Details

sample80.0ms

Algorithm

intervals

Results

32.0ms	55×	body	1280	valid
13.0ms	38×	body	640	valid
12.0ms	152×	body	80	valid
10.0ms	27×	body	320	valid
2.0ms	12×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

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

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite26.0ms

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:

9.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
2.0ms	(/ 1.0 (tan B))
2.0ms	(/ 1.0 (sin B))
9.0ms	(* x (/ 1.0 (tan B)))

series284.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
36.0ms	(/ 1.0 (tan B))
18.0ms	(/ 1.0 (sin B))
111.0ms	(* x (/ 1.0 (tan B)))

simplify53.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	438	696
1	1724	639
2	5002	635

prune371.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite7.0ms

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:

2.0ms	(/ 1.0 (tan B))
0.0ms	(fma x (- (/ 1.0 (tan B))) (/ 1.0 (sin B)))
2.0ms	(/ 1.0 (sin B))

series164.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(/ 1.0 (tan B))
106.0ms	(fma x (- (/ 1.0 (tan B))) (/ 1.0 (sin B)))
23.0ms	(/ 1.0 (sin B))

simplify58.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (52.0ms)

Iter	Nodes	Cost
0	245	416
1	692	382
2	2107	382
3	5001	377

prune264.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (sin B))
0.1b	(/ 1.0 (sin B))
0.2b	(* (* x (/ 1.0 (sin B))) (cos B))
0.3b	(* x (/ 1.0 (sin B)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
29×	`add-cube-cbrt` `*-un-lft-identity`
28×	`times-frac`
22×	`add-exp-log` `add-cbrt-cube`
16×	`associate-r`
11×	`pow1`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-/r` `associate-/l`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `associate-l` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`div-inv`
2×	`frac-2neg` `associate-r/` `clear-num` `-commutative` `unswap-sqr`
1×	`associate-*l/`

Counts

4 → 115

Calls

4 calls:

2.0ms	(/ 1.0 (sin B))
2.0ms	(/ 1.0 (sin B))
13.0ms	(* (* x (/ 1.0 (sin B))) (cos B))
8.0ms	(* x (/ 1.0 (sin B)))

series205.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(/ 1.0 (sin B))
19.0ms	(/ 1.0 (sin B))
106.0ms	(* (* x (/ 1.0 (sin B))) (cos B))
61.0ms	(* x (/ 1.0 (sin B)))

simplify56.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	325	672
1	1587	587
2	5001	587

prune351.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-exp-log` `add-sqr-sqrt` `*-un-lft-identity` `add-cbrt-cube`
18×	`add-cube-cbrt`
15×	`times-frac`
8×	`add-log-exp`
7×	`associate-l`
6×	`pow1` `fma-def` `associate-/r*`
5×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`associate-r` `div-inv`
2×	`frac-2neg` `associate-*l/` `clear-num` `sum-log`
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` `unswap-sqr`

Counts

4 → 104

Calls

4 calls:

10.0ms	(+ (- (* (/ (* x 1.0) (sin B)) (cos B))) (/ 1.0 (sin B)))
3.0ms	(/ (* x 1.0) (sin B))
2.0ms	(/ 1.0 (sin B))
10.0ms	(* (/ (* x 1.0) (sin B)) (cos B))

series288.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(+ (- (* (/ (* x 1.0) (sin B)) (cos B))) (/ 1.0 (sin B)))
55.0ms	(/ (* x 1.0) (sin B))
23.0ms	(/ 1.0 (sin B))
105.0ms	(* (/ (* x 1.0) (sin B)) (cos B))

simplify61.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	440	756
1	2045	660
2	5001	655

prune306.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes73.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	10
1	26	10
2	26	10

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.0s	1686×	body	1280	valid
538.0ms	1496×	body	640	valid
391.0ms	4890×	body	80	valid
192.0ms	727×	body	320	valid
70.0ms	379×	body	160	valid