Details

sample523.0ms

Algorithm

intervals

Results

186.0ms	55×	body	1280	valid
76.0ms	50×	body	640	valid
49.0ms	144×	body	80	valid
26.0ms	24×	body	320	valid
18.0ms	59×	body	80	nan
8.0ms	11×	body	160	valid

simplify3.9s

Counts

1 → 1

Iterations

Useful iterations: 2 (58.0ms)

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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.7b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))
7.3b	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (* x (/ 1.0 (tan B)))))
16.6b	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

rewrite56.0ms

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))
27.0ms	(* 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)))))
17.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

series1.3s

Counts

4 → 12

Calls

4 calls:

66.0ms	(/ 1.0 (tan B))
175.0ms	(* x (/ 1.0 (tan B)))
545.0ms	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (* x (/ 1.0 (tan B)))))
529.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

simplify3.5s

Counts

135 → 135

Iterations

Useful iterations: 3 (2.1s)

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

prune961.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 13.2b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ F (sin B))
0.2b	(/ (* x 1.0) (tan B))
7.3b	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (/ (* x 1.0) (tan B))))
16.6b	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

rewrite67.0ms

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:

11.0ms	(/ F (sin B))
33.0ms	(/ (* 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))))
14.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

series1.3s

Counts

4 → 12

Calls

4 calls:

72.0ms	(/ F (sin B))
182.0ms	(/ (* x 1.0) (tan B))
471.0ms	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (/ (* x 1.0) (tan B))))
529.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

simplify1.6s

Counts

123 → 123

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	292	1805
1	677	1732
2	1811	1610
done	5001	1575

prune1.1s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 13.2b

localize47.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* x 1.0) (tan B))
0.3b	(pow (fma 2.0 x (fma F F 2.0)) (- 1.0))
7.3b	(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))))
16.2b	(pow (pow (fma 2.0 x (fma F F 2.0)) (- 1.0)) (/ 1 2.0))

rewrite24.0ms

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:

11.0ms	(/ (* 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))))
7.0ms	(pow (pow (fma 2.0 x (fma F F 2.0)) (- 1.0)) (/ 1 2.0))

series1.8s

Counts

4 → 12

Calls

4 calls:

195.0ms	(/ (* x 1.0) (tan B))
494.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- 1.0))
609.0ms	(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))))
541.0ms	(pow (pow (fma 2.0 x (fma F F 2.0)) (- 1.0)) (/ 1 2.0))

simplify2.1s

Counts

109 → 109

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	280	2047
1	682	1933
2	1835	1800
done	5000	1744

prune965.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 13.2b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* x 1.0) (tan B))
0.3b	(* F (/ 1 (sin B)))
7.3b	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (* F (/ 1 (sin B))) (- (/ (* x 1.0) (tan B))))
16.6b	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

rewrite72.0ms

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:

34.0ms	(/ (* x 1.0) (tan B))
22.0ms	(* 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)))

series1.3s

Counts

4 → 12

Calls

4 calls:

173.0ms	(/ (* x 1.0) (tan B))
74.0ms	(* F (/ 1 (sin B)))
527.0ms	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (* F (/ 1 (sin B))) (- (/ (* x 1.0) (tan B))))
560.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

simplify1.6s

Counts

132 → 132

Iterations

Useful iterations: done (1.6s)

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

prune878.0ms

Pruning

20 alts after pruning (18 fresh and 2 done)

Merged error: 13.2b

regimes549.0ms

Accuracy

0% (0.4b remaining)

Error of 13.9b against oracle of 13.5b and baseline of 13.9b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	43
1	32	43
2	37	43
done	37	43

end0.0ms

sample10.6s

Algorithm

intervals

Results

4.6s	1667×	body	1280	valid
1.9s	1344×	body	640	valid
1.8s	4897×	body	80	valid
904.0ms	1629×	body	80	nan
591.0ms	711×	body	320	valid
215.0ms	333×	body	160	valid