Details

sample384.0ms

Algorithm

intervals

Results

51.0ms	50×	body	1280	valid
34.0ms	55×	body	640	valid
20.0ms	148×	body	80	valid
9.0ms	60×	body	80	nan
8.0ms	18×	body	320	valid
3.0ms	11×	body	160	valid

simplify1.8s

Counts

1 → 1

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	20	27
1	43	26
2	88	24
3	164	24
4	341	24
5	851	24
6	3297	24
done	5000	24

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.4b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ F (sin B))
0.3b	(* x (/ 1.0 (tan B)))
5.4b	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (* x (/ 1.0 (tan B)))))
17.3b	(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))
9.0ms	(* 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)))

series837.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ F (sin B))
110.0ms	(* x (/ 1.0 (tan B)))
341.0ms	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (* x (/ 1.0 (tan B)))))
334.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

simplify818.0ms

Counts

134 → 134

Iterations

Useful iterations: 2 (314.0ms)

Iter	Nodes	Cost
0	307	1903
1	736	1820
2	2391	1698
done	5000	1698

prune634.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 11.7b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x 1.0) (tan B))
0.1b	(/ F (sin B))
5.4b	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (/ (* x 1.0) (tan B))))
17.3b	(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))))
4.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

series828.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(/ (* x 1.0) (tan B))
47.0ms	(/ F (sin B))
348.0ms	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (/ (* x 1.0) (tan B))))
325.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

simplify709.0ms

Counts

123 → 123

Iterations

Useful iterations: 2 (294.0ms)

Iter	Nodes	Cost
0	292	1805
1	686	1732
2	2147	1610
done	5001	1610

prune590.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 11.7b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (sin B))
0.2b	(* F (/ 1 (sin B)))
5.4b	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (* F (/ 1 (sin B))) (- (/ (* x 1.0) (tan B))))
17.3b	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 129

Calls

4 calls:

2.0ms	(/ 1 (sin B))
8.0ms	(* F (/ 1 (sin B)))
0.0ms	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (* F (/ 1 (sin B))) (- (/ (* x 1.0) (tan B))))
4.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

series738.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ 1 (sin B))
47.0ms	(* F (/ 1 (sin B)))
346.0ms	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (* F (/ 1 (sin B))) (- (/ (* x 1.0) (tan B))))
324.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

simplify834.0ms

Counts

141 → 141

Iterations

Useful iterations: 2 (354.0ms)

Iter	Nodes	Cost
0	287	1957
1	697	1733
2	2088	1606
done	5000	1606

prune579.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 11.7b

localize21.0ms

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)))
5.4b	(fma (/ 1 (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))) (/ F (sin B)) (- (/ (* x 1.0) (tan B))))
17.3b	(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))

series1.6s

Counts

4 → 12

Calls

4 calls:

47.0ms	(/ F (sin B))
840.0ms	(/ 1 (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)))
438.0ms	(fma (/ 1 (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))) (/ F (sin B)) (- (/ (* x 1.0) (tan B))))
318.0ms	(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

simplify976.0ms

Counts

135 → 135

Iterations

Useful iterations: 2 (512.0ms)

Iter	Nodes	Cost
0	322	2674
1	733	2506
2	2321	2304
done	5000	2304

prune473.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 11.7b

regimes257.0ms

Accuracy

0% (0.4b remaining)

Error of 13.6b against oracle of 13.1b and baseline of 13.6b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	24
1	21	24
2	27	24
done	27	24

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.7s	1680×	body	1280	valid
954.0ms	1485×	body	640	valid
667.0ms	4748×	body	80	valid
305.0ms	695×	body	320	valid
162.0ms	1629×	body	80	nan
95.0ms	329×	body	160	valid