Details

sample314.0ms

Algorithm

intervals

Results

29.0ms	62×	body	1280	valid
11.0ms	42×	body	640	valid
10.0ms	146×	body	80	valid
4.0ms	20×	body	320	valid
2.0ms	14×	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	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))
0.2b	(/ 1.0 (tan B))
0.2b	(* x (/ 1.0 (tan B)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
28×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
14×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `associate-/r` `associate-/l` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-l` `div-inv`
2×	`tan-quot` `frac-2neg` `associate-*r/` `prod-exp` `clear-num` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `*-commutative` `frac-sub` `flip--`

Counts

4 → 101

Calls

4 calls:

7.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
4.0ms	(/ 1.0 (sin B))
18.0ms	(/ 1.0 (tan B))
10.0ms	(* x (/ 1.0 (tan B)))

series301.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
22.0ms	(/ 1.0 (sin B))
35.0ms	(/ 1.0 (tan B))
123.0ms	(* x (/ 1.0 (tan B)))

simplify46.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	386	627
1	1479	584
2	5001	584

prune271.0ms

Filtered

113 candidates to 88 candidates (77.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	105	8	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	106	8	114

Merged error: 0.0b

Counts

114 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
13×	`add-exp-log` `add-cbrt-cube`
12×	`times-frac`
6×	`pow1` `associate-/r*` `add-log-exp`
4×	`associate-/l*`
3×	`cbrt-undiv` `div-exp` `associate-r` `associate-l` `div-inv`
2×	`frac-2neg` `associate-*r/` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `*-commutative` `frac-sub` `flip--` `distribute-lft-out--` `sub-div` `unswap-sqr`

Counts

4 → 81

Calls

4 calls:

6.0ms	(- (/ 1.0 (sin B)) (* 1.0 (/ (* x (cos B)) (sin B))))
3.0ms	(/ 1.0 (sin B))
4.0ms	(* x (cos B))
8.0ms	(/ (* x (cos B)) (sin B))

series267.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(- (/ 1.0 (sin B)) (* 1.0 (/ (* x (cos B)) (sin B))))
18.0ms	(/ 1.0 (sin B))
36.0ms	(* x (cos B))
95.0ms	(/ (* x (cos B)) (sin B))

simplify44.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	333	572
1	1375	511
2	5001	511

prune193.0ms

Filtered

93 candidates to 68 candidates (73.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	92	9	101

Merged error: 0.0b

Counts

101 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (sin B))
0.1b	(/ 1.0 (sin B))
0.2b	(* (* x (/ 1.0 (sin B))) (cos B))
0.3b	(* x (/ 1.0 (sin B)))

rewrite26.0ms

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

Counts

4 → 107

Calls

4 calls:

4.0ms	(/ 1.0 (sin B))
4.0ms	(/ 1.0 (sin B))
7.0ms	(* (* x (/ 1.0 (sin B))) (cos B))
7.0ms	(* x (/ 1.0 (sin B)))

series199.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(/ 1.0 (sin B))
19.0ms	(/ 1.0 (sin B))
103.0ms	(* (* x (/ 1.0 (sin B))) (cos B))
59.0ms	(* x (/ 1.0 (sin B)))

simplify56.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	315	645
1	1562	560
2	5001	560

prune224.0ms

Filtered

119 candidates to 84 candidates (70.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	119	9	128

Merged error: 0.0b

Counts

128 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

45×	`times-frac`
34×	`add-exp-log` `add-sqr-sqrt`
32×	`add-cube-cbrt` `*-un-lft-identity`
22×	`add-cbrt-cube`
15×	`div-exp`
11×	`associate-/r*`
9×	`associate-/l*`
8×	`cbrt-undiv`
7×	`pow1` `div-inv`
5×	`prod-exp`
4×	`add-log-exp`
3×	`rec-exp` `frac-2neg` `1-exp` `associate-r` `associate-l` `clear-num` `cbrt-unprod`
1×	`pow-flip` `pow-prod-down` `associate-/r/` `*-commutative` `inv-pow` `unswap-sqr`

Counts

4 → 122

Calls

4 calls:

3.0ms	(/ 1.0 (sin B))
4.0ms	(* x (cos B))
5.0ms	(/ (sin B) (* x (cos B)))
7.0ms	(/ 1 (/ (sin B) (* x (cos B))))

series194.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ 1.0 (sin B))
37.0ms	(* x (cos B))
65.0ms	(/ (sin B) (* x (cos B)))
74.0ms	(/ 1 (/ (sin B) (* x (cos B))))

simplify56.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	419	846
1	1818	733
2	5001	690

prune205.0ms

Filtered

134 candidates to 80 candidates (59.7%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	134	9	143

Merged error: 0.0b

Counts

143 → 9

regimes69.0ms

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	12	8
1	12	8

end0.0ms

sample1.9s

Algorithm

intervals

Results

773.0ms	1741×	body	1280	valid
381.0ms	1369×	body	640	valid
328.0ms	4873×	body	80	valid
149.0ms	756×	body	320	valid
50.0ms	363×	body	160	valid