Details

sample69.0ms

Algorithm

intervals

Results

31.0ms	67×	body	1280	valid
12.0ms	45×	body	640	valid
9.0ms	159×	body	80	valid
4.0ms	23×	body	320	valid
1.0ms	10×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	18	7
1	33	6
2	43	6
3	54	6
4	60	6
5	62	6
6	62	6

prune5.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma (- x) (/ 1.0 (tan B)) (/ 1.0 (sin B)))
0.1b	(/ 1.0 (sin B))
0.2b	(/ 1.0 (tan 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×	`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))
4.0ms	(/ 1.0 (tan B))

series182.0ms

Counts

3 → 9

Calls

3 calls:

119.0ms	(fma (- x) (/ 1.0 (tan B)) (/ 1.0 (sin B)))
26.0ms	(/ 1.0 (sin B))
36.0ms	(/ 1.0 (tan B))

simplify56.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (49.0ms)

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)

Merged error: 0.0b

localize12.0ms

Local error

Found 3 expressions with local error:

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

series140.0ms

Counts

3 → 9

Calls

3 calls:

99.0ms	(fma (- x) (* 1.0 (/ (cos B) (sin B))) (/ 1.0 (sin B)))
18.0ms	(/ 1.0 (sin B))
23.0ms	(/ (cos B) (sin B))

simplify61.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 3 (54.0ms)

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

prune231.0ms

Filtered

77 candidates to 60 candidates (77.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1 (* x (cos B)))
0.1b	(/ 1.0 (sin B))
0.1b	(* x (cos B))
0.2b	(* (/ 1.0 (sin B)) (- 1 (* x (cos B))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 117

Calls

4 calls:

6.0ms	(- 1 (* x (cos B)))
3.0ms	(/ 1.0 (sin B))
4.0ms	(* x (cos B))
9.0ms	(* (/ 1.0 (sin B)) (- 1 (* x (cos B))))

series164.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- 1 (* x (cos B)))
18.0ms	(/ 1.0 (sin B))
38.0ms	(* x (cos B))
71.0ms	(* (/ 1.0 (sin B)) (- 1 (* x (cos B))))

simplify57.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	423	840
1	2124	739
2	5002	734

prune290.0ms

Filtered

129 candidates to 91 candidates (70.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 72

Calls

3 calls:

3.0ms	(- 1 (* x (cos B)))
4.0ms	(* x (cos B))
6.0ms	(/ (- 1 (* x (cos B))) (sin B))

series142.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(- 1 (* x (cos B)))
37.0ms	(* x (cos B))
67.0ms	(/ (- 1 (* x (cos B))) (sin B))

simplify98.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (92.0ms)

Iter	Nodes	Cost
0	251	500
1	1081	453
2	4681	448
3	5001	447

prune189.0ms

Filtered

81 candidates to 60 candidates (74.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes70.0ms

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

735.0ms	1725×	body	1280	valid
406.0ms	1482×	body	640	valid
298.0ms	4868×	body	80	valid
135.0ms	693×	body	320	valid
51.0ms	359×	body	160	valid