Details

sample319.0ms

Algorithm

intervals

Results

25.0ms	60×	body	1280	valid
11.0ms	170×	body	80	valid
11.0ms	42×	body	640	valid
3.0ms	19×	body	320	valid
1.0ms	10×	body	160	valid

simplify17.0ms

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

prune11.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.2b

Counts

2 → 2

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
0.2b	(/ 1.0 (sin B))
0.2b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

105×	`*-un-lft-identity`
104×	`add-sqr-sqrt`
99×	`frac-add` `distribute-neg-frac`
90×	`associate-*r/`
89×	`add-cube-cbrt`
79×	`associate-/l*`
69×	`associate-/r*`
52×	`fma-def`
48×	`times-frac`
42×	`associate-r`
33×	`clear-num`
26×	`distribute-rgt-neg-in`
24×	`distribute-lft-neg-in`
23×	`frac-2neg`
20×	`un-div-inv`
13×	`add-exp-log` `add-cbrt-cube`
10×	`associate-l`
8×	`add-log-exp`
6×	`pow1` `unswap-sqr`
5×	`div-inv`
4×	`tan-quot` `expm1-log1p-u` `associate-/r/` `log1p-expm1-u`
3×	`cbrt-undiv` `div-exp` `*-commutative` `distribute-lft-out`
2×	`prod-exp` `sum-log` `cbrt-unprod`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `flip3-+` `pow-prod-down` `neg-log` `flip-+`

Counts

4 → 273

Calls

4 calls:

47.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
4.0ms	(/ 1.0 (sin B))
23.0ms	(/ 1.0 (tan B))
11.0ms	(* x (/ 1.0 (tan B)))

series298.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
21.0ms	(/ 1.0 (sin B))
36.0ms	(/ 1.0 (tan B))
125.0ms	(* x (/ 1.0 (tan B)))

simplify53.0ms

Algorithm

egg-herbie

Counts

285 → 285

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1300	2252
1	5001	2148

prune522.0ms

Filtered

285 candidates to 198 candidates (69.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	276	9	285
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	278	9	287

Merged error: 0b

Counts

287 → 9

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

299×	`times-frac`
248×	`*-un-lft-identity`
240×	`add-sqr-sqrt` `add-cube-cbrt`
199×	`associate-/r*`
171×	`frac-add` `distribute-neg-frac`
110×	`fma-def`
99×	`associate-/l*`
55×	`distribute-rgt-neg-in`
53×	`distribute-lft-neg-in`
33×	`frac-2neg` `clear-num`
30×	`associate-/r/`
23×	`div-inv`
10×	`add-exp-log` `add-cbrt-cube`
7×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`tan-quot` `pow1` `expm1-log1p-u` `log1p-expm1-u` `associate-/l/` `distribute-lft-out`
2×	`sum-log`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `flip3-+` `neg-log` `flip-+`

Counts

3 → 409

Calls

3 calls:

90.0ms	(+ (- (/ x (/ (tan B) 1.0))) (/ 1.0 (sin B)))
7.0ms	(/ x (/ (tan B) 1.0))
4.0ms	(/ 1.0 (sin B))

series249.0ms

Counts

3 → 9

Calls

3 calls:

116.0ms	(+ (- (/ x (/ (tan B) 1.0))) (/ 1.0 (sin B)))
114.0ms	(/ x (/ (tan B) 1.0))
19.0ms	(/ 1.0 (sin B))

simplify91.0ms

Algorithm

egg-herbie

Counts

418 → 418

Iterations

Useful iterations: 1 (48.0ms)

Iter	Nodes	Cost
0	2477	4247
1	5002	4094

prune887.0ms

Filtered

418 candidates to 326 candidates (78.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	412	6	418
Fresh	7	1	8
Picked	1	0	1
Done	0	0	0
Total	420	7	427

