Details

sample316.0ms

Algorithm

intervals

Results

24.0ms	59×	body	1280	valid
16.0ms	59×	body	640	valid
9.0ms	150×	body	80	valid
3.0ms	17×	body	320	valid
1.0ms	11×	body	160	valid

simplify18.0ms

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

prune10.0ms

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

localize13.0ms

Local error

Found 3 expressions with local error:

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

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r` `associate-/l`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`
1×	`tan-quot` `associate-/r/` `fma-udef`

Counts

3 → 69

Calls

3 calls:

1.0ms	(fma (- x) (/ 1.0 (tan B)) (/ 1.0 (sin B)))
18.0ms	(/ 1.0 (tan B))
6.0ms	(/ 1.0 (sin B))

series173.0ms

Counts

3 → 9

Calls

3 calls:

104.0ms	(fma (- x) (/ 1.0 (tan B)) (/ 1.0 (sin B)))
38.0ms	(/ 1.0 (tan B))
30.0ms	(/ 1.0 (sin B))

simplify61.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (53.0ms)

Iter	Nodes	Cost
0	246	416
1	694	382
2	2127	382
3	5002	377

prune226.0ms

Filtered

78 candidates to 64 candidates (82.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	69	9	78
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	71	9	80

Merged error: 0.0b

Counts

80 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
28×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
13×	`add-exp-log` `associate-l` `add-cbrt-cube`
6×	`pow1` `associate-/r` `associate-/l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-r` `div-inv`
2×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `unswap-sqr`
1×	`pow-prod-down` `associate-l/` `-commutative` `fma-udef`

Counts

4 → 102

Calls

4 calls:

1.0ms	(fma (- x) (* (/ 1.0 (sin B)) (cos B)) (/ 1.0 (sin B)))
4.0ms	(/ 1.0 (sin B))
3.0ms	(/ 1.0 (sin B))
7.0ms	(* (/ 1.0 (sin B)) (cos B))

series182.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(fma (- x) (* (/ 1.0 (sin B)) (cos B)) (/ 1.0 (sin B)))
19.0ms	(/ 1.0 (sin B))
19.0ms	(/ 1.0 (sin B))
41.0ms	(* (/ 1.0 (sin B)) (cos B))

simplify121.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	279	660
1	1109	594
2	4890	592
3	5001	592

prune289.0ms

Filtered

114 candidates to 92 candidates (80.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	112	2	114
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	112	11	123

Merged error: 0.0b

Counts

123 → 11

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
23×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
16×	`associate-l`
12×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`associate-r` `prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in`
3×	`expm1-log1p-u` `prod-exp` `associate-/r` `cbrt-unprod` `log1p-expm1-u` `associate-/l` `add-log-exp` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `sub-neg` `flip3--` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `flip--` `div-inv`
1×	`frac-2neg` `associate-*l/` `clear-num`

Counts

3 → 97

Calls

3 calls:

3.0ms	(/ 1.0 (sin B))
4.0ms	(* x (cos B))
9.0ms	(* (/ 1.0 (sin B)) (- 1 (* x (cos B))))

series134.0ms

Counts

3 → 9

Calls

3 calls:

19.0ms	(/ 1.0 (sin B))
36.0ms	(* x (cos B))
78.0ms	(* (/ 1.0 (sin B)) (- 1 (* x (cos B))))

simplify57.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	415	714
1	2101	633
2	5001	629

prune231.0ms

Filtered

106 candidates to 75 candidates (70.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	101	5	106
Fresh	4	5	9
Picked	1	0	1
Done	0	1	1
Total	106	11	117

Merged error: 0.0b

Counts

117 → 11

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1`
3×	`associate-r` `associate-l` `associate-/r` `associate-/l`
2×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-sub` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `flip--` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

2 → 52

Calls

2 calls:

5.0ms	(/ (- 1 (* x (cos B))) (sin B))
4.0ms	(* x (cos B))

series107.0ms

Counts

2 → 6

Calls

2 calls:

70.0ms	(/ (- 1 (* x (cos B))) (sin B))
37.0ms	(* x (cos B))

simplify78.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 3 (72.0ms)

Iter	Nodes	Cost
0	201	379
1	822	347
2	3341	343
3	5002	342

prune121.0ms

Filtered

58 candidates to 44 candidates (75.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	57	1	58
Fresh	2	7	9
Picked	0	1	1
Done	0	1	1
Total	59	10	69

Merged error: 0.0b

Counts

69 → 10

regimes83.0ms

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	6
1	14	6

end0.0ms

sample1.8s

Algorithm

intervals

Results

729.0ms	1754×	body	1280	valid
356.0ms	1374×	body	640	valid
310.0ms	4991×	body	80	valid
125.0ms	683×	body	320	valid
49.0ms	350×	body	160	valid