Details

sample417.0ms

Algorithm

intervals

Results

53.0ms	59×	body	1280	valid
14.0ms	41×	body	640	valid
14.0ms	152×	body	80	valid
6.0ms	24×	body	320	valid
2.0ms	14×	body	160	valid

simplify15.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	18	7
1	33	6
2	43	6
3	54	6
4	60	6
5	62	6
6	62	6
done	62	6

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize16.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma (- x) (/ 1.0 (tan B)) (/ 1.0 (sin B)))
0.2b	(/ 1.0 (tan B))
0.2b	(/ 1.0 (sin B))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r` `associate-/l`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`
1×	`tan-quot` `associate-/r/` `fma-udef`

Counts

3 → 69

Calls

3 calls:

0.0ms	(fma (- x) (/ 1.0 (tan B)) (/ 1.0 (sin B)))
6.0ms	(/ 1.0 (tan B))
8.0ms	(/ 1.0 (sin B))

series178.0ms

Counts

3 → 9

Calls

3 calls:

104.0ms	(fma (- x) (/ 1.0 (tan B)) (/ 1.0 (sin B)))
46.0ms	(/ 1.0 (tan B))
27.0ms	(/ 1.0 (sin B))

simplify58.0ms

Counts

78 → 78

Iterations

Useful iterations: 3 (53.0ms)

Iter	Nodes	Cost
0	246	416
1	694	382
2	2127	382
3	5002	377
done	5002	377

prune239.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma (- x) (* 1.0 (/ (cos B) (sin B))) (/ 1.0 (sin B)))
0.2b	(/ 1.0 (sin B))
0.2b	(/ (cos B) (sin B))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r` `associate-/l`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`
1×	`fma-udef`

Counts

3 → 68

Calls

3 calls:

0.0ms	(fma (- x) (* 1.0 (/ (cos B) (sin B))) (/ 1.0 (sin B)))
8.0ms	(/ 1.0 (sin B))
10.0ms	(/ (cos B) (sin B))

series143.0ms

Counts

3 → 9

Calls

3 calls:

103.0ms	(fma (- x) (* 1.0 (/ (cos B) (sin B))) (/ 1.0 (sin B)))
20.0ms	(/ 1.0 (sin B))
21.0ms	(/ (cos B) (sin B))

simplify59.0ms

Counts

77 → 77

Iterations

Useful iterations: 3 (54.0ms)

Iter	Nodes	Cost
0	241	480
1	721	438
2	2196	438
3	5001	433
done	5001	433

prune230.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (- x) (* 1.0 (/ (cos B) (sin B)))) (/ 1.0 (sin B)))
0.2b	(/ 1.0 (sin B))
0.2b	(/ (cos B) (sin B))
0.3b	(* (- x) (* 1.0 (/ (cos B) (sin B))))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
17×	`add-exp-log` `add-cbrt-cube`
10×	`associate-l`
9×	`pow1`
6×	`associate-/r` `associate-/l` `add-log-exp`
5×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u`
3×	`cbrt-undiv` `distribute-lft-neg-in` `distribute-rgt-neg-in` `div-exp` `pow-prod-down`
2×	`frac-2neg` `clear-num` `div-inv`
1×	`+-commutative` `distribute-lft-neg-out` `neg-mul-1` `fma-def` `flip3-+` `associate-r` `frac-add` `sum-log` `*-commutative` `flip-+`

Counts

4 → 104

Calls

4 calls:

32.0ms	(+ (* (- x) (* 1.0 (/ (cos B) (sin B)))) (/ 1.0 (sin B)))
5.0ms	(/ 1.0 (sin B))
9.0ms	(/ (cos B) (sin B))
31.0ms	(* (- x) (* 1.0 (/ (cos B) (sin B))))

series251.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(+ (* (- x) (* 1.0 (/ (cos B) (sin B)))) (/ 1.0 (sin B)))
20.0ms	(/ 1.0 (sin B))
20.0ms	(/ (cos B) (sin B))
104.0ms	(* (- x) (* 1.0 (/ (cos B) (sin B))))

simplify50.0ms

Counts

116 → 116

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	448	809
1	1765	734
2	5001	731
done	5001	731

prune305.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ (* (- x) (* 1.0 (cos B))) (sin B)) (/ 1.0 (sin B)))
0.1b	(* (- x) (* 1.0 (cos B)))
0.2b	(/ (* (- x) (* 1.0 (cos B))) (sin B))
0.2b	(/ 1.0 (sin B))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
20×	`add-exp-log` `add-cbrt-cube`
19×	`add-sqr-sqrt` `add-cube-cbrt`
15×	`times-frac`
10×	`associate-l`
9×	`pow1`
7×	`fma-def`
6×	`prod-exp` `associate-/r*` `cbrt-unprod` `add-log-exp`
5×	`div-inv`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `associate-/l*`
3×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `pow-prod-down`
2×	`distribute-lft-neg-out` `frac-2neg` `clear-num`
1×	`+-commutative` `neg-mul-1` `distribute-rgt-out` `flip3-+` `distribute-frac-neg` `associate-r` `frac-add` `sum-log` `*-commutative` `flip-+` `distribute-lft-out`

Counts

4 → 106

Calls

4 calls:

37.0ms	(+ (/ (* (- x) (* 1.0 (cos B))) (sin B)) (/ 1.0 (sin B)))
22.0ms	(* (- x) (* 1.0 (cos B)))
26.0ms	(/ (* (- x) (* 1.0 (cos B))) (sin B))
5.0ms	(/ 1.0 (sin B))

series279.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(+ (/ (* (- x) (* 1.0 (cos B))) (sin B)) (/ 1.0 (sin B)))
43.0ms	(* (- x) (* 1.0 (cos B)))
105.0ms	(/ (* (- x) (* 1.0 (cos B))) (sin B))
20.0ms	(/ 1.0 (sin B))

simplify50.0ms

Counts

118 → 118

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	447	772
1	1938	687
2	5002	680
done	5002	680

prune279.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

regimes61.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	9
1	15	9
done	15	9

end0.0ms

sample2.4s

Algorithm

intervals

Results

979.0ms	1701×	body	1280	valid
515.0ms	1454×	body	640	valid
405.0ms	4906×	body	80	valid
166.0ms	715×	body	320	valid
55.0ms	338×	body	160	valid