Details

sample59.0ms

Algorithm

intervals

Results

21.0ms	51×	body	1280	valid
13.0ms	51×	body	640	valid
10.0ms	162×	body	80	valid
3.0ms	16×	body	320	valid
1.0ms	9×	body	160	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	18	7
1	31	6
2	39	6
3	50	6
4	53	6
5	53	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
28×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
14×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `associate-/r` `associate-/l` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-l` `div-inv`
2×	`tan-quot` `frac-2neg` `associate-*r/` `prod-exp` `clear-num` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `*-commutative` `frac-sub` `flip--`

Counts

4 → 101

Calls

4 calls:

6.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
3.0ms	(/ 1.0 (sin B))
4.0ms	(/ 1.0 (tan B))
12.0ms	(* x (/ 1.0 (tan B)))

series292.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
24.0ms	(/ 1.0 (sin B))
34.0ms	(/ 1.0 (tan B))
111.0ms	(* x (/ 1.0 (tan B)))

simplify44.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	386	627
1	1479	584
2	5001	584

prune318.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
0.1b	(/ 1 (sin B))
0.1b	(* x (cos B))
0.2b	(/ (* x (cos B)) (sin B))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
16×	`add-cube-cbrt`
15×	`add-exp-log` `times-frac`
13×	`add-cbrt-cube`
7×	`pow1` `div-inv`
6×	`associate-/r*` `add-log-exp`
4×	`div-exp` `associate-/l*`
3×	`cbrt-undiv` `distribute-rgt-out--` `associate-r` `associate-l` `difference-of-squares`
2×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `distribute-lft-out--`
1×	`sub-neg` `rec-exp` `flip3--` `pow-flip` `diff-log` `1-exp` `pow-prod-down` `*-commutative` `frac-sub` `flip--` `inv-pow` `sub-div` `unswap-sqr`

Counts

4 → 92

Calls

4 calls:

10.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
4.0ms	(/ 1 (sin B))
4.0ms	(* x (cos B))
5.0ms	(/ (* x (cos B)) (sin B))

series247.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
19.0ms	(/ 1 (sin B))
36.0ms	(* x (cos B))
98.0ms	(/ (* x (cos B)) (sin B))

simplify43.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	309	612
1	1342	540
2	5002	535

prune371.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1 (sin B)) (/ x (/ (sin B) (cos B))))
0.1b	(/ 1 (sin B))
0.1b	(/ x (/ (sin B) (cos B)))
0.2b	(/ (sin B) (cos B))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

110×	`times-frac`
92×	`add-sqr-sqrt`
72×	`*-un-lft-identity`
62×	`add-cube-cbrt`
19×	`associate-/r*`
15×	`add-exp-log`
13×	`add-cbrt-cube`
9×	`associate-/l*` `difference-of-squares`
8×	`div-inv`
6×	`div-exp` `add-log-exp`
5×	`pow1` `cbrt-undiv`
3×	`frac-2neg` `clear-num` `distribute-lft-out--`
1×	`sub-neg` `rec-exp` `quot-tan` `flip3--` `pow-flip` `diff-log` `1-exp` `associate-/r/` `frac-sub` `flip--` `inv-pow`

Counts

4 → 154

Calls

4 calls:

32.0ms	(- (/ 1 (sin B)) (/ x (/ (sin B) (cos B))))
4.0ms	(/ 1 (sin B))
6.0ms	(/ x (/ (sin B) (cos B)))
4.0ms	(/ (sin B) (cos B))

series219.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(- (/ 1 (sin B)) (/ x (/ (sin B) (cos B))))
13.0ms	(/ 1 (sin B))
94.0ms	(/ x (/ (sin B) (cos B)))
20.0ms	(/ (sin B) (cos B))

simplify58.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	545	1386
1	2180	1303
2	5002	1302

prune438.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (cbrt (/ (sin B) (cos B))) (cbrt (/ (sin B) (cos B))))
0.6b	(cbrt (/ (sin B) (cos B)))
0.6b	(cbrt (/ (sin B) (cos B)))
0.6b	(cbrt (/ (sin B) (cos B)))

rewrite28.0ms

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×	`add-cbrt-cube` `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 → 144

Calls

4 calls:

13.0ms	(* (cbrt (/ (sin B) (cos B))) (cbrt (/ (sin B) (cos B))))
3.0ms	(cbrt (/ (sin B) (cos B)))
3.0ms	(cbrt (/ (sin B) (cos B)))
3.0ms	(cbrt (/ (sin B) (cos B)))

series500.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(* (cbrt (/ (sin B) (cos B))) (cbrt (/ (sin B) (cos B))))
117.0ms	(cbrt (/ (sin B) (cos B)))
114.0ms	(cbrt (/ (sin B) (cos B)))
119.0ms	(cbrt (/ (sin B) (cos B)))

simplify50.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	273	1687
1	1029	1583
2	5001	1532

prune553.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes55.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	8
1	14	8

end0.0ms

sample1.8s

Algorithm

intervals

Results

735.0ms	1707×	body	1280	valid
380.0ms	1431×	body	640	valid
301.0ms	4924×	body	80	valid
128.0ms	680×	body	320	valid
48.0ms	373×	body	160	valid