Details

sample362.0ms

Algorithm

intervals

Results

87.0ms	166×	body	80	valid
79.0ms	51×	body	1280	valid
42.0ms	41×	body	640	valid
13.0ms	20×	body	320	valid
13.0ms	55×	body	80	nan
3.0ms	6×	body	160	valid

simplify1.5s

Counts

1 → 1

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	20	27
1	43	26
2	91	24
3	169	24
4	384	24
5	1755	24
done	5000	24

prune27.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.4b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))
7.0b	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (* x (/ 1.0 (tan B)))))
16.8b	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
37×	`times-frac`
36×	`*-un-lft-identity` `add-cube-cbrt`
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×	`associate-/r` `unpow-prod-down` `associate-l` `associate-/l`
2×	`cbrt-undiv` `div-exp` `prod-exp` `tan-quot` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`neg-sub0` `pow-to-exp` `pow-neg` `clear-num` `neg-mul-1` `pow-pow` `frac-2neg` `pow-prod-down` `pow-exp` `associate-r/` `-commutative` `fma-udef` `pow-sub` `sqr-pow`

Counts

4 → 123

Calls

4 calls:

9.0ms	(/ 1.0 (tan B))
29.0ms	(* 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)))))
26.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

series1.3s

Counts

4 → 12

Calls

4 calls:

69.0ms	(/ 1.0 (tan B))
184.0ms	(* x (/ 1.0 (tan B)))
493.0ms	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (* x (/ 1.0 (tan B)))))
533.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

simplify1.3s

Counts

135 → 135

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	285	1919
1	761	1837
2	2627	1720
done	5000	1715

prune1.4s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.9b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x 1.0) (tan B))
0.1b	(/ F (sin B))
7.0b	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (/ (* x 1.0) (tan B))))
16.8b	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt` `pow-unpow` `*-un-lft-identity` `times-frac` `add-cube-cbrt`
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×	`clear-num` `frac-2neg`
1×	`neg-sub0` `pow-to-exp` `pow-neg` `neg-mul-1` `pow-pow` `pow-exp` `prod-exp` `tan-quot` `associate-/r/` `cbrt-unprod` `fma-udef` `pow-sub` `sqr-pow`

Counts

4 → 111

Calls

4 calls:

25.0ms	(/ (* x 1.0) (tan B))
8.0ms	(/ 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))))
10.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

series1.2s

Counts

4 → 12

Calls

4 calls:

201.0ms	(/ (* x 1.0) (tan B))
66.0ms	(/ F (sin B))
428.0ms	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (/ (* x 1.0) (tan B))))
455.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

simplify1.3s

Counts

123 → 123

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	292	1805
1	737	1729
2	2651	1614
done	5000	1613

prune1.1s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.9b

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (sin B))
0.2b	(* F (/ 1 (sin B)))
7.0b	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (* F (/ 1 (sin B))) (- (/ (* x 1.0) (tan B))))
16.8b	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

rewrite49.0ms

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×	`associate-/r` `unpow-prod-down` `associate-l` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `1-exp` `cbrt-unprod`
1×	`neg-sub0` `pow-to-exp` `pow-neg` `clear-num` `neg-mul-1` `pow-pow` `frac-2neg` `pow-prod-down` `pow-exp` `associate-r/` `un-div-inv` `-commutative` `fma-udef` `pow-flip` `inv-pow` `pow-sub` `sqr-pow`

Counts

4 → 129

Calls

4 calls:

10.0ms	(/ 1 (sin B))
26.0ms	(* 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))))
6.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

series1.1s

Counts

4 → 12

Calls

4 calls:

22.0ms	(/ 1 (sin B))
69.0ms	(* 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))))
474.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

simplify1.4s

Counts

141 → 141

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	287	1957
1	753	1799
2	2692	1612
done	5000	1611

prune1.3s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 12.9b

localize71.0ms

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)))
7.0b	(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))))
16.8b	(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

rewrite65.0ms

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×	`clear-num` `pow-pow` `frac-2neg` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `fma-udef` `pow-flip` `inv-pow`

Counts

4 → 132

Calls

4 calls:

25.0ms	(* F (/ 1 (sin B)))
23.0ms	(/ 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))))
9.0ms	(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

series2.9s

Counts

4 → 12

Calls

4 calls:

70.0ms	(* F (/ 1 (sin B)))
1.3s	(/ 1 (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)))
687.0ms	(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))))
884.0ms	(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

simplify1.5s

Counts

144 → 144

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	337	2807
1	866	2600
2	3225	2341
done	5001	2339

prune1.1s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 12.9b

regimes502.0ms

Accuracy

0% (0.3b remaining)

Error of 13.8b against oracle of 13.5b and baseline of 13.8b

bsearch0.0ms

simplify11.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample10.5s

Algorithm

intervals

Results

4.2s	1691×	body	1280	valid
2.3s	1344×	body	640	valid
2.0s	4849×	body	80	valid
687.0ms	707×	body	320	valid
437.0ms	1604×	body	80	nan
184.0ms	338×	body	160	valid