Details

sample324.0ms

Algorithm

intervals

Results

27.0ms	63×	body	1280	valid
13.0ms	47×	body	640	valid
11.0ms	151×	body	80	valid
3.0ms	17×	body	320	valid
2.0ms	15×	body	160	valid

simplify17.0ms

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

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

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 (sin B))
0.2b	(/ 1.0 (tan B))

rewrite26.0ms

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)))
3.0ms	(/ 1.0 (sin B))
6.0ms	(/ 1.0 (tan B))

series170.0ms

Counts

3 → 9

Calls

3 calls:

101.0ms	(fma (- x) (/ 1.0 (tan B)) (/ 1.0 (sin B)))
19.0ms	(/ 1.0 (sin B))
50.0ms	(/ 1.0 (tan B))

simplify60.0ms

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

prune229.0ms

Filtered

78 candidates to 64 candidates (82.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	68	10	78
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	10	79

Merged error: 0.0b

Counts

79 → 10

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite10.0ms

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×	`fma-udef`

Counts

3 → 68

Calls

3 calls:

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

series141.0ms

Counts

3 → 9

Calls

3 calls:

99.0ms	(fma (- x) (* 1.0 (/ (cos B) (sin B))) (/ 1.0 (sin B)))
19.0ms	(/ 1.0 (sin B))
22.0ms	(/ (cos B) (sin B))

simplify61.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 3 (55.0ms)

Iter	Nodes	Cost
0	241	480
1	721	438
2	2196	438
3	5001	433

prune194.0ms

Filtered

77 candidates to 60 candidates (77.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	77	10	87

Merged error: 0.0b

Counts

87 → 10

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite20.0ms

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:

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

series135.0ms

Counts

3 → 9

Calls

3 calls:

21.0ms	(/ 1.0 (sin B))
76.0ms	(* (/ 1.0 (sin B)) (- 1 (* x (cos B))))
37.0ms	(* x (cos B))

simplify56.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	415	714
1	2094	633
2	5002	629

prune220.0ms

Filtered

106 candidates to 75 candidates (70.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	102	4	106
Fresh	3	5	8
Picked	1	0	1
Done	0	1	1
Total	106	10	116

Merged error: 0.0b

Counts

116 → 10

localize10.0ms

Local error

Found 2 expressions with local error:

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

4.0ms	(* x (cos B))
6.0ms	(/ (- 1 (* x (cos B))) (sin B))

series105.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(* x (cos B))
69.0ms	(/ (- 1 (* x (cos B))) (sin B))

simplify77.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 3 (71.0ms)

Iter	Nodes	Cost
0	201	379
1	826	347
2	3353	343
3	5001	342

prune113.0ms

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	1	7	8
Picked	0	1	1
Done	0	1	1
Total	58	10	68

Merged error: 0.0b

Counts

68 → 10

regimes80.0ms

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

746.0ms	1717×	body	1280	valid
382.0ms	1407×	body	640	valid
330.0ms	4975×	body	80	valid
140.0ms	719×	body	320	valid
47.0ms	348×	body	160	valid