Details

sample382.0ms

Algorithm

intervals

Results

52.0ms	51×	body	1280	valid
27.0ms	43×	body	640	valid
21.0ms	157×	body	80	valid
9.0ms	20×	body	320	valid
6.0ms	54×	body	80	nan
3.0ms	11×	body	160	valid

simplify2.8s

Counts

1 → 1

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	20	27
1	43	26
2	88	24
3	165	24
4	352	24
5	935	24
6	4035	24
done	5000	24

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))
7.7b	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (* x (/ 1.0 (tan B)))))
18.6b	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
37×	`times-frac`
36×	`add-cube-cbrt` `*-un-lft-identity`
30×	`pow-unpow`
14×	`associate-r`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
12×	`add-exp-log`
11×	`add-cbrt-cube`
7×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`unpow-prod-down` `associate-l` `associate-/r` `associate-/l`
2×	`tan-quot` `cbrt-undiv` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`neg-sub0` `pow-to-exp` `pow-neg` `neg-mul-1` `pow-pow` `frac-2neg` `associate-r/` `pow-prod-down` `pow-exp` `clear-num` `-commutative` `fma-udef` `pow-sub` `sqr-pow`

Counts

4 → 123

Calls

4 calls:

2.0ms	(/ 1.0 (tan B))
8.0ms	(* x (/ 1.0 (tan B)))
0.0ms	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (* x (/ 1.0 (tan B)))))
7.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

series815.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ 1.0 (tan B))
108.0ms	(* x (/ 1.0 (tan B)))
337.0ms	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (* x (/ 1.0 (tan B)))))
330.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

simplify1.1s

Counts

135 → 135

Iterations

Useful iterations: 2 (231.0ms)

Iter	Nodes	Cost
0	285	1919
1	710	1835
2	2666	1712
done	5000	1712

prune642.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.8b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ F (sin B))
0.2b	(/ (* x 1.0) (tan B))
7.7b	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (/ (* x 1.0) (tan B))))
18.6b	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt` `add-cube-cbrt` `pow-unpow` `*-un-lft-identity` `times-frac`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
12×	`add-exp-log`
11×	`add-cbrt-cube`
6×	`associate-/r*`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `associate-/l*` `add-log-exp`
3×	`cbrt-undiv` `unpow-prod-down` `div-exp`
2×	`frac-2neg` `clear-num`
1×	`tan-quot` `neg-sub0` `pow-to-exp` `pow-neg` `neg-mul-1` `pow-pow` `pow-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `fma-udef` `pow-sub` `sqr-pow`

Counts

4 → 111

Calls

4 calls:

2.0ms	(/ F (sin B))
3.0ms	(/ (* x 1.0) (tan B))
0.0ms	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (/ (* x 1.0) (tan B))))
4.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

series822.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(/ F (sin B))
108.0ms	(/ (* x 1.0) (tan B))
343.0ms	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (/ (* x 1.0) (tan B))))
324.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

simplify850.0ms

Counts

123 → 123

Iterations

Useful iterations: 2 (221.0ms)

Iter	Nodes	Cost
0	292	1805
1	699	1732
2	2484	1610
done	5001	1610

prune577.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 12.8b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* x (cos B))
0.2b	(/ (* x (cos B)) (sin B))
7.7b	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (* 1.0 (/ (* x (cos B)) (sin B)))))
18.6b	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

30×	`pow-unpow`
26×	`add-sqr-sqrt`
24×	`add-cube-cbrt` `*-un-lft-identity`
21×	`times-frac`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
12×	`add-exp-log`
11×	`add-cbrt-cube`
7×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down` `associate-r` `associate-l` `associate-/r*` `div-inv`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
1×	`neg-sub0` `pow-to-exp` `pow-neg` `neg-mul-1` `pow-pow` `frac-2neg` `pow-prod-down` `pow-exp` `clear-num` `-commutative` `fma-udef` `associate-/l` `pow-sub` `unswap-sqr` `sqr-pow`

Counts

4 → 101

Calls

4 calls:

3.0ms	(* x (cos B))
4.0ms	(/ (* x (cos B)) (sin B))
0.0ms	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (* 1.0 (/ (* x (cos B)) (sin B)))))
4.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

series898.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* x (cos B))
92.0ms	(/ (* x (cos B)) (sin B))
449.0ms	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (* 1.0 (/ (* x (cos B)) (sin B)))))
322.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

simplify902.0ms

Counts

113 → 113

Iterations

Useful iterations: 2 (198.0ms)

Iter	Nodes	Cost
0	255	1739
1	633	1672
2	2363	1539
done	5001	1539

prune521.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 12.8b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (tan B) (* x 1.0))
0.2b	(/ 1 (/ (tan B) (* x 1.0)))
7.7b	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (/ 1 (/ (tan B) (* x 1.0)))))
18.6b	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

54×	`times-frac`
38×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
31×	`add-exp-log`
30×	`pow-unpow`
18×	`add-cbrt-cube`
14×	`div-exp`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
8×	`associate-/r*` `div-inv`
7×	`cbrt-undiv`
6×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down` `rec-exp` `1-exp`
2×	`frac-2neg` `clear-num` `cbrt-unprod`
1×	`tan-quot` `neg-sub0` `pow-to-exp` `pow-neg` `neg-mul-1` `pow-flip` `pow-pow` `pow-exp` `associate-/r/` `fma-udef` `associate-/l/` `inv-pow` `pow-sub` `sqr-pow`

Counts

4 → 140

Calls

4 calls:

3.0ms	(/ (tan B) (* x 1.0))
6.0ms	(/ 1 (/ (tan B) (* x 1.0)))
0.0ms	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (/ 1 (/ (tan B) (* x 1.0)))))
4.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

series769.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ (tan B) (* x 1.0))
82.0ms	(/ 1 (/ (tan B) (* x 1.0)))
328.0ms	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (/ 1 (/ (tan B) (* x 1.0)))))
308.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

simplify1.7s

Counts

152 → 152

Iterations

Useful iterations: 2 (284.0ms)

Iter	Nodes	Cost
0	326	2376
1	817	2202
2	3281	1947
done	5001	1947

prune531.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 12.8b

regimes276.0ms

Accuracy

0% (0.4b remaining)

Error of 14.1b against oracle of 13.7b and baseline of 14.1b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	27
1	25	27
2	29	27
3	35	27
done	35	27

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.6s	1645×	body	1280	valid
869.0ms	1337×	body	640	valid
665.0ms	4855×	body	80	valid
306.0ms	683×	body	320	valid
158.0ms	1499×	body	80	nan
101.0ms	337×	body	160	valid