Details

sample504.0ms

Algorithm

intervals

Results

265.0ms	52×	body	1280	valid
63.0ms	59×	body	640	valid
41.0ms	139×	body	80	valid
17.0ms	63×	body	80	nan
13.0ms	16×	body	320	valid
5.0ms	10×	body	160	valid

simplify1.4s

Counts

1 → 1

Iterations

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

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.6b

localize83.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ F (sin B))
0.2b	(/ 1.0 (tan B))
6.4b	(* (pow (fma F F (fma x 2.0 2.0)) (/ (- 1.0) 2.0)) (/ F (sin B)))
14.4b	(pow (fma F F (fma x 2.0 2.0)) (/ (- 1.0) 2.0))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-sqr-sqrt`
60×	`times-frac`
50×	`*-un-lft-identity` `add-cube-cbrt`
34×	`pow-unpow`
22×	`add-exp-log`
13×	`add-cbrt-cube` `associate-r`
9×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
8×	`unpow-prod-down`
7×	`associate-l`
6×	`associate-/r` `prod-exp` `associate-/l` `unswap-sqr`
5×	`pow1` `div-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp` `sqr-pow`
3×	`neg-sub0` `pow-to-exp` `cbrt-undiv` `pow-neg` `neg-mul-1` `div-sub` `pow-exp` `distribute-frac-neg` `pow-sub`
2×	`frac-times` `clear-num` `frac-2neg` `associate-*l/` `cbrt-unprod`
1×	`pow-pow` `tan-quot` `associate-r/` `associate-/r/` `-commutative`

Counts

4 → 160

Calls

4 calls:

5.0ms	(/ F (sin B))
9.0ms	(/ 1.0 (tan B))
35.0ms	(* (pow (fma F F (fma x 2.0 2.0)) (/ (- 1.0) 2.0)) (/ F (sin B)))
14.0ms	(pow (fma F F (fma x 2.0 2.0)) (/ (- 1.0) 2.0))

series878.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(/ F (sin B))
57.0ms	(/ 1.0 (tan B))
534.0ms	(* (pow (fma F F (fma x 2.0 2.0)) (/ (- 1.0) 2.0)) (/ F (sin B)))
201.0ms	(pow (fma F F (fma x 2.0 2.0)) (/ (- 1.0) 2.0))

simplify2.9s

Counts

172 → 172

Iterations

Iter	Nodes
done	5001
2	3725
1	801
0	304

prune1.6s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize72.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.2b	(/ F (* (pow (fma F F (fma 2.0 x 2.0)) (/ 1.0 2.0)) (sin B)))
0.3b	(* (pow (fma F F (fma 2.0 x 2.0)) (/ 1.0 2.0)) (sin B))
14.4b	(pow (fma F F (fma 2.0 x 2.0)) (/ 1.0 2.0))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
25×	`*-un-lft-identity` `add-cube-cbrt`
22×	`add-exp-log`
21×	`times-frac`
13×	`pow-unpow` `add-cbrt-cube`
7×	`unpow-prod-down` `associate-l`
6×	`prod-exp` `associate-/l*`
5×	`pow1` `div-exp`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `cbrt-undiv` `associate-r` `pow-exp` `div-inv` `unswap-sqr` `sqr-pow`
2×	`clear-num` `frac-2neg` `cbrt-unprod`
1×	`pow-pow` `tan-quot` `associate-/r/` `*-commutative`

Counts

4 → 111

Calls

4 calls:

5.0ms	(/ 1.0 (tan B))
8.0ms	(/ F (* (pow (fma F F (fma 2.0 x 2.0)) (/ 1.0 2.0)) (sin B)))
27.0ms	(* (pow (fma F F (fma 2.0 x 2.0)) (/ 1.0 2.0)) (sin B))
7.0ms	(pow (fma F F (fma 2.0 x 2.0)) (/ 1.0 2.0))

series1.6s

Counts

4 → 12

Calls

4 calls:

