(/ 1.0 (sin B))
13.0ms	(/ (* x 1.0) (tan B))

series254.0ms

Counts

3 → 9

Calls

3 calls:

120.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
21.0ms	(/ 1.0 (sin B))
113.0ms	(/ (* x 1.0) (tan B))

simplify37.0ms

Counts

100 → 100

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	350	492
1	1353	445
2	5002	440
done	5002	440

prune260.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt` `*-un-lft-identity`
17×	`add-cube-cbrt`
13×	`add-exp-log` `add-cbrt-cube`
12×	`times-frac`
8×	`add-log-exp`
6×	`pow1` `fma-def` `associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`cbrt-undiv` `div-exp` `associate-r` `associate-l` `div-inv`
2×	`distribute-rgt-neg-in` `frac-2neg` `prod-exp` `clear-num` `sum-log` `cbrt-unprod` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `distribute-lft-neg-in` `associate-+l-` `neg-mul-1` `flip3-+` `associate-r/` `pow-prod-down` `neg-log` `frac-add` `-commutative` `flip-+` `distribute-neg-frac` `unswap-sqr`

Counts

4 → 96

Calls

4 calls:

16.0ms	(+ (- (* 1.0 (/ (* x (cos B)) (sin B)))) (/ 1.0 (sin B)))
6.0ms	(/ 1.0 (sin B))
9.0ms	(* x (cos B))
15.0ms	(/ (* x (cos B)) (sin B))

series266.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(+ (- (* 1.0 (/ (* x (cos B)) (sin B)))) (/ 1.0 (sin B)))
19.0ms	(/ 1.0 (sin B))
40.0ms	(* x (cos B))
99.0ms	(/ (* x (cos B)) (sin B))

simplify44.0ms

Counts

108 → 108

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	375	642
1	1519	573
2	5001	568
done	5001	568

prune274.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (sin B)) (cbrt (sin B)))
0.7b	(cbrt (sin B))
0.7b	(cbrt (sin B))
0.7b	(cbrt (sin B))

rewrite23.0ms

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×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `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 → 81

Calls

4 calls:

17.0ms	(* (cbrt (sin B)) (cbrt (sin B)))
1.0ms	(cbrt (sin B))
1.0ms	(cbrt (sin B))
2.0ms	(cbrt (sin B))

series399.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(* (cbrt (sin B)) (cbrt (sin B)))
95.0ms	(cbrt (sin B))
95.0ms	(cbrt (sin B))
97.0ms	(cbrt (sin B))

simplify95.0ms

Counts

93 → 93

Iterations

Useful iterations: 3 (90.0ms)

Iter	Nodes	Cost
0	160	483
1	568	430
2	3134	398
3	5001	392
done	5001	392

prune288.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes70.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	9
1	22	9
2	28	9
3	28	9
done	28	9

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.0s	1753×	body	1280	valid
522.0ms	1484×	body	640	valid
381.0ms	4893×	body	80	valid
165.0ms	713×	body	320	valid
56.0ms	343×	body	160	valid