Details

sample387.0ms

Algorithm

intervals

Results

56.0ms	56×	body	1280	valid
33.0ms	49×	body	640	valid
21.0ms	150×	body	80	valid
9.0ms	21×	body	320	valid
6.0ms	54×	body	80	nan
3.0ms	10×	body	160	valid

simplify2.0s

Counts

1 → 1

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	20	27
1	43	26
2	88	24
3	164	24
4	341	24
5	852	24
6	2805	24
done	5001	24

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.9b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ F (sin B))
0.3b	(* x (/ 1.0 (tan B)))
7.1b	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (* x (/ 1.0 (tan B)))))
18.7b	(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×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`tan-quot` `neg-sub0` `pow-to-exp` `pow-neg` `neg-mul-1` `pow-pow` `frac-2neg` `associate-r/` `pow-prod-down` `pow-exp` `clear-num` `associate-/r/` `-commutative` `fma-udef` `pow-sub` `sqr-pow`

Counts

4 → 122

Calls

4 calls:

2.0ms	(/ F (sin 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)))))
6.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

series869.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ F (sin B))
113.0ms	(* x (/ 1.0 (tan B)))
351.0ms	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (* x (/ 1.0 (tan B)))))
350.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

simplify772.0ms

Counts

134 → 134

Iterations

Useful iterations: done (767.0ms)

Iter	Nodes	Cost
0	307	1903
1	736	1820
2	1873	1698
done	5002	1664

prune637.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 13.6b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* x 1.0) (tan B))
0.2b	(/ F (sin B))
7.1b	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (/ (* x 1.0) (tan B))))
18.7b	(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:

4.0ms	(/ (* x 1.0) (tan B))
2.0ms	(/ F (sin 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))))
5.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

series861.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(/ (* x 1.0) (tan B))
54.0ms	(/ F (sin B))
355.0ms	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (/ (* x 1.0) (tan B))))
340.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

simplify780.0ms

Counts

123 → 123

Iterations

Useful iterations: 2 (262.0ms)

Iter	Nodes	Cost
0	292	1805
1	686	1732
2	1833	1610
done	5000	1610

prune610.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 13.6b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ F (sin B))
0.3b	(/ 1 (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)))
7.1b	(fma (/ 1 (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))) (/ F (sin B)) (- (/ (* x 1.0) (tan B))))
18.7b	(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

rewrite12.0ms

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:

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

series1.7s

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ F (sin B))
872.0ms	(/ 1 (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)))
459.0ms	(fma (/ 1 (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))) (/ F (sin B)) (- (/ (* x 1.0) (tan B))))
336.0ms	(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

simplify712.0ms

Counts

135 → 135

Iterations

Useful iterations: done (708.0ms)

Iter	Nodes	Cost
0	322	2674
1	733	2506
2	1834	2304
done	5000	2271

prune556.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.6b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* x 1.0) (tan B))
0.2b	(/ F (sin B))
7.2b	(/ (/ F (sin B)) (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)))
18.7b	(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

184×	`times-frac`
106×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
45×	`unpow-prod-down`
25×	`add-exp-log`
17×	`associate-/l*`
16×	`add-cbrt-cube`
15×	`sqr-pow`
13×	`pow-unpow` `associate-/r*`
12×	`div-exp` `div-inv`
6×	`cbrt-undiv`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `frac-2neg` `pow-exp` `clear-num`
1×	`tan-quot` `pow-pow` `prod-exp` `associate-/r/` `cbrt-unprod` `associate-/l/`

Counts

4 → 214

Calls

4 calls:

3.0ms	(/ (* x 1.0) (tan B))
2.0ms	(/ F (sin B))
8.0ms	(/ (/ F (sin B)) (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)))
2.0ms	(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

series824.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(/ (* x 1.0) (tan B))
48.0ms	(/ F (sin B))
330.0ms	(/ (/ F (sin B)) (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)))
334.0ms	(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

simplify994.0ms

Counts

226 → 226

Iterations

Useful iterations: 2 (536.0ms)

Iter	Nodes	Cost
0	425	5432
1	974	5196
2	2927	5043
done	5000	5043

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes185.0ms

Accuracy

98.3% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 10.2b

bsearch250.0ms

Steps

Iters	Range		Point
10	0.0002557396131854704	208948952.3113414	15392.909464798095
6	-1.7466667409204087e+24	-1.4029587726052624e+23	-2.0995950722645005e+23

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	74
1	46	74
2	52	74
done	52	74

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.7s	1699×	body	1280	valid
896.0ms	1372×	body	640	valid
674.0ms	4790×	body	80	valid
306.0ms	673×	body	320	valid
172.0ms	1651×	body	80	nan
103.0ms	348×	body	160	valid