Details

sample88.0ms

Algorithm

intervals

Results

32.0ms	53×	body	1280	valid
20.0ms	49×	body	640	valid
18.0ms	155×	body	80	valid
5.0ms	18×	body	320	valid
3.0ms	14×	body	160	valid

simplify11.0ms

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

rewrite28.0ms

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

series276.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
19.0ms	(/ 1.0 (sin B))
35.0ms	(/ 1.0 (tan B))
109.0ms	(* x (/ 1.0 (tan B)))

simplify51.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (43.0ms)

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

prune331.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

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))
0.1b	(/ (* x 1.0) (tan B))

rewrite40.0ms

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:

31.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
2.0ms	(/ 1.0 (sin B))
4.0ms	(/ (* x 1.0) (tan B))

series240.0ms

Counts

3 → 9

Calls

3 calls:

114.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
19.0ms	(/ 1.0 (sin B))
107.0ms	(/ (* x 1.0) (tan B))

simplify39.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	350	492
1	1353	445
2	5002	440

prune259.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite27.0ms

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-l`
11×	`pow1`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-/r` `associate-/l`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `associate-r` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`div-inv`
2×	`frac-2neg` `associate-l/` `clear-num` `-commutative` `unswap-sqr`
1×	`associate-*r/`

Counts

4 → 115

Calls

4 calls:

2.0ms	(/ 1.0 (sin B))
2.0ms	(/ 1.0 (sin B))
8.0ms	(* (/ 1.0 (sin B)) (cos B))
12.0ms	(* x (* (/ 1.0 (sin B)) (cos B)))

series175.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ 1.0 (sin B))
18.0ms	(/ 1.0 (sin B))
38.0ms	(* (/ 1.0 (sin B)) (cos B))
101.0ms	(* x (* (/ 1.0 (sin B)) (cos B)))

simplify45.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	328	712
1	1345	620
2	5001	620

prune304.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (/ 1.0 (tan B))) (cbrt (/ 1.0 (tan B))))
0.5b	(cbrt (/ 1.0 (tan B)))
0.5b	(cbrt (/ 1.0 (tan B)))
0.5b	(cbrt (/ 1.0 (tan B)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

110×	`cbrt-prod`
81×	`add-sqr-sqrt`
69×	`times-frac`
57×	`add-cube-cbrt` `*-un-lft-identity`
17×	`swap-sqr` `associate-r` `associate-l`
11×	`pow1`
9×	`pow1/3` `unswap-sqr`
7×	`tan-quot` `cbrt-div` `associate-/r/` `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 → 158

Calls

4 calls:

20.0ms	(* (cbrt (/ 1.0 (tan B))) (cbrt (/ 1.0 (tan B))))
2.0ms	(cbrt (/ 1.0 (tan B)))
2.0ms	(cbrt (/ 1.0 (tan B)))
2.0ms	(cbrt (/ 1.0 (tan B)))

series670.0ms

Counts

4 → 12

Calls

4 calls:

205.0ms	(* (cbrt (/ 1.0 (tan B))) (cbrt (/ 1.0 (tan B))))
153.0ms	(cbrt (/ 1.0 (tan B)))
154.0ms	(cbrt (/ 1.0 (tan B)))
158.0ms	(cbrt (/ 1.0 (tan B)))

simplify49.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	328	1516
1	1190	1464
2	5001	1390

prune561.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes44.0ms

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	17	9
1	25	9
2	27	9
3	27	9

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.1s	1741×	body	1280	valid
581.0ms	1449×	body	640	valid
506.0ms	4906×	body	80	valid
195.0ms	682×	body	320	valid
77.0ms	362×	body	160	valid