Details

sample311.0ms

Algorithm

intervals

Results

19.0ms	46×	body	1280	valid
14.0ms	55×	body	640	valid
11.0ms	151×	body	80	valid
4.0ms	23×	body	320	valid
2.0ms	12×	body	160	valid

simplify16.0ms

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 (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 0.2b

Counts

2 → 1

localize12.0ms

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))
0.1b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

99×	`frac-sub`
96×	`add-sqr-sqrt`
90×	`associate-*r/`
84×	`*-un-lft-identity`
79×	`associate-/l*`
70×	`add-cube-cbrt`
69×	`associate-/r*`
33×	`times-frac` `clear-num`
23×	`frac-2neg`
20×	`un-div-inv`
14×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `add-log-exp` `difference-of-squares` `unswap-sqr`
4×	`associate-l`
3×	`cbrt-undiv` `div-exp` `div-inv`
2×	`tan-quot` `prod-exp` `associate-/r/` `cbrt-unprod` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `*-commutative` `flip--`

Counts

4 → 217

Calls

4 calls:

29.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
3.0ms	(/ 1.0 (sin B))
18.0ms	(/ 1.0 (tan B))
11.0ms	(* x (/ 1.0 (tan B)))

series313.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
19.0ms	(/ 1.0 (sin B))
36.0ms	(/ 1.0 (tan B))
130.0ms	(* x (/ 1.0 (tan B)))

simplify52.0ms

Algorithm

egg-herbie

Counts

229 → 229

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1159	2295
1	5001	2214

prune382.0ms

Filtered

229 candidates to 146 candidates (36.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	219	10	229
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	220	10	230

Merged error: 0.0b

Counts

230 → 10

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite311.0ms

Algorithm

rewrite-expression-head

Rules

875×	`times-frac`
783×	`add-sqr-sqrt`
574×	`*-un-lft-identity`
562×	`add-cube-cbrt`
377×	`sqrt-prod`
369×	`frac-sub`
352×	`associate-/r*`
289×	`associate-/l*`
193×	`associate-l`
96×	`associate-r`
76×	`unswap-sqr`
53×	`frac-2neg` `clear-num`
32×	`*-commutative`
28×	`div-inv`
20×	`difference-of-squares`
17×	`add-exp-log` `add-cbrt-cube`
13×	`associate-/r/`
7×	`cbrt-undiv` `div-exp`
5×	`add-log-exp`
4×	`distribute-lft-out--`
3×	`pow1`
2×	`prod-exp` `cbrt-unprod`
1×	`tan-quot` `sub-neg` `flip3--` `diff-log` `flip--` `associate-/l/`

Counts

3 → 853

Calls

3 calls:

223.0ms	(- (/ 1.0 (sin B)) (/ (* (sqrt 1.0) x) (/ (tan B) (sqrt 1.0))))
3.0ms	(/ 1.0 (sin B))
21.0ms	(/ (* (sqrt 1.0) x) (/ (tan B) (sqrt 1.0)))

series428.0ms

Counts

3 → 9

Calls

3 calls:

202.0ms	(- (/ 1.0 (sin B)) (/ (* (sqrt 1.0) x) (/ (tan B) (sqrt 1.0))))
18.0ms	(/ 1.0 (sin B))
207.0ms	(/ (* (sqrt 1.0) x) (/ (tan B) (sqrt 1.0)))

simplify230.0ms

Algorithm

egg-herbie

Counts

862 → 862

Iterations

Useful iterations: 1 (102.0ms)

Iter	Nodes	Cost
0	4751	15990
1	5002	15763

prune1.4s

Filtered

862 candidates to 451 candidates (47.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	857	5	862
Fresh	6	3	9
Picked	1	0	1
Done	0	0	0
Total	864	8	872

Merged error: 0.0b

Counts

872 → 8

localize15.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (* (sqrt 1.0) x) (tan B))
0.2b	(/ (- (* 1.0 (/ 1 (sqrt 1.0))) (* (sin B) (/ (* (sqrt 1.0) x) (tan B)))) (/ (sin B) (sqrt 1.0)))
0.2b	(* (sin B) (/ (* (sqrt 1.0) x) (tan B)))

rewrite417.0ms

Algorithm

rewrite-expression-head

Rules

4273×	`add-sqr-sqrt`
2471×	`times-frac`
1455×	`unswap-sqr`
1212×	`*-un-lft-identity`
881×	`sqrt-prod`
741×	`add-cube-cbrt`
690×	`difference-of-squares`
652×	`associate-*r/`
444×	`associate-/l*`
377×	`associate-/l/`
375×	`frac-sub`
249×	`associate-l`
229×	`associate-/r*`
123×	`un-div-inv`
122×	`associate-r`
92×	`distribute-lft-out--`
85×	`clear-num`
44×	`frac-2neg`
41×	`div-inv`
24×	`*-commutative`
22×	`add-exp-log` `add-cbrt-cube`
14×	`associate-/r/`
7×	`cbrt-undiv` `div-exp`
5×	`pow1` `prod-exp` `cbrt-unprod`
3×	`add-log-exp`
2×	`tan-quot`
1×	`flip3--` `div-sub` `pow-prod-down` `flip--`

