Details

sample545.0ms

Algorithm

intervals

Results

179.0ms	48×	body	1280	valid
67.0ms	43×	body	640	valid
61.0ms	163×	body	80	valid
29.0ms	25×	body	320	valid
15.0ms	53×	body	80	nan
7.0ms	9×	body	160	valid

simplify2.3s

Counts

1 → 1

Iterations

Useful iterations: 2 (32.0ms)

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

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.7b

localize91.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))
8.8b	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (* x (/ 1.0 (tan B)))))
18.9b	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

rewrite83.0ms

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))
40.0ms	(* 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)))))
19.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

series1.6s

Counts

4 → 12

Calls

4 calls:

77.0ms	(/ 1.0 (tan B))
222.0ms	(* x (/ 1.0 (tan B)))
688.0ms	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (* x (/ 1.0 (tan B)))))
661.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

simplify2.2s

Counts

135 → 135

Iterations

Useful iterations: done (2.2s)

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

prune1.8s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 15.3b

localize70.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ F (sin B))
0.2b	(/ (* x 1.0) (tan B))
8.8b	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (/ (* x 1.0) (tan B))))
18.9b	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

rewrite73.0ms

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))
22.0ms	(/ (* 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)))

series1.7s

Counts

4 → 12

Calls

4 calls:

107.0ms	(/ F (sin B))
222.0ms	(/ (* x 1.0) (tan B))
691.0ms	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (/ (* x 1.0) (tan B))))
648.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

simplify2.2s

Counts

123 → 123

Iterations

Useful iterations: done (2.2s)

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

prune1.7s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 15.3b

localize93.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* x 1.0) (tan B))
0.3b	(* F (/ 1 (sin B)))
8.8b	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (* F (/ 1 (sin B))) (- (/ (* x 1.0) (tan B))))
18.9b	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

rewrite83.0ms

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:

23.0ms	(/ (* x 1.0) (tan B))
36.0ms	(* 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))))
15.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

series1.7s

Counts

4 → 12

Calls

4 calls:

232.0ms	(/ (* x 1.0) (tan B))
110.0ms	(* F (/ 1 (sin B)))
707.0ms	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (* F (/ 1 (sin B))) (- (/ (* x 1.0) (tan B))))
650.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

simplify2.7s

Counts

132 → 132

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	315	1938
1	837	1820
2	3100	1619
done	5001	1618

prune1.7s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 15.0b

localize101.0ms

Local error

Found 4 expressions with local error:

0.3b	(* F (/ 1 (sin B)))
0.6b	(pow (fma 2.0 x (fma F F 2.0)) (- (* (cbrt 1.0) (cbrt 1.0))))
8.8b	(fma (pow (pow (fma 2.0 x (fma F F 2.0)) (- (* (cbrt 1.0) (cbrt 1.0)))) (/ (cbrt 1.0) 2.0)) (* F (/ 1 (sin B))) (- (/ (* x 1.0) (tan B))))
18.2b	(pow (pow (fma 2.0 x (fma F F 2.0)) (- (* (cbrt 1.0) (cbrt 1.0)))) (/ (cbrt 1.0) 2.0))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
29×	`add-cube-cbrt` `times-frac`
28×	`pow-unpow`
16×	`add-exp-log`
13×	`unpow-prod-down` `associate-r`
9×	`cbrt-prod` `add-cbrt-cube`
7×	`pow1`
5×	`pow-exp`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `associate-l` `unswap-sqr` `sqr-pow`
2×	`pow-pow` `div-exp` `cbrt-unprod` `div-inv`
1×	`cbrt-undiv` `neg-sub0` `distribute-lft-neg-in` `pow-neg` `neg-mul-1` `rec-exp` `distribute-rgt-neg-in` `1-exp` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `fma-udef` `pow-sub`

Counts

4 → 116

Calls

4 calls:

37.0ms	(* F (/ 1 (sin B)))
7.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (* (cbrt 1.0) (cbrt 1.0))))
1.0ms	(fma (pow (pow (fma 2.0 x (fma F F 2.0)) (- (* (cbrt 1.0) (cbrt 1.0)))) (/ (cbrt 1.0) 2.0)) (* F (/ 1 (sin B))) (- (/ (* x 1.0) (tan B))))
20.0ms	(pow (pow (fma 2.0 x (fma F F 2.0)) (- (* (cbrt 1.0) (cbrt 1.0)))) (/ (cbrt 1.0) 2.0))

series3.6s

Counts

4 → 12

Calls

4 calls:

99.0ms	(* F (/ 1 (sin B)))
1.4s	(pow (fma 2.0 x (fma F F 2.0)) (- (* (cbrt 1.0) (cbrt 1.0))))
1.0s	(fma (pow (pow (fma 2.0 x (fma F F 2.0)) (- (* (cbrt 1.0) (cbrt 1.0)))) (/ (cbrt 1.0) 2.0)) (* F (/ 1 (sin B))) (- (/ (* x 1.0) (tan B))))
1.1s	(pow (pow (fma 2.0 x (fma F F 2.0)) (- (* (cbrt 1.0) (cbrt 1.0)))) (/ (cbrt 1.0) 2.0))

simplify2.7s

Counts

128 → 128

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	336	2894
1	943	2632
2	3606	2414
done	5000	2394

prune1.7s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 15.0b

regimes1.1s

Accuracy

0% (0.4b remaining)

Error of 13.3b against oracle of 12.9b and baseline of 13.3b

bsearch0.0ms

simplify11.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	27
1	25	27
2	31	27
done	31	27

end0.0ms

sample13.1s

Algorithm

intervals

Results

6.4s	1719×	body	1280	valid
2.3s	1374×	body	640	valid
1.8s	4716×	body	80	valid
872.0ms	667×	body	320	valid
552.0ms	1601×	body	80	nan
246.0ms	350×	body	160	valid