Details

sample411.0ms

Algorithm

intervals

Results

161.0ms	54×	body	1280	valid
58.0ms	38×	body	640	valid
48.0ms	157×	body	80	valid
16.0ms	54×	body	80	nan
12.0ms	14×	body	320	valid
10.0ms	16×	body	160	valid

simplify3.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
6	2738
5	849
4	325
3	161
2	90
1	43
0	20

prune43.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.4b

localize74.0ms

Local error

Found 4 expressions with local error:

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

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

214×	`times-frac`
133×	`add-sqr-sqrt`
128×	`*-un-lft-identity` `add-cube-cbrt`
51×	`unpow-prod-down`
34×	`associate-/r*`
30×	`pow-unpow`
25×	`add-exp-log`
17×	`sqr-pow`
16×	`add-cbrt-cube`
14×	`associate-l`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
12×	`associate-/r/`
11×	`div-exp`
9×	`div-inv`
7×	`pow1`
6×	`neg-sub0` `pow-neg` `associate-/l*` `pow-sub`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `associate-r` `pow-exp`
2×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`neg-mul-1` `pow-pow` `pow-prod-down` `associate-l/` `tan-quot` `-commutative`

Counts

4 → 262

Calls

4 calls:

28.0ms	(/ F (/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))))
15.0ms	(* (/ 1.0 (tan B)) x)
9.0ms	(/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0))))
8.0ms	(pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))

series1.2s

Counts

4 → 12

Calls

4 calls:

499.0ms	(/ F (/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))))
133.0ms	(* (/ 1.0 (tan B)) x)
355.0ms	(/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0))))
239.0ms	(pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))

simplify3.8s

Counts

274 → 274

Iterations

Iter	Nodes
done	5004
2	4220
1	1302
0	497

prune2.5s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize70.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ x (tan B))
0.2b	(/ F (/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))))
0.3b	(/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0))))
16.2b	(pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

213×	`times-frac`
128×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
51×	`unpow-prod-down`
37×	`associate-/r*`
30×	`pow-unpow`
22×	`add-exp-log`
17×	`sqr-pow`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `add-cbrt-cube`
12×	`associate-/r/`
11×	`div-exp`
9×	`div-inv` `associate-/l*`
6×	`neg-sub0` `pow-neg` `pow-sub`
5×	`pow1` `cbrt-undiv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `clear-num` `frac-2neg` `pow-exp`
1×	`neg-mul-1` `pow-pow` `tan-quot`

Counts

4 → 257

Calls

4 calls:

10.0ms	(/ x (tan B))
25.0ms	(/ F (/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))))
10.0ms	(/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0))))
11.0ms	(pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))

series1.1s

Counts

4 → 12

Calls

4 calls:

167.0ms	(/ x (tan B))
437.0ms	(/ F (/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))))
291.0ms	(/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0))))
171.0ms	(pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))

simplify4.0s

Counts

269 → 269

Iterations

Iter	Nodes
done	5004
2	4052
1	1238
0	480

prune2.4s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize76.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ x (tan B))
0.2b	(/ F (pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0)))
0.4b	(* (/ 1 (sin B)) (/ F (pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0))))
16.2b	(pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

91×	`add-sqr-sqrt`
86×	`times-frac`
61×	`*-un-lft-identity`
57×	`add-cube-cbrt`
56×	`add-exp-log`
27×	`unpow-prod-down`
25×	`associate-r`
24×	`div-exp`
20×	`add-cbrt-cube`
16×	`prod-exp`
13×	`pow-unpow` `associate-l`
12×	`unswap-sqr`
11×	`sqr-pow`
10×	`associate-/r*`
7×	`pow1`
6×	`pow-to-exp` `cbrt-undiv` `pow-exp` `associate-/l*`
5×	`div-inv`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg`
1×	`frac-times` `pow-pow` `pow-prod-down` `associate-l/` `tan-quot` `associate-r/` `associate-/r/` `*-commutative`

Counts

4 → 190

Calls

4 calls:

5.0ms	(/ x (tan B))
12.0ms	(/ F (pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0)))
35.0ms	(* (/ 1 (sin B)) (/ F (pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0))))
6.0ms	(pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0))

series1.3s

Counts

4 → 12

Calls

4 calls:

153.0ms	(/ x (tan B))
371.0ms	(/ F (pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0)))
540.0ms	(* (/ 1 (sin B)) (/ F (pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0))))
218.0ms	(pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0))

simplify2.8s

Counts

202 → 202

Iterations

Iter	Nodes
done	5013
2	2900
1	962
0	353

prune1.8s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize73.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ x (sin B)) (cos B))
0.2b	(/ F (/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))))
0.3b	(/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0))))
16.2b	(pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

214×	`times-frac`
133×	`add-sqr-sqrt`
128×	`*-un-lft-identity` `add-cube-cbrt`
51×	`unpow-prod-down`
34×	`associate-/r*`
30×	`pow-unpow`
25×	`add-exp-log`
17×	`sqr-pow`
16×	`add-cbrt-cube`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `associate-l`
11×	`div-exp` `associate-/r/`
9×	`div-inv`
7×	`pow1`
6×	`neg-sub0` `pow-neg` `associate-/l*` `pow-sub`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `associate-r` `pow-exp`
2×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`neg-mul-1` `pow-pow` `pow-prod-down` `associate-l/` `-commutative`

Counts

4 → 261

Calls

4 calls:

31.0ms	(* (/ x (sin B)) (cos B))
21.0ms	(/ F (/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))))
9.0ms	(/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0))))
12.0ms	(pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))

series1.6s

Counts

4 → 12

Calls

4 calls:

157.0ms	(* (/ x (sin B)) (cos B))
469.0ms	(/ F (/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))))
764.0ms	(/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0))))
221.0ms	(pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))

simplify3.8s

Counts

273 → 273

Iterations

Iter	Nodes
done	5002
2	4344
1	1296
0	488

prune2.0s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.0b

regimes480.0ms

Accuracy

97.9% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 10.3b

bsearch391.0ms

Steps

Iters	Range		Point
10	1.415873715001122e+23	1.34232255763024e+37	1.0855066767324344e+24
7	-84463.33967257517	-1026.6337297585196	-73198.40425548062

simplify14.0ms

Iterations

Iter	Nodes
done	46
1	46
0	41

end0.0ms

sample9.0s

Algorithm

intervals

Results

3.7s	1709×	body	1280	valid
2.4s	1420×	body	640	valid
1.4s	4667×	body	80	valid
582.0ms	710×	body	320	valid
340.0ms	1640×	body	80	nan
247.0ms	354×	body	160	valid