Details

sample121.0ms

Algorithm

intervals

Results

44.0ms	55×	body	1280	valid
28.0ms	53×	body	640	valid
20.0ms	154×	body	80	valid
8.0ms	21×	body	320	valid
3.0ms	10×	body	160	valid

simplify75.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	10	12
1	18	12
2	33	11
3	43	11
4	54	11
5	59	11
6	61	11
done	61	11

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
0.1b	(/ 1.0 (sin B))
0.1b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
29×	`add-cube-cbrt`
28×	`times-frac`
14×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
6×	`pow1` `fma-def` `associate-/r` `associate-/l`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `div-exp` `associate-l` `div-inv`
2×	`tan-quot` `frac-2neg` `associate-*r/` `prod-exp` `clear-num` `sum-log` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `neg-sub0` `distribute-lft-neg-in` `associate-+l-` `neg-mul-1` `distribute-rgt-neg-in` `flip3-+` `pow-prod-down` `neg-log` `frac-add` `*-commutative` `flip-+` `distribute-neg-frac` `distribute-lft-out`

Counts

4 → 117

Calls

4 calls:

18.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
6.0ms	(/ 1.0 (sin B))
16.0ms	(/ 1.0 (tan B))
19.0ms	(* x (/ 1.0 (tan B)))

series372.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
20.0ms	(/ 1.0 (sin B))
49.0ms	(/ 1.0 (tan B))
142.0ms	(* x (/ 1.0 (tan B)))

simplify2.6s

Counts

129 → 129

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	188	1244
1	433	1180
2	1188	1075
3	3683	1067
done	5001	1067

prune471.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 3 expressions with local error:

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

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
20×	`fma-def`
18×	`add-sqr-sqrt` `add-cube-cbrt` `times-frac`
10×	`add-exp-log` `add-cbrt-cube`
9×	`distribute-rgt-neg-in`
8×	`distribute-lft-neg-in`
7×	`add-log-exp`
6×	`associate-/r*`
4×	`div-inv` `associate-/l*`
3×	`tan-quot` `pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `associate-/r/` `log1p-expm1-u`
2×	`frac-2neg` `clear-num` `sum-log` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `flip3-+` `neg-log` `frac-add` `prod-exp` `cbrt-unprod` `flip-+` `distribute-neg-frac`

Counts

3 → 91

Calls

3 calls:

95.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
10.0ms	(/ 1.0 (sin B))
21.0ms	(/ (* x 1.0) (tan B))

series333.0ms

Counts

3 → 9

Calls

3 calls:

185.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
26.0ms	(/ 1.0 (sin B))
121.0ms	(/ (* x 1.0) (tan B))

simplify2.7s

Counts

100 → 100

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	150	887
1	348	843
2	1039	755
3	3938	747
done	5000	747

prune364.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt` `*-un-lft-identity`
17×	`add-cube-cbrt`
13×	`add-exp-log` `add-cbrt-cube`
12×	`times-frac`
8×	`add-log-exp`
6×	`pow1` `fma-def` `associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`cbrt-undiv` `div-exp` `associate-r` `associate-l` `div-inv`
2×	`distribute-rgt-neg-in` `frac-2neg` `prod-exp` `clear-num` `sum-log` `cbrt-unprod` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `distribute-lft-neg-in` `associate-+l-` `neg-mul-1` `flip3-+` `associate-r/` `pow-prod-down` `neg-log` `frac-add` `-commutative` `flip-+` `distribute-neg-frac` `unswap-sqr`

Counts

4 → 96

Calls

4 calls:

42.0ms	(+ (- (* 1.0 (/ (* x (cos B)) (sin B)))) (/ 1.0 (sin B)))
18.0ms	(* x (cos B))
12.0ms	(/ 1.0 (sin B))
26.0ms	(/ (* x (cos B)) (sin B))

series430.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(+ (- (* 1.0 (/ (* x (cos B)) (sin B)))) (/ 1.0 (sin B)))
54.0ms	(* x (cos B))
32.0ms	(/ 1.0 (sin B))
171.0ms	(/ (* x (cos B)) (sin B))

simplify4.0s

Counts

108 → 108

Iterations

Useful iterations: 3 (1.5s)

Iter	Nodes	Cost
0	162	1113
1	374	1066
2	1105	948
3	4914	937
done	5000	937

prune448.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 3 expressions with local error:

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

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 62

Calls

3 calls:

0.0ms	(fma (- (/ (* x 1.0) (sin B))) (cos B) (/ 1.0 (sin B)))
6.0ms	(/ 1.0 (sin B))
12.0ms	(/ (* x 1.0) (sin B))

series232.0ms

Counts

3 → 9

Calls

3 calls:

135.0ms	(fma (- (/ (* x 1.0) (sin B))) (cos B) (/ 1.0 (sin B)))
35.0ms	(/ 1.0 (sin B))
61.0ms	(/ (* x 1.0) (sin B))

simplify2.7s

Counts

71 → 71

Iterations

Useful iterations: 2 (161.0ms)

Iter	Nodes	Cost
0	120	737
1	259	713
2	754	629
3	2825	629
done	5000	629

prune305.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes100.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	13	14
2	19	14
done	19	14

end0.0ms

sample6.4s

Algorithm

intervals

Results

2.7s	1706×	body	1280	valid
1.3s	1451×	body	640	valid
987.0ms	4938×	body	80	valid
853.0ms	726×	body	320	valid
291.0ms	334×	body	160	valid