Details

sample513.0ms

Algorithm

intervals

Results

121.0ms	52×	body	1280	valid
114.0ms	139×	body	80	valid
83.0ms	59×	body	640	valid
17.0ms	63×	body	80	nan
17.0ms	16×	body	320	valid
6.0ms	10×	body	160	valid

simplify2.5s

Counts

1 → 1

Iterations

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

prune32.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.6b

localize78.0ms

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))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

81×	`times-frac`
78×	`add-sqr-sqrt`
65×	`*-un-lft-identity` `add-cube-cbrt`
34×	`pow-unpow`
22×	`add-exp-log`
21×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
13×	`add-cbrt-cube` `associate-r` `associate-/l*`
8×	`unpow-prod-down`
7×	`neg-mul-1` `associate-l`
6×	`associate-/r*` `prod-exp` `unswap-sqr`
5×	`pow1` `div-exp`
4×	`neg-sub0` `expm1-log1p-u` `div-sub` `distribute-frac-neg` `log1p-expm1-u` `div-inv` `add-log-exp` `sqr-pow`
3×	`pow-to-exp` `cbrt-undiv` `pow-neg` `pow-exp` `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 → 190

Calls

4 calls:

5.0ms	(/ F (sin B))
8.0ms	(/ (- 1.0) (tan B))
45.0ms	(* (pow (fma F F (fma x 2.0 2.0)) (/ (- 1.0) 2.0)) (/ F (sin B)))
13.0ms	(pow (fma F F (fma x 2.0 2.0)) (/ (- 1.0) 2.0))

series1.0s

Counts

4 → 12

Calls

4 calls:

88.0ms	(/ F (sin B))
66.0ms	(/ (- 1.0) (tan B))
606.0ms	(* (pow (fma F F (fma x 2.0 2.0)) (/ (- 1.0) 2.0)) (/ F (sin B)))
246.0ms	(pow (fma F F (fma x 2.0 2.0)) (/ (- 1.0) 2.0))

simplify3.4s

Counts

202 → 202

Iterations

Iter	Nodes
done	5001
2	4179
1	892
0	338

prune2.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize42.0ms

Local error

Found 4 expressions with local error:

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

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
42×	`times-frac`
40×	`*-un-lft-identity` `add-cube-cbrt`
22×	`add-exp-log`
13×	`pow-unpow` `add-cbrt-cube` `associate-/l*`
12×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
7×	`unpow-prod-down` `associate-l`
6×	`prod-exp`
5×	`pow1` `div-exp`
4×	`expm1-log1p-u` `associate-/r*` `neg-mul-1` `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×	`neg-sub0` `pow-pow` `div-sub` `tan-quot` `distribute-frac-neg` `associate-/r/` `*-commutative`

Counts

4 → 141

Calls

4 calls:

12.0ms	(/ (- 1.0) (tan B))
9.0ms	(/ F (* (pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0)) (sin B)))
12.0ms	(* (pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0)) (sin B))
4.0ms	(pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0))

series1.5s

Counts

4 → 12

Calls

4 calls:

70.0ms	(/ (- 1.0) (tan B))
538.0ms	(/ F (* (pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0)) (sin B)))
706.0ms	(* (pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0)) (sin B))
215.0ms	(pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0))

simplify2.2s

Counts

153 → 153

Iterations

Iter	Nodes
done	5000
2	3028
1	754
0	302

prune1.6s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize70.0ms

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 x 2.0 2.0)) (/ 1.0 2.0))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

105×	`cbrt-prod`
99×	`times-frac`
72×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
27×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
13×	`pow-unpow`
9×	`neg-mul-1`
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 → 167

Calls

4 calls:

5.0ms	(cbrt (/ (- 1.0) (tan B)))
5.0ms	(cbrt (/ (- 1.0) (tan B)))
5.0ms	(cbrt (/ (- 1.0) (tan B)))
4.0ms	(pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

284.0ms	(cbrt (/ (- 1.0) (tan B)))
266.0ms	(cbrt (/ (- 1.0) (tan B)))
254.0ms	(cbrt (/ (- 1.0) (tan B)))
259.0ms	(pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0))

simplify1.3s

Counts

179 → 179

Iterations

Iter	Nodes
done	5001
2	1365
1	493
0	240

prune2.6s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize91.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (/ (- 1.0) (tan B)))
0.5b	(cbrt (/ (- 1.0) (tan B)))
0.6b	(cbrt (tan B))
14.4b	(pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

73×	`cbrt-prod`
69×	`times-frac`
53×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
18×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
13×	`pow-unpow`
6×	`neg-mul-1`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-div` `unpow-prod-down` `pow1/3` `tan-quot` `div-inv`
2×	`associate-/r/`
1×	`pow-to-exp` `pow-pow` `pow-exp` `sqr-pow`

Counts

4 → 135

Calls

4 calls:

9.0ms	(cbrt (/ (- 1.0) (tan B)))
8.0ms	(cbrt (/ (- 1.0) (tan B)))
3.0ms	(cbrt (tan B))
6.0ms	(pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0))

series845.0ms

Counts

4 → 12

Calls

4 calls:

231.0ms	(cbrt (/ (- 1.0) (tan B)))
241.0ms	(cbrt (/ (- 1.0) (tan B)))
146.0ms	(cbrt (tan B))
227.0ms	(pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0))

simplify1.5s

Counts

147 → 147

Iterations

Iter	Nodes
done	5001
2	1494
1	546
0	265

prune1.9s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

regimes646.0ms

Accuracy

98.3% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 11.1b

bsearch514.0ms

Steps

Iters	Range		Point
7	5493762008314.814	631776370996477.2	5611841369517.248
9	-2.8555728020291845e+22	-29272228678884.97	-29785009876925.473

simplify9.0ms

Iterations

Iter	Nodes
done	46
1	46
0	37

end0.0ms

sample9.7s

Algorithm

intervals

Results

3.3s	1698×	body	1280	valid
2.6s	1407×	body	640	valid
1.6s	4690×	body	80	valid
982.0ms	711×	body	320	valid
420.0ms	1650×	body	80	nan
186.0ms	351×	body	160	valid