74.0ms	(/ 1.0 (tan B))
591.0ms	(/ F (* (pow (fma F F (fma 2.0 x 2.0)) (/ 1.0 2.0)) (sin B)))
733.0ms	(* (pow (fma F F (fma 2.0 x 2.0)) (/ 1.0 2.0)) (sin B))
239.0ms	(pow (fma F F (fma 2.0 x 2.0)) (/ 1.0 2.0))

simplify1.2s

Counts

123 → 123

Iterations

Iter	Nodes
done	5000
2	2498
1	645
0	256

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize57.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (sin B) (pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0))) F)
0.3b	(/ 1 (/ (* (sin B) (pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0))) F))
0.3b	(* (sin B) (pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0)))
14.4b	(pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-exp-log`
45×	`times-frac`
38×	`add-sqr-sqrt`
33×	`*-un-lft-identity` `add-cube-cbrt`
26×	`div-exp`
20×	`add-cbrt-cube`
15×	`prod-exp`
13×	`pow-unpow`
10×	`associate-/r*`
7×	`cbrt-undiv` `unpow-prod-down` `associate-r` `div-inv`
6×	`pow-to-exp` `pow1` `pow-exp`
5×	`rec-exp` `1-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`associate-l` `cbrt-unprod` `unswap-sqr` `sqr-pow`
2×	`clear-num` `frac-2neg`
1×	`pow-pow` `associate-/r/` `*-commutative` `pow-flip` `inv-pow`

Counts

4 → 145

Calls

4 calls:

11.0ms	(/ (* (sin B) (pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0))) F)
25.0ms	(/ 1 (/ (* (sin B) (pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0))) F))
37.0ms	(* (sin B) (pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0)))
7.0ms	(pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0))

series1.3s

Counts

4 → 12

Calls

4 calls:

233.0ms	(/ (* (sin B) (pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0))) F)
524.0ms	(/ 1 (/ (* (sin B) (pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0))) F))
360.0ms	(* (sin B) (pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0)))
215.0ms	(pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0))

simplify2.6s

Counts

157 → 157

Iterations

Iter	Nodes
done	5001
2	3992
1	754
0	282

prune1.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize85.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (/ 1.0 (tan B)))
0.5b	(cbrt (/ 1.0 (tan B)))
0.5b	(cbrt (/ 1.0 (tan B)))
14.4b	(pow (fma F F (fma 2.0 x 2.0)) (/ 1.0 2.0))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

42×	`cbrt-prod`
36×	`times-frac`
33×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
13×	`pow-unpow`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`cbrt-div` `unpow-prod-down` `pow1/3` `tan-quot` `associate-/r/`
1×	`pow-to-exp` `pow-pow` `pow-exp` `sqr-pow`

Counts

4 → 104

Calls

4 calls:

6.0ms	(cbrt (/ 1.0 (tan B)))
5.0ms	(cbrt (/ 1.0 (tan B)))
5.0ms	(cbrt (/ 1.0 (tan B)))
7.0ms	(pow (fma F F (fma 2.0 x 2.0)) (/ 1.0 2.0))

series932.0ms

Counts

4 → 12

Calls

4 calls:

240.0ms	(cbrt (/ 1.0 (tan B)))
244.0ms	(cbrt (/ 1.0 (tan B)))
245.0ms	(cbrt (/ 1.0 (tan B)))
203.0ms	(pow (fma F F (fma 2.0 x 2.0)) (/ 1.0 2.0))

simplify2.1s

Counts

116 → 116

Iterations

Iter	Nodes
done	5000
3	4977
2	1056
1	370
0	169

prune1.3s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

regimes598.0ms

Accuracy

98.1% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 10.5b

bsearch453.0ms

Steps

Iters	Range		Point
7	5493762008314.814	631776370996477.2	5611841369517.248
9	-2.8555728020291845e+22	-29272228678884.97	-5.738898656227044e+20

simplify9.0ms

Iterations

Iter	Nodes
done	59
1	59
0	48

end0.0ms

sample9.7s

Algorithm

intervals

Results

3.9s	1698×	body	1280	valid
2.2s	4690×	body	80	valid
1.8s	1407×	body	640	valid
707.0ms	711×	body	320	valid
417.0ms	1650×	body	80	nan
225.0ms	351×	body	160	valid