Details

sample622.0ms

Algorithm

intervals

Results

168.0ms	58×	body	1280	valid
163.0ms	140×	body	80	valid
84.0ms	48×	body	640	valid
46.0ms	22×	body	320	valid
8.0ms	38×	body	80	nan
5.0ms	11×	body	160	valid

simplify4.0s

Counts

1 → 1

Iterations

Useful iterations: 2 (40.0ms)

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

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.2b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))
5.8b	(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)))

rewrite54.0ms

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))
21.0ms	(* 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)))))
9.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

series1.2s

Counts

4 → 12

Calls

4 calls:

82.0ms	(/ 1.0 (tan B))
141.0ms	(* x (/ 1.0 (tan B)))
512.0ms	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (* x (/ 1.0 (tan B)))))
506.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

simplify3.6s

Counts

135 → 135

Iterations

Useful iterations: 3 (2.2s)

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

prune1.0s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 11.5b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x 1.0) (tan B))
0.1b	(/ F (sin B))
5.8b	(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)))

rewrite42.0ms

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:

18.0ms	(/ (* x 1.0) (tan B))
6.0ms	(/ 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))))
13.0ms	(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))
74.0ms	(/ F (sin B))
525.0ms	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (/ (* x 1.0) (tan B))))
495.0ms	(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

prune869.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 11.5b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x 1.0) (tan B))
0.2b	(* F (/ 1 (sin B)))
5.8b	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (* F (/ 1 (sin B))) (- (/ (* x 1.0) (tan B))))
17.3b	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 120

Calls

4 calls:

11.0ms	(/ (* x 1.0) (tan B))
29.0ms	(* 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))))
7.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

series1.3s

Counts

4 → 12

Calls

4 calls:

212.0ms	(/ (* x 1.0) (tan B))
100.0ms	(* F (/ 1 (sin B)))
515.0ms	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (* F (/ 1 (sin B))) (- (/ (* x 1.0) (tan B))))
485.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

simplify2.0s

Counts

132 → 132

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	315	1938
1	761	1757
2	1971	1607
done	5001	1572

prune910.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 11.5b

localize55.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (pow (sqrt (fma 2.0 x (fma F F 2.0))) (- (/ 1.0 2.0))) (pow (sqrt (fma 2.0 x (fma F F 2.0))) (- (/ 1.0 2.0))))
5.8b	(fma (* (pow (sqrt (fma 2.0 x (fma F F 2.0))) (- (/ 1.0 2.0))) (pow (sqrt (fma 2.0 x (fma F F 2.0))) (- (/ 1.0 2.0)))) (/ F (sin B)) (- (/ (* x 1.0) (tan B))))
17.3b	(sqrt (fma 2.0 x (fma F F 2.0)))
17.3b	(sqrt (fma 2.0 x (fma F F 2.0)))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
44×	`unpow-prod-down`
28×	`sqrt-prod`
18×	`add-cube-cbrt` `*-un-lft-identity`
16×	`add-exp-log` `unswap-sqr`
12×	`swap-sqr` `sqr-pow`
10×	`associate-r` `associate-l`
9×	`prod-exp`
7×	`pow-neg`
6×	`pow1` `neg-sub0` `pow-to-exp` `pow-exp` `add-cbrt-cube` `pow-sub`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `associate-l/`
1×	`pow2` `pow-prod-down` `pow-sqr` `un-div-inv` `*-commutative` `pow-prod-up` `cbrt-unprod` `fma-udef`

Counts

4 → 121

Calls

4 calls:

72.0ms	(* (pow (sqrt (fma 2.0 x (fma F F 2.0))) (- (/ 1.0 2.0))) (pow (sqrt (fma 2.0 x (fma F F 2.0))) (- (/ 1.0 2.0))))
1.0ms	(fma (* (pow (sqrt (fma 2.0 x (fma F F 2.0))) (- (/ 1.0 2.0))) (pow (sqrt (fma 2.0 x (fma F F 2.0))) (- (/ 1.0 2.0)))) (/ F (sin B)) (- (/ (* x 1.0) (tan B))))
3.0ms	(sqrt (fma 2.0 x (fma F F 2.0)))
4.0ms	(sqrt (fma 2.0 x (fma F F 2.0)))

series2.6s

Counts

4 → 12

Calls

4 calls:

1.4s	(* (pow (sqrt (fma 2.0 x (fma F F 2.0))) (- (/ 1.0 2.0))) (pow (sqrt (fma 2.0 x (fma F F 2.0))) (- (/ 1.0 2.0))))
873.0ms	(fma (* (pow (sqrt (fma 2.0 x (fma F F 2.0))) (- (/ 1.0 2.0))) (pow (sqrt (fma 2.0 x (fma F F 2.0))) (- (/ 1.0 2.0)))) (/ F (sin B)) (- (/ (* x 1.0) (tan B))))
175.0ms	(sqrt (fma 2.0 x (fma F F 2.0)))
142.0ms	(sqrt (fma 2.0 x (fma F F 2.0)))

simplify3.7s

Counts

133 → 133

Iterations

Useful iterations: done (3.7s)

Iter	Nodes	Cost
0	197	4337
1	440	3145
2	1326	2829
3	4810	2769
done	5000	2767

prune608.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 11.5b

regimes478.0ms

Accuracy

0% (0.5b remaining)

Error of 13.7b against oracle of 13.3b and baseline of 13.7b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	39
1	24	39
2	29	39
done	29	39

end0.0ms

sample10.5s

Algorithm

intervals

Results

3.8s	1661×	body	1280	valid
2.4s	1399×	body	640	valid
2.0s	4707×	body	80	valid
1.2s	692×	body	320	valid
396.0ms	1614×	body	80	nan
217.0ms	385×	body	160	valid