Details

sample456.0ms

Algorithm

intervals

Results

48.0ms	48×	body	1280	valid
42.0ms	150×	body	80	valid
30.0ms	51×	body	640	valid
10.0ms	25×	body	320	valid
5.0ms	51×	body	80	nan
2.0ms	8×	body	160	valid

simplify43.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	43	15
1	91	14
2	169	14
3	378	14
4	1100	14
5	5001	14
done	5001	14

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.5b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ F (sin B))
0.3b	(* x (/ 1.0 (tan B)))
7.1b	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* x (/ 1.0 (tan B)))))
17.5b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite88.0ms

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×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`tan-quot` `neg-sub0` `pow-to-exp` `pow-neg` `neg-mul-1` `pow-pow` `frac-2neg` `associate-r/` `pow-prod-down` `pow-exp` `clear-num` `associate-/r/` `-commutative` `fma-udef` `pow-sub` `sqr-pow`

Counts

4 → 122

Calls

4 calls:

5.0ms	(/ F (sin B))
18.0ms	(* x (/ 1.0 (tan B)))
0.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* x (/ 1.0 (tan B)))))
58.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series571.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ F (sin B))
121.0ms	(* x (/ 1.0 (tan B)))
238.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* x (/ 1.0 (tan B)))))
161.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify65.0ms

Counts

134 → 134

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	666	1019
1	2629	931
2	5001	928
done	5001	928

prune597.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x 1.0) (tan B))
0.2b	(/ F (sin B))
7.1b	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
17.5b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite71.0ms

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	(/ (* x 1.0) (tan B))
5.0ms	(/ F (sin B))
0.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
51.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series562.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(/ (* x 1.0) (tan B))
56.0ms	(/ F (sin B))
237.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
153.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify54.0ms

Counts

123 → 123

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	616	964
1	2352	876
2	5001	873
done	5001	873

prune519.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ F (sin B))
0.2b	(/ (* x (cos B)) (sin B))
7.1b	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* 1.0 (/ (* x (cos B)) (sin B)))))
17.5b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite71.0ms

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×	`neg-sub0` `pow-to-exp` `pow-neg` `neg-mul-1` `pow-pow` `pow-exp` `prod-exp` `cbrt-unprod` `fma-udef` `pow-sub` `sqr-pow`

Counts

4 → 110

Calls

4 calls:

5.0ms	(/ F (sin B))
14.0ms	(/ (* x (cos B)) (sin B))
0.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* 1.0 (/ (* x (cos B)) (sin B)))))
48.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series522.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ F (sin B))
99.0ms	(/ (* x (cos B)) (sin B))
230.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* 1.0 (/ (* x (cos B)) (sin B)))))
143.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify52.0ms

Counts

122 → 122

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	600	1011
1	2303	913
2	5001	910
done	5001	910

prune518.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ F (sin B))
0.3b	(/ 1 (/ (tan B) (* x 1.0)))
7.1b	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ 1 (/ (tan B) (* x 1.0)))))
17.5b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

60×	`times-frac`
44×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
30×	`pow-unpow`
28×	`add-exp-log`
15×	`add-cbrt-cube`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `div-exp`
10×	`associate-/r*`
8×	`div-inv`
6×	`pow1` `cbrt-undiv` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down` `rec-exp` `1-exp` `prod-exp`
2×	`frac-2neg` `clear-num`
1×	`neg-sub0` `pow-to-exp` `pow-neg` `neg-mul-1` `pow-flip` `pow-pow` `pow-exp` `associate-/r/` `cbrt-unprod` `fma-udef` `inv-pow` `pow-sub` `sqr-pow`

Counts

4 → 145

Calls

4 calls:

5.0ms	(/ F (sin B))
15.0ms	(/ 1 (/ (tan B) (* x 1.0)))
0.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ 1 (/ (tan B) (* x 1.0)))))
51.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series523.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ F (sin B))
90.0ms	(/ 1 (/ (tan B) (* x 1.0)))
232.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ 1 (/ (tan B) (* x 1.0)))))
149.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify70.0ms

Counts

157 → 157

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	759	1261
1	3286	1134
2	5002	1088
done	5002	1088

prune521.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes214.0ms

Accuracy

97.8% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 14.2b

bsearch301.0ms

Steps

Iters	Range		Point
8	3.8522157627345126e+68	4.06665183914022e+71	3.894573343315853e+68
10	-8.375797978149412e+17	-8808000.967096206	-176977675840.16245

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	46
1	56	46
2	56	46
done	56	46

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.6s	1690×	body	1280	valid
825.0ms	1363×	body	640	valid
627.0ms	4783×	body	80	valid
270.0ms	670×	body	320	valid
170.0ms	1633×	body	80	nan
95.0ms	353×	body	160	valid