Details

sample300.0ms

Algorithm

intervals

Results

63.0ms	49×	body	1280	valid
55.0ms	58×	body	80	nan
43.0ms	45×	body	640	valid
31.0ms	162×	body	80	valid
13.0ms	22×	body	320	valid
6.0ms	16×	body	160	valid

simplify3.7s

Counts

1 → 1

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	20	27
1	43	26
2	91	24
3	169	24
4	366	24
5	915	24
6	3219	24
done	5001	24

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.7b

localize71.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))
6.1b	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (* x (/ 1.0 (tan B)))))
14.7b	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

rewrite79.0ms

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:

12.0ms	(/ 1.0 (tan B))
37.0ms	(* x (/ 1.0 (tan B)))
1.0ms	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (* x (/ 1.0 (tan B)))))
18.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

series1.3s

Counts

4 → 12

Calls

4 calls:

63.0ms	(/ 1.0 (tan B))
171.0ms	(* x (/ 1.0 (tan B)))
556.0ms	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (* x (/ 1.0 (tan B)))))
527.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

simplify3.3s

Counts

135 → 135

Iterations

Useful iterations: 3 (2.1s)

Iter	Nodes	Cost
0	285	1919
1	690	1835
2	1768	1712
3	4856	1677
done	5000	1677

prune1.1s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 9.3b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x 1.0) (tan B))
0.1b	(/ F (sin B))
6.1b	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (/ (* x 1.0) (tan B))))
14.7b	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

rewrite28.0ms

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:

11.0ms	(/ (* x 1.0) (tan B))
6.0ms	(/ F (sin B))
1.0ms	(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)))

series1.3s

Counts

4 → 12

Calls

4 calls:

183.0ms	(/ (* x 1.0) (tan B))
70.0ms	(/ F (sin B))
568.0ms	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (/ (* x 1.0) (tan B))))
488.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

simplify1.5s

Counts

123 → 123

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	292	1805
1	677	1732
2	1805	1610
done	5000	1575

prune996.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 9.3b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ F (sin B))
0.4b	(/ 1 (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)))
6.1b	(fma (/ 1 (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))) (/ F (sin B)) (- (/ (* x 1.0) (tan B))))
14.6b	(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

39×	`times-frac`
36×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
16×	`add-exp-log`
15×	`unpow-prod-down`
13×	`pow-unpow`
10×	`associate-/r*`
8×	`add-cbrt-cube`
7×	`div-exp`
6×	`associate-/l*`
5×	`pow1` `sqr-pow`
4×	`expm1-log1p-u` `pow-to-exp` `pow-exp` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `1-exp` `div-inv`
2×	`cbrt-undiv` `frac-2neg` `clear-num`
1×	`pow-flip` `pow-pow` `fma-udef` `inv-pow`

Counts

4 → 123

Calls

4 calls:

8.0ms	(/ F (sin B))
18.0ms	(/ 1 (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)))
1.0ms	(fma (/ 1 (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))) (/ F (sin B)) (- (/ (* x 1.0) (tan B))))
9.0ms	(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

series3.0s

Counts

4 → 12

Calls

4 calls:

66.0ms	(/ F (sin B))
1.3s	(/ 1 (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)))
1.1s	(fma (/ 1 (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))) (/ F (sin B)) (- (/ (* x 1.0) (tan B))))
519.0ms	(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

simplify1.2s

Counts

135 → 135

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	322	2674
1	727	2506
2	1803	2304
done	5000	2261

prune930.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 9.2b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin B) F)
0.2b	(/ 1 (/ (sin B) F))
6.1b	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ 1 (/ (sin B) F)) (- (/ (* x 1.0) (tan B))))
14.7b	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 165

Calls

4 calls:

17.0ms	(/ (sin B) F)
11.0ms	(/ 1 (/ (sin B) F))
0.0ms	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ 1 (/ (sin B) F)) (- (/ (* x 1.0) (tan B))))
7.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

series1.1s

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ (sin B) F)
63.0ms	(/ 1 (/ (sin B) F))
524.0ms	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ 1 (/ (sin B) F)) (- (/ (* x 1.0) (tan B))))
505.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

simplify3.4s

Counts

177 → 177

Iterations

Useful iterations: done (3.4s)

Iter	Nodes	Cost
0	352	2628
1	810	2356
2	1866	2111
3	4907	2057
done	5000	2055

prune997.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 9.2b

regimes489.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify11.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	28
1	27	28
2	32	28
done	32	28

end0.0ms

sample10.0s

Algorithm

intervals

Results

4.1s	1594×	body	1280	valid
2.1s	1429×	body	640	valid
1.8s	4814×	body	80	valid
725.0ms	700×	body	320	valid
469.0ms	1618×	body	80	nan
210.0ms	334×	body	160	valid