Details

sample325.0ms

Algorithm

intervals

Results

144.0ms	59×	body	1280	valid
52.0ms	48×	body	640	valid
34.0ms	144×	body	80	valid
13.0ms	21×	body	320	valid
10.0ms	58×	body	80	nan
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

prune29.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.0b

localize86.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (tan B))
0.2b	(* x (/ 1.0 (tan B)))
7.6b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
16.4b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite314.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 163

Calls

4 calls:

5.0ms	(/ 1.0 (tan B))
15.0ms	(* x (/ 1.0 (tan B)))
224.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
63.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series921.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(/ 1.0 (tan B))
154.0ms	(* x (/ 1.0 (tan B)))
439.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
254.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify2.1s

Counts

175 → 175

Iterations

Iter	Nodes
done	5000
2	3970
1	883
0	314

prune1.6s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.2b	(* x (/ 1.0 (tan B)))
0.3b	(* F (/ (pow (fma F F (fma 2.0 x 2.0)) (- (/ 1.0 2.0))) (sin B)))
0.4b	(/ (pow (fma F F (fma 2.0 x 2.0)) (- (/ 1.0 2.0))) (sin B))
16.4b	(pow (fma F F (fma 2.0 x 2.0)) (- (/ 1.0 2.0)))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 182

Calls

4 calls:

22.0ms	(* x (/ 1.0 (tan B)))
46.0ms	(* F (/ (pow (fma F F (fma 2.0 x 2.0)) (- (/ 1.0 2.0))) (sin B)))
8.0ms	(/ (pow (fma F F (fma 2.0 x 2.0)) (- (/ 1.0 2.0))) (sin B))
6.0ms	(pow (fma F F (fma 2.0 x 2.0)) (- (/ 1.0 2.0)))

series1.4s

Counts

4 → 12

Calls

4 calls:

175.0ms	(* x (/ 1.0 (tan B)))
539.0ms	(* F (/ (pow (fma F F (fma 2.0 x 2.0)) (- (/ 1.0 2.0))) (sin B)))
536.0ms	(/ (pow (fma F F (fma 2.0 x 2.0)) (- (/ 1.0 2.0))) (sin B))
178.0ms	(pow (fma F F (fma 2.0 x 2.0)) (- (/ 1.0 2.0)))

simplify1.9s

Counts

194 → 194

Iterations

Iter	Nodes
done	5002
2	3759
1	942
0	348

prune1.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* 1.0 x) (tan B))
0.3b	(* F (/ (pow (fma F F (fma 2.0 x 2.0)) (- (/ 1.0 2.0))) (sin B)))
0.4b	(/ (pow (fma F F (fma 2.0 x 2.0)) (- (/ 1.0 2.0))) (sin B))
16.4b	(pow (fma F F (fma 2.0 x 2.0)) (- (/ 1.0 2.0)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 171

Calls

4 calls:

18.0ms	(/ (* 1.0 x) (tan B))
32.0ms	(* F (/ (pow (fma F F (fma 2.0 x 2.0)) (- (/ 1.0 2.0))) (sin B)))
8.0ms	(/ (pow (fma F F (fma 2.0 x 2.0)) (- (/ 1.0 2.0))) (sin B))
6.0ms	(pow (fma F F (fma 2.0 x 2.0)) (- (/ 1.0 2.0)))

series1.4s

Counts

4 → 12

Calls

4 calls:

189.0ms	(/ (* 1.0 x) (tan B))
531.0ms	(* F (/ (pow (fma F F (fma 2.0 x 2.0)) (- (/ 1.0 2.0))) (sin B)))
470.0ms	(/ (pow (fma F F (fma 2.0 x 2.0)) (- (/ 1.0 2.0))) (sin B))
222.0ms	(pow (fma F F (fma 2.0 x 2.0)) (- (/ 1.0 2.0)))

simplify2.0s

Counts

183 → 183

Iterations

Iter	Nodes
done	5001
2	3729
1	901
0	333

prune1.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (* 1.0 x) (sin B)) (cos B))
0.3b	(* F (/ (pow (fma F F (fma 2.0 x 2.0)) (- (/ 1.0 2.0))) (sin B)))
0.4b	(/ (pow (fma F F (fma 2.0 x 2.0)) (- (/ 1.0 2.0))) (sin B))
16.4b	(pow (fma F F (fma 2.0 x 2.0)) (- (/ 1.0 2.0)))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

66×	`add-sqr-sqrt` `times-frac`
54×	`*-un-lft-identity` `add-cube-cbrt`
30×	`pow-unpow`
29×	`add-exp-log`
28×	`associate-r`
25×	`unpow-prod-down`
20×	`add-cbrt-cube`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
10×	`associate-l`
9×	`pow1` `sqr-pow`
8×	`div-exp` `prod-exp`
7×	`associate-/l*`
6×	`cbrt-unprod`
5×	`div-inv` `unswap-sqr`
4×	`expm1-log1p-u` `cbrt-undiv` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `associate-/r*` `pow-exp`
2×	`neg-sub0` `pow-neg` `pow-prod-down` `*-commutative` `pow-sub` `associate-/l/`
1×	`clear-num` `neg-mul-1` `pow-pow` `frac-2neg` `associate-l/` `associate-r/`

Counts

4 → 176

Calls

4 calls:

30.0ms	(* (/ (* 1.0 x) (sin B)) (cos B))
49.0ms	(* F (/ (pow (fma F F (fma 2.0 x 2.0)) (- (/ 1.0 2.0))) (sin B)))
15.0ms	(/ (pow (fma F F (fma 2.0 x 2.0)) (- (/ 1.0 2.0))) (sin B))
13.0ms	(pow (fma F F (fma 2.0 x 2.0)) (- (/ 1.0 2.0)))

series1.4s

Counts

4 → 12

Calls

4 calls:

183.0ms	(* (/ (* 1.0 x) (sin B)) (cos B))
491.0ms	(* F (/ (pow (fma F F (fma 2.0 x 2.0)) (- (/ 1.0 2.0))) (sin B)))
477.0ms	(/ (pow (fma F F (fma 2.0 x 2.0)) (- (/ 1.0 2.0))) (sin B))
232.0ms	(pow (fma F F (fma 2.0 x 2.0)) (- (/ 1.0 2.0)))

simplify2.3s

Counts

188 → 188

Iterations

Iter	Nodes
done	5001
2	4162
1	932
0	343

prune1.6s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes423.0ms

Accuracy

93.4% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 10.8b

bsearch567.0ms

Steps

Iters	Range		Point
9	8.361756585565377e-18	1.2276075427297e-12	1.2123799789468031e-12
10	-3813544086202141.0	-769416.9694931002	-30757712.29803883

simplify21.0ms

Iterations

Iter	Nodes
done	82
3	82
2	76
1	60
0	40

end0.0ms

sample10.3s

Algorithm

intervals

Results

3.5s	1700×	body	1280	valid
2.9s	1414×	body	640	valid
2.0s	4731×	body	80	valid
686.0ms	680×	body	320	valid
398.0ms	1608×	body	80	nan
178.0ms	328×	body	160	valid