Details

sample334.0ms

Algorithm

intervals

Results

32.0ms	56×	body	1280	valid
16.0ms	48×	body	640	valid
14.0ms	171×	body	80	valid
4.0ms	18×	body	320	valid
1.0ms	9×	body	160	valid

simplify15.0ms

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

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize13.0ms

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))
0.2b	(/ 1.0 (tan B))
0.2b	(* x (/ 1.0 (tan B)))

rewrite41.0ms

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:

19.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
4.0ms	(/ 1.0 (sin B))
2.0ms	(/ 1.0 (tan B))
11.0ms	(* x (/ 1.0 (tan B)))

series304.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
22.0ms	(/ 1.0 (sin B))
36.0ms	(/ 1.0 (tan B))
125.0ms	(* x (/ 1.0 (tan B)))

simplify52.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (43.0ms)

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

prune358.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite20.0ms

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:

9.0ms	(+ (- (* 1.0 (/ (* x (cos B)) (sin B)))) (/ 1.0 (sin B)))
2.0ms	(/ 1.0 (sin B))
3.0ms	(* x (cos B))
4.0ms	(/ (* x (cos B)) (sin B))

series267.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(+ (- (* 1.0 (/ (* x (cos B)) (sin B)))) (/ 1.0 (sin B)))
24.0ms	(/ 1.0 (sin B))
37.0ms	(* x (cos B))
100.0ms	(/ (* x (cos B)) (sin B))

simplify47.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	375	642
1	1519	573
2	5001	568

prune288.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 116

Calls

4 calls:

13.0ms	(+ (- (* 1.0 (* x (/ (cos B) (sin B))))) (/ 1.0 (sin B)))
2.0ms	(/ 1.0 (sin B))
3.0ms	(/ (cos B) (sin B))
8.0ms	(* x (/ (cos B) (sin B)))

series245.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(+ (- (* 1.0 (* x (/ (cos B) (sin B))))) (/ 1.0 (sin B)))
19.0ms	(/ 1.0 (sin B))
19.0ms	(/ (cos B) (sin B))
100.0ms	(* x (/ (cos B) (sin B)))

simplify53.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	435	826
1	1770	753
2	5001	748

prune351.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (/ 1.0 (sin B)))
0.4b	(cbrt (/ 1.0 (sin B)))
0.4b	(cbrt (/ 1.0 (sin B)))
0.6b	(* (cbrt (/ 1.0 (sin B))) (cbrt (/ 1.0 (sin B))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

103×	`cbrt-prod`
81×	`add-sqr-sqrt`
69×	`times-frac`
57×	`add-cube-cbrt` `*-un-lft-identity`
16×	`swap-sqr` `associate-r` `associate-l`
11×	`pow1`
9×	`pow1/3` `unswap-sqr`
7×	`cbrt-div` `div-inv`
6×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 152

Calls

4 calls:

2.0ms	(cbrt (/ 1.0 (sin B)))
2.0ms	(cbrt (/ 1.0 (sin B)))
2.0ms	(cbrt (/ 1.0 (sin B)))
18.0ms	(* (cbrt (/ 1.0 (sin B))) (cbrt (/ 1.0 (sin B))))

series622.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(cbrt (/ 1.0 (sin B)))
145.0ms	(cbrt (/ 1.0 (sin B)))
148.0ms	(cbrt (/ 1.0 (sin B)))
188.0ms	(* (cbrt (/ 1.0 (sin B))) (cbrt (/ 1.0 (sin B))))

simplify54.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	309	1462
1	1156	1406
2	5001	1336

prune571.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes68.0ms

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	18	9
1	26	9
2	28	9
3	28	9

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.0s	1750×	body	1280	valid
514.0ms	1415×	body	640	valid
401.0ms	4932×	body	80	valid
164.0ms	701×	body	320	valid
66.0ms	363×	body	160	valid