Details

sample415.0ms

Algorithm

intervals

Results

119.0ms	43×	body	640	valid
116.0ms	54×	body	1280	valid
49.0ms	171×	body	80	valid
19.0ms	20×	body	320	valid
11.0ms	53×	body	80	nan
3.0ms	6×	body	160	valid

simplify1.7s

Counts

1 → 1

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	20	27
1	43	26
2	91	24
3	170	24
4	385	24
5	1758	24
done	5000	24

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.8b

localize58.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))
7.8b	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (* x (/ 1.0 (tan B)))))
16.7b	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

rewrite62.0ms

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:

6.0ms	(/ 1.0 (tan B))
18.0ms	(* 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)))))
31.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

series1.3s

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ 1.0 (tan B))
186.0ms	(* x (/ 1.0 (tan B)))
564.0ms	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (* x (/ 1.0 (tan B)))))
511.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

simplify1.7s

Counts

135 → 135

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	285	1919
1	759	1839
2	2622	1720
done	5000	1715

prune1.1s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 14.4b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ F (sin B))
0.1b	(/ (* x 1.0) (tan B))
7.8b	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (/ (* x 1.0) (tan B))))
16.7b	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

rewrite35.0ms

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:

6.0ms	(/ F (sin B))
18.0ms	(/ (* 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)))

series1.3s

Counts

4 → 12

Calls

4 calls:

87.0ms	(/ F (sin B))
159.0ms	(/ (* x 1.0) (tan B))
596.0ms	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (/ (* x 1.0) (tan B))))
459.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

simplify1.7s

Counts

123 → 123

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	292	1805
1	734	1732
2	2644	1618
done	5001	1613

prune1.0s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 14.3b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x 1.0) (tan B))
0.8b	(pow (fma 2.0 x (fma F F 2.0)) (- 1.0))
7.8b	(fma (pow (pow (fma 2.0 x (fma F F 2.0)) (- 1.0)) (/ 1 2.0)) (/ F (sin B)) (- (/ (* x 1.0) (tan B))))
15.6b	(pow (pow (fma 2.0 x (fma F F 2.0)) (- 1.0)) (/ 1 2.0))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 97

Calls

4 calls:

22.0ms	(/ (* x 1.0) (tan B))
3.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- 1.0))
0.0ms	(fma (pow (pow (fma 2.0 x (fma F F 2.0)) (- 1.0)) (/ 1 2.0)) (/ F (sin B)) (- (/ (* x 1.0) (tan B))))
8.0ms	(pow (pow (fma 2.0 x (fma F F 2.0)) (- 1.0)) (/ 1 2.0))

series1.7s

Counts

4 → 12

Calls

4 calls:

140.0ms	(/ (* x 1.0) (tan B))
490.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- 1.0))
531.0ms	(fma (pow (pow (fma 2.0 x (fma F F 2.0)) (- 1.0)) (/ 1 2.0)) (/ F (sin B)) (- (/ (* x 1.0) (tan B))))
512.0ms	(pow (pow (fma 2.0 x (fma F F 2.0)) (- 1.0)) (/ 1 2.0))

simplify1.7s

Counts

109 → 109

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	280	2047
1	747	1945
2	3041	1806
done	5000	1801

prune936.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 14.1b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (sin B))
0.2b	(* F (/ 1 (sin B)))
7.8b	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (* F (/ 1 (sin B))) (- (/ (* x 1.0) (tan B))))
16.7b	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

rewrite61.0ms

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:

6.0ms	(/ 1 (sin B))
41.0ms	(* F (/ 1 (sin B)))
1.0ms	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (* F (/ 1 (sin B))) (- (/ (* x 1.0) (tan B))))
8.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

series1.1s

Counts

4 → 12

Calls

4 calls:

16.0ms	(/ 1 (sin B))
66.0ms	(* F (/ 1 (sin B)))
541.0ms	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (* F (/ 1 (sin B))) (- (/ (* x 1.0) (tan B))))
511.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

simplify1.8s

Counts

141 → 141

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	287	1957
1	750	1796
2	2694	1612
done	5001	1611

prune772.0ms

Pruning

18 alts after pruning (16 fresh and 2 done)

Merged error: 14.1b

regimes427.0ms

Accuracy

0% (0.4b remaining)

Error of 13.5b against oracle of 13.1b and baseline of 13.5b

bsearch0.0ms

simplify9.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	26
1	24	26
2	29	26
done	29	26

end0.0ms

sample10.8s

Algorithm

intervals

Results

4.2s	1584×	body	1280	valid
2.7s	1364×	body	640	valid
2.0s	4941×	body	80	valid
653.0ms	693×	body	320	valid
441.0ms	1616×	body	80	nan
188.0ms	348×	body	160	valid