Counts

3 → 1459

Calls

3 calls:

10.0ms	(/ (* (sqrt 1.0) x) (tan B))
179.0ms	(/ (- (* 1.0 (/ 1 (sqrt 1.0))) (* (sin B) (/ (* (sqrt 1.0) x) (tan B)))) (/ (sin B) (sqrt 1.0)))
25.0ms	(* (sin B) (/ (* (sqrt 1.0) x) (tan B)))

series605.0ms

Counts

3 → 9

Calls

3 calls:

150.0ms	(/ (* (sqrt 1.0) x) (tan B))
316.0ms	(/ (- (* 1.0 (/ 1 (sqrt 1.0))) (* (sin B) (/ (* (sqrt 1.0) x) (tan B)))) (/ (sin B) (sqrt 1.0)))
139.0ms	(* (sin B) (/ (* (sqrt 1.0) x) (tan B)))

simplify346.0ms

Algorithm

egg-herbie

Counts

1468 → 1468

Iterations

Useful iterations: 1 (71.0ms)

Iter	Nodes	Cost
0	3819	37581
1	5001	36725

prune2.5s

Filtered

1468 candidates to 639 candidates (56.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	1464	4	1468
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	1469	7	1476

Merged error: 0.0b

Counts

1476 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (sin B) (/ (* (sqrt 1.0) x) (sin B))) (cos B))
0.1b	(/ (* (sqrt 1.0) x) (sin B))
0.2b	(/ (- (* 1.0 (/ 1 (sqrt 1.0))) (* (* (sin B) (/ (* (sqrt 1.0) x) (sin B))) (cos B))) (/ (sin B) (sqrt 1.0)))
0.2b	(* (sin B) (/ (* (sqrt 1.0) x) (sin B)))

rewrite540.0ms

Algorithm

rewrite-expression-head

Rules

5590×	`add-sqr-sqrt`
2937×	`times-frac`
2285×	`unswap-sqr`
1494×	`*-un-lft-identity`
1017×	`sqrt-prod`
883×	`add-cube-cbrt`
828×	`difference-of-squares`
674×	`associate-*r/`
470×	`associate-/l*`
456×	`associate-l`
400×	`associate-*l/`
377×	`associate-/l/`
375×	`frac-sub`
232×	`associate-/r*`
188×	`associate-r`
138×	`distribute-lft-out--`
126×	`un-div-inv`
87×	`clear-num`
50×	`div-inv`
45×	`frac-2neg`
37×	`add-exp-log` `add-cbrt-cube`
30×	`*-commutative`
13×	`prod-exp` `cbrt-unprod`
12×	`associate-/r/`
11×	`pow1`
9×	`cbrt-undiv` `div-exp`
4×	`pow-prod-down` `add-log-exp`
1×	`flip3--` `div-sub` `flip--`

Counts

4 → 1756

Calls

4 calls:

39.0ms	(* (* (sin B) (/ (* (sqrt 1.0) x) (sin B))) (cos B))
9.0ms	(/ (* (sqrt 1.0) x) (sin B))
207.0ms	(/ (- (* 1.0 (/ 1 (sqrt 1.0))) (* (* (sin B) (/ (* (sqrt 1.0) x) (sin B))) (cos B))) (/ (sin B) (sqrt 1.0)))
25.0ms	(* (sin B) (/ (* (sqrt 1.0) x) (sin B)))

series515.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(* (* (sin B) (/ (* (sqrt 1.0) x) (sin B))) (cos B))
97.0ms	(/ (* (sqrt 1.0) x) (sin B))
280.0ms	(/ (- (* 1.0 (/ 1 (sqrt 1.0))) (* (* (sin B) (/ (* (sqrt 1.0) x) (sin B))) (cos B))) (/ (sin B) (sqrt 1.0)))
47.0ms	(* (sin B) (/ (* (sqrt 1.0) x) (sin B)))

simplify440.0ms

Algorithm

egg-herbie

Counts

1768 → 1768

Iterations

Useful iterations: 1 (83.0ms)

Iter	Nodes	Cost
0	4449	49734
1	5002	48731

prune3.1s

Filtered

1768 candidates to 773 candidates (56.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	1767	1	1768
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	1770	5	1775

Merged error: 0b

Counts

1775 → 5

regimes62.0ms

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	22	16
1	22	16

end0.0ms

sample1.7s

Algorithm

intervals

Results

664.0ms	1628×	body	1280	valid
378.0ms	1470×	body	640	valid
306.0ms	4957×	body	80	valid
140.0ms	739×	body	320	valid
44.0ms	354×	body	160	valid