Details

sample312.0ms

Algorithm

intervals

Results

25.0ms	60×	body	1280	valid
11.0ms	170×	body	80	valid
10.0ms	42×	body	640	valid
3.0ms	19×	body	320	valid
1.0ms	10×	body	160	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

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

prune9.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 0.2b

Counts

2 → 1

localize13.0ms

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)))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

99×	`frac-add` `distribute-neg-frac`
90×	`associate-*r/`
86×	`*-un-lft-identity`
79×	`associate-/l*`
75×	`add-sqr-sqrt`
70×	`add-cube-cbrt`
69×	`associate-/r*`
33×	`clear-num`
28×	`times-frac`
23×	`frac-2neg`
20×	`un-div-inv`
14×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
6×	`pow1`
4×	`associate-l`
3×	`cbrt-undiv` `div-exp` `div-inv` `distribute-lft-out`
2×	`tan-quot` `distribute-rgt-neg-in` `prod-exp` `sum-log` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `neg-sub0` `associate-+l-` `flip3-+` `pow-prod-down` `neg-log` `*-commutative` `flip-+`

Counts

4 → 213

Calls

4 calls:

41.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
3.0ms	(/ 1.0 (sin B))
18.0ms	(/ 1.0 (tan B))
11.0ms	(* x (/ 1.0 (tan B)))

series305.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
19.0ms	(/ 1.0 (sin B))
35.0ms	(/ 1.0 (tan B))
130.0ms	(* x (/ 1.0 (tan B)))

simplify51.0ms

Algorithm

egg-herbie

Counts

225 → 225

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1210	2296
1	5001	2112

prune367.0ms

Filtered

225 candidates to 142 candidates (63.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	216	9	225
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	217	9	226

Merged error: 0b

Counts

226 → 9

localize14.0ms

Local error

Found 3 expressions with local error:

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

rewrite510.0ms

Algorithm

rewrite-expression-head

Rules

835×	`times-frac`
691×	`add-sqr-sqrt`
576×	`*-un-lft-identity`
562×	`add-cube-cbrt`
369×	`frac-add` `distribute-neg-frac`
365×	`sqrt-prod`
352×	`associate-/r*`
289×	`associate-/l*`
193×	`associate-l`
96×	`associate-r`
64×	`unswap-sqr`
53×	`frac-2neg` `clear-num`
32×	`*-commutative`
28×	`div-inv`
17×	`add-exp-log` `add-cbrt-cube`
13×	`associate-/r/`
7×	`cbrt-undiv` `div-exp` `add-log-exp`
5×	`distribute-lft-out`
4×	`distribute-rgt-neg-in`
3×	`pow1`
2×	`prod-exp` `sum-log` `cbrt-unprod`
1×	`tan-quot` `+-commutative` `neg-sub0` `associate-+l-` `flip3-+` `neg-log` `flip-+` `associate-/l/`

Counts

3 → 835

Calls

3 calls:

417.0ms	(+ (- (/ (* (sqrt 1.0) x) (/ (tan B) (sqrt 1.0)))) (/ 1.0 (sin B)))
21.0ms	(/ (* (sqrt 1.0) x) (/ (tan B) (sqrt 1.0)))
4.0ms	(/ 1.0 (sin B))

series409.0ms

Counts

3 → 9

Calls

3 calls:

183.0ms	(+ (- (/ (* (sqrt 1.0) x) (/ (tan B) (sqrt 1.0)))) (/ 1.0 (sin B)))
207.0ms	(/ (* (sqrt 1.0) x) (/ (tan B) (sqrt 1.0)))
19.0ms	(/ 1.0 (sin B))

simplify229.0ms

Algorithm

egg-herbie

Counts

844 → 844

Iterations

Useful iterations: 1 (93.0ms)

Iter	Nodes	Cost
0	4876	15785
1	5002	15551

prune1.4s

Filtered

844 candidates to 442 candidates (52.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	839	5	844
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	846	7	853

Merged error: 0b

Counts

853 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite211.0ms

Algorithm

rewrite-expression-head

Rules

300×	`add-sqr-sqrt`
245×	`associate-/l*`
220×	`associate-*l/`
198×	`frac-add` `distribute-neg-frac`
196×	`*-un-lft-identity`
178×	`add-cube-cbrt`
173×	`associate-l`
132×	`times-frac`
102×	`associate-/r*`
79×	`sqrt-prod`
70×	`associate-r`
62×	`unswap-sqr`
34×	`frac-2neg` `clear-num`
32×	`add-exp-log` `add-cbrt-cube`
19×	`*-commutative`
12×	`prod-exp` `cbrt-unprod` `distribute-lft-out`
11×	`distribute-rgt-neg-in`
9×	`pow1`
8×	`add-log-exp`
7×	`cbrt-undiv` `div-exp`
3×	`pow-prod-down` `div-inv`
2×	`sum-log`
1×	`+-commutative` `neg-sub0` `associate-+l-` `flip3-+` `neg-log` `flip-+`

