Details

sample443.0ms

Algorithm

intervals

Results

124.0ms	41×	body	640	valid
109.0ms	51×	body	1280	valid
52.0ms	162×	body	80	valid
28.0ms	21×	body	320	valid
13.0ms	51×	body	80	nan
6.0ms	9×	body	160	valid

simplify1.7s

Counts

1 → 1

Iterations

Useful iterations: 2 (37.0ms)

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

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.3b

localize55.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))
6.3b	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (* x (/ 1.0 (tan B)))))
20.2b	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

rewrite66.0ms

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))
20.0ms	(* 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)))))
33.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

series1.3s

Counts

4 → 12

Calls

4 calls:

64.0ms	(/ 1.0 (tan B))
173.0ms	(* x (/ 1.0 (tan B)))
513.0ms	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (* x (/ 1.0 (tan B)))))
509.0ms	(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

prune976.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 15.7b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ F (sin B))
0.1b	(/ (* x 1.0) (tan B))
6.3b	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (/ (* x 1.0) (tan B))))
20.2b	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

rewrite58.0ms

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:

9.0ms	(/ F (sin B))
32.0ms	(/ (* 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))))
13.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

series1.2s

Counts

4 → 12

Calls

4 calls:

65.0ms	(/ F (sin B))
167.0ms	(/ (* x 1.0) (tan B))
490.0ms	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (/ (* x 1.0) (tan B))))
477.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

simplify1.7s

Counts

123 → 123

Iterations

Useful iterations: done (1.7s)

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

prune962.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 15.7b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (sin B))
0.2b	(* F (/ 1 (sin B)))
6.3b	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (* F (/ 1 (sin B))) (- (/ (* x 1.0) (tan B))))
20.2b	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

rewrite46.0ms

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:

11.0ms	(/ 1 (sin B))
24.0ms	(* 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))))
7.0ms	(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))
79.0ms	(* F (/ 1 (sin B)))
488.0ms	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (* F (/ 1 (sin B))) (- (/ (* x 1.0) (tan B))))
496.0ms	(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

prune950.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 15.7b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(* F (/ 1 (sin B)))
0.3b	(/ 1 (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)))
6.3b	(fma (/ 1 (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))) (* F (/ 1 (sin B))) (- (/ (* x 1.0) (tan B))))
20.1b	(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 132

Calls

4 calls:

18.0ms	(* F (/ 1 (sin B)))
20.0ms	(/ 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 (/ 1 (sin B))) (- (/ (* x 1.0) (tan B))))
10.0ms	(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

series2.5s

Counts

4 → 12

Calls

4 calls:

84.0ms	(* F (/ 1 (sin B)))
1.2s	(/ 1 (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)))
763.0ms	(fma (/ 1 (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))) (* F (/ 1 (sin B))) (- (/ (* x 1.0) (tan B))))
432.0ms	(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

simplify1.8s

Counts

144 → 144

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	337	2807
1	864	2600
2	3228	2307
done	5000	2305

prune1.2s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 15.7b

regimes407.0ms

Accuracy

0% (0.4b remaining)

Error of 13.4b against oracle of 13.1b and baseline of 13.4b

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample10.3s

Algorithm

intervals

Results

4.4s	1657×	body	1280	valid
2.1s	1412×	body	640	valid
2.0s	4768×	body	80	valid
642.0ms	680×	body	320	valid
315.0ms	1514×	body	80	nan
201.0ms	362×	body	160	valid