Merged error: 0b

Counts

427 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (- (/ 1 (/ (/ (tan B) 1.0) x))) (/ 1.0 (sin B)))
0.1b	(/ (/ (tan B) 1.0) x)
0.2b	(/ 1.0 (sin B))
0.3b	(/ 1 (/ (/ (tan B) 1.0) x))

rewrite391.0ms

Algorithm

rewrite-expression-head

Rules

1758×	`times-frac`
1012×	`*-un-lft-identity`
991×	`add-sqr-sqrt` `add-cube-cbrt`
604×	`associate-/r*`
441×	`frac-add` `distribute-neg-frac`
328×	`fma-def`
248×	`associate-/l*`
169×	`distribute-rgt-neg-in`
162×	`distribute-lft-neg-in`
91×	`associate-/r/`
89×	`div-inv`
72×	`clear-num`
68×	`frac-2neg`
48×	`associate-/l/`
32×	`add-exp-log`
20×	`add-cbrt-cube`
19×	`div-exp`
10×	`cbrt-undiv`
8×	`distribute-lft-out` `add-log-exp`
5×	`pow1`
4×	`tan-quot` `expm1-log1p-u` `log1p-expm1-u` `remove-double-div`
3×	`rec-exp` `1-exp`
2×	`sum-log`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `pow-flip` `flip3-+` `neg-log` `flip-+` `inv-pow`

Counts

4 → 1136

Calls

4 calls:

248.0ms	(+ (- (/ 1 (/ (/ (tan B) 1.0) x))) (/ 1.0 (sin B)))
8.0ms	(/ (/ (tan B) 1.0) x)
3.0ms	(/ 1.0 (sin B))
18.0ms	(/ 1 (/ (/ (tan B) 1.0) x))

series288.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(+ (- (/ 1 (/ (/ (tan B) 1.0) x))) (/ 1.0 (sin B)))
52.0ms	(/ (/ (tan B) 1.0) x)
18.0ms	(/ 1.0 (sin B))
90.0ms	(/ 1 (/ (/ (tan B) 1.0) x))

simplify155.0ms

Algorithm

egg-herbie

Counts

1148 → 1148

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5001	14252

prune3.1s

Filtered

1148 candidates to 928 candidates (80.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	1145	3	1148
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	1148	7	1155

Merged error: 0b

Counts

1155 → 7

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

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

224×	`add-sqr-sqrt`
204×	`associate-/l*`
190×	`*-un-lft-identity`
189×	`frac-add` `distribute-neg-frac`
166×	`add-cube-cbrt`
162×	`associate-*r/`
141×	`associate-r`
121×	`times-frac`
106×	`fma-def`
96×	`associate-/r*`
76×	`associate-l`
54×	`distribute-rgt-neg-in`
52×	`distribute-lft-neg-in`
41×	`clear-num`
32×	`frac-2neg`
28×	`unswap-sqr`
27×	`un-div-inv`
22×	`*-commutative`
13×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`div-inv`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out`
3×	`cbrt-undiv` `div-exp`
2×	`prod-exp` `sum-log` `cbrt-unprod`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `distribute-rgt-out` `flip3-+` `pow-prod-down` `neg-log` `flip-+`

Counts

4 → 431

Calls

4 calls:

97.0ms	(+ (- (* 1.0 (/ (* x (cos B)) (sin B)))) (/ 1.0 (sin B)))
4.0ms	(* x (cos B))
3.0ms	(/ 1.0 (sin B))
8.0ms	(/ (* x (cos B)) (sin B))

series261.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(+ (- (* 1.0 (/ (* x (cos B)) (sin B)))) (/ 1.0 (sin B)))
36.0ms	(* x (cos B))
21.0ms	(/ 1.0 (sin B))
99.0ms	(/ (* x (cos B)) (sin B))

simplify91.0ms

Algorithm

egg-herbie

Counts

443 → 443

Iterations

Useful iterations: 1 (45.0ms)

Iter	Nodes	Cost
0	2229	4743
1	5001	4617

prune826.0ms

Filtered

443 candidates to 308 candidates (69.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	442	1	443
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	444	6	450

Merged error: 0b

Counts

450 → 6

regimes59.0ms

Accuracy

0% (0.2b 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	17	8
1	17	8

end0.0ms

sample1.7s

Algorithm

intervals

Results

681.0ms	1667×	body	1280	valid
370.0ms	1452×	body	640	valid
287.0ms	4947×	body	80	valid
122.0ms	713×	body	320	valid
43.0ms	348×	body	160	valid