Counts

4 → 455

Calls

4 calls:

128.0ms	(+ (- (* (/ (* (sqrt 1.0) x) (sin B)) (* (sqrt 1.0) (cos B)))) (/ 1.0 (sin B)))
3.0ms	(/ 1.0 (sin B))
9.0ms	(/ (* (sqrt 1.0) x) (sin B))
36.0ms	(* (/ (* (sqrt 1.0) x) (sin B)) (* (sqrt 1.0) (cos B)))

series518.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(+ (- (* (/ (* (sqrt 1.0) x) (sin B)) (* (sqrt 1.0) (cos B)))) (/ 1.0 (sin B)))
24.0ms	(/ 1.0 (sin B))
97.0ms	(/ (* (sqrt 1.0) x) (sin B))
212.0ms	(* (/ (* (sqrt 1.0) x) (sin B)) (* (sqrt 1.0) (cos B)))

simplify120.0ms

Algorithm

egg-herbie

Counts

467 → 467

Iterations

Useful iterations: 1 (55.0ms)

Iter	Nodes	Cost
0	2668	7347
1	5001	7246

prune918.0ms

Filtered

467 candidates to 302 candidates (64.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	465	2	467
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	467	7	474

Merged error: 0b

Counts

474 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (- (* (/ x 1) (/ (* 1.0 (cos B)) (sin B)))) (/ 1.0 (sin B)))
0.2b	(/ 1.0 (sin B))
0.2b	(/ (* 1.0 (cos B)) (sin B))
0.3b	(* (/ x 1) (/ (* 1.0 (cos B)) (sin B)))

rewrite411.0ms

Algorithm

rewrite-expression-head

Rules

2381×	`associate-/l*`
1728×	`frac-add` `distribute-neg-frac`
1620×	`frac-times`
1476×	`add-sqr-sqrt`
1452×	`associate-/r*`
1271×	`*-un-lft-identity`
1232×	`add-cube-cbrt`
494×	`clear-num`
484×	`frac-2neg`
367×	`associate-r`
346×	`associate-l`
180×	`associate-*r/`
119×	`unswap-sqr`
113×	`*-commutative`
112×	`times-frac`
90×	`associate-*l/`
41×	`add-exp-log`
32×	`add-cbrt-cube`
30×	`un-div-inv`
15×	`div-exp`
13×	`prod-exp`
10×	`cbrt-undiv`
9×	`cbrt-unprod`
8×	`add-log-exp`
6×	`pow1` `distribute-lft-neg-in` `div-inv`
5×	`distribute-rgt-out`
4×	`distribute-lft-out`
3×	`distribute-rgt-neg-in` `1-exp`
2×	`sum-log`
1×	`+-commutative` `neg-sub0` `associate-+l-` `distribute-lft1-in` `flip3-+` `pow-prod-down` `neg-log` `flip-+`

Counts

4 → 2121

Calls

4 calls:

150.0ms	(+ (- (* (/ x 1) (/ (* 1.0 (cos B)) (sin B)))) (/ 1.0 (sin B)))
3.0ms	(/ 1.0 (sin B))
8.0ms	(/ (* 1.0 (cos B)) (sin B))
33.0ms	(* (/ x 1) (/ (* 1.0 (cos B)) (sin B)))

series276.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(+ (- (* (/ x 1) (/ (* 1.0 (cos B)) (sin B)))) (/ 1.0 (sin B)))
18.0ms	(/ 1.0 (sin B))
42.0ms	(/ (* 1.0 (cos B)) (sin B))
109.0ms	(* (/ x 1) (/ (* 1.0 (cos B)) (sin B)))

simplify449.0ms

Algorithm

egg-herbie

Counts

2133 → 2133

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5002	46983

prune3.2s

Filtered

2133 candidates to 995 candidates (46.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	2130	3	2133
Fresh	3	2	5
Picked	1	0	1
Done	0	1	1
Total	2134	6	2140

Merged error: 0b

Counts

2140 → 6

regimes66.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	12
1	31	12
2	36	12
3	36	12

end0.0ms

sample1.7s

Algorithm

intervals

Results

674.0ms	1667×	body	1280	valid
373.0ms	1452×	body	640	valid
303.0ms	4947×	body	80	valid
132.0ms	713×	body	320	valid
43.0ms	348×	body	160	valid