Details

sample62.0ms

Algorithm

intervals

Results

26.0ms	62×	body	1280	valid
11.0ms	42×	body	640	valid
9.0ms	146×	body	80	valid
4.0ms	20×	body	320	valid
2.0ms	14×	body	160	valid

simplify12.0ms

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

prune6.0ms

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

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)))

rewrite29.0ms

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:

8.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
4.0ms	(/ 1.0 (sin B))
7.0ms	(/ 1.0 (tan B))
7.0ms	(* x (/ 1.0 (tan B)))

series272.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
21.0ms	(/ 1.0 (sin B))
33.0ms	(/ 1.0 (tan B))
107.0ms	(* x (/ 1.0 (tan B)))

simplify51.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (42.0ms)

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

prune308.0ms

Filtered

129 candidates to 104 candidates (80.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	120	9	129
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	121	9	130

Merged error: 0.0b

Counts

130 → 9

localize11.0ms

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

rewrite30.0ms

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:

19.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
3.0ms	(/ 1.0 (sin B))
5.0ms	(/ (* x 1.0) (tan B))

series242.0ms

Counts

3 → 9

Calls

3 calls:

114.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
18.0ms	(/ 1.0 (sin B))
109.0ms	(/ (* x 1.0) (tan B))

simplify45.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (34.0ms)

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

prune217.0ms

Filtered

100 candidates to 79 candidates (79.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	100	9	109

Merged error: 0.0b

Counts

109 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

126×	`times-frac`
107×	`add-sqr-sqrt`
105×	`*-un-lft-identity`
98×	`add-cube-cbrt`
91×	`prod-diff`
28×	`div-inv`
15×	`add-exp-log`
13×	`fma-neg` `add-cbrt-cube`
7×	`pow1`
6×	`associate-/r*` `add-log-exp`
4×	`expm1-log1p-u` `div-exp` `log1p-expm1-u` `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 → 204

Calls

4 calls:

13.0ms	(- (/ 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))

series242.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
13.0ms	(/ 1 (sin B))
35.0ms	(* x (cos B))
99.0ms	(/ (* x (cos B)) (sin B))

simplify88.0ms

Algorithm

egg-herbie

Counts

216 → 216

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	579	3808
1	2173	2513
2	5001	2510

prune279.0ms

Filtered

216 candidates to 96 candidates (44.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	215	1	216
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	215	10	225

Merged error: 0.0b

Counts

225 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (tan B)) (cbrt (tan B)))
0.7b	(cbrt (tan B))
0.7b	(cbrt (tan B))
0.7b	(cbrt (tan B))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
7×	`tan-quot` `cbrt-div`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
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 → 87

Calls

4 calls:

7.0ms	(* (cbrt (tan B)) (cbrt (tan B)))
2.0ms	(cbrt (tan B))
2.0ms	(cbrt (tan B))
2.0ms	(cbrt (tan B))

series487.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(* (cbrt (tan B)) (cbrt (tan B)))
113.0ms	(cbrt (tan B))
118.0ms	(cbrt (tan B))
113.0ms	(cbrt (tan B))

simplify74.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 3 (67.0ms)

Iter	Nodes	Cost
0	174	531
1	545	493
2	2172	461
3	5001	457

prune243.0ms

Filtered

99 candidates to 73 candidates (73.7%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	99	0	99
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	99	10	109

Merged error: 0.0b

Counts

109 → 10

regimes78.0ms

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	7
1	20	7
2	20	7

end0.0ms

sample1.9s

Algorithm

intervals

Results

776.0ms	1741×	body	1280	valid
375.0ms	1369×	body	640	valid
318.0ms	4873×	body	80	valid
147.0ms	756×	body	320	valid
49.0ms	363×	body	160	valid