Details

sample64.0ms

Algorithm

intervals

Results

25.0ms	53×	body	1280	valid
12.0ms	49×	body	640	valid
9.0ms	149×	body	80	valid
5.0ms	26×	body	320	valid
2.0ms	13×	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	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

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 (tan B))
0.1b	(/ 1.0 (sin B))

rewrite9.0ms

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)))
4.0ms	(/ 1.0 (tan B))
4.0ms	(/ 1.0 (sin B))

series157.0ms

Counts

3 → 9

Calls

3 calls:

97.0ms	(fma (- x) (/ 1.0 (tan B)) (/ 1.0 (sin B)))
40.0ms	(/ 1.0 (tan B))
20.0ms	(/ 1.0 (sin B))

simplify59.0ms

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

prune247.0ms

Filtered

78 candidates to 64 candidates (82.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	70	8	78
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	8	79

Merged error: 0.0b

Counts

79 → 8

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)))
3.0ms	(/ 1.0 (sin B))
4.0ms	(/ (cos B) (sin B))

series138.0ms

Counts

3 → 9

Calls

3 calls:

98.0ms	(fma (- x) (* 1.0 (/ (cos B) (sin B))) (/ 1.0 (sin B)))
18.0ms	(/ 1.0 (sin B))
23.0ms	(/ (cos B) (sin B))

simplify59.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 3 (53.0ms)

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

prune239.0ms

Filtered

77 candidates to 60 candidates (77.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	76	1	77
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	77	8	85

Merged error: 0.0b

Counts

85 → 8

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

96×	`add-sqr-sqrt`
75×	`*-un-lft-identity`
72×	`prod-diff`
69×	`add-cube-cbrt`
38×	`distribute-rgt-in` `distribute-lft-in`
35×	`associate-l`
30×	`associate-r`
19×	`times-frac`
18×	`frac-times`
12×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
11×	`unswap-sqr`
10×	`flip3--` `flip--`
9×	`associate-*l/`
8×	`*-commutative`
7×	`pow1`
4×	`frac-2neg` `clear-num` `difference-of-squares`
3×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `sub-neg` `associate-*r/` `div-exp` `pow-prod-down` `div-inv` `distribute-lft-out--`

Counts

3 → 193

Calls

3 calls:

20.0ms	(* (/ 1.0 (sin B)) (- 1 (* x (cos B))))
3.0ms	(/ 1.0 (sin B))
4.0ms	(* x (cos B))

series130.0ms

Counts

3 → 9

Calls

3 calls:

76.0ms	(* (/ 1.0 (sin B)) (- 1 (* x (cos B))))
18.0ms	(/ 1.0 (sin B))
36.0ms	(* x (cos B))

simplify46.0ms

Algorithm

egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1013	2785
1	5001	1992

prune351.0ms

Filtered

202 candidates to 99 candidates (49.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	197	5	202
Fresh	5	2	7
Picked	0	1	1
Done	0	0	0
Total	202	8	210

Merged error: 0.0b

Counts

210 → 8

localize16.0ms

Local error

Found 2 expressions with local error:

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

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

898×	`times-frac`
676×	`add-sqr-sqrt`
536×	`*-un-lft-identity`
398×	`add-cube-cbrt`
302×	`sqrt-prod`
210×	`associate-r`
164×	`associate-l`
93×	`unswap-sqr`
92×	`difference-of-squares`
46×	`distribute-lft-out--`
28×	`associate-/r*`
25×	`associate-/l*`
24×	`*-commutative` `div-inv`
16×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/r/`
6×	`cbrt-undiv` `div-exp`
4×	`pow1`
3×	`prod-exp` `cbrt-unprod`
2×	`expm1-log1p-u` `frac-2neg` `associate-*r/` `clear-num` `log1p-expm1-u` `associate-/l/` `add-log-exp`
1×	`flip3--` `pow-prod-down` `flip--`

Counts

2 → 582

Calls

2 calls:

4.0ms	(* x (cos B))
34.0ms	(/ (* (sqrt 1.0) (- 1 (* x (cos B)))) (/ (sin B) (sqrt 1.0)))

series212.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(* x (cos B))
177.0ms	(/ (* (sqrt 1.0) (- 1 (* x (cos B)))) (/ (sin B) (sqrt 1.0)))

simplify125.0ms

Algorithm

egg-herbie

Counts

588 → 588

Iterations

Useful iterations: 1 (43.0ms)

Iter	Nodes	Cost
0	2267	10555
1	5002	10147

prune1.1s

Filtered

588 candidates to 266 candidates (45.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	586	2	588
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	588	8	596

Merged error: 0.0b

Counts

596 → 8

regimes73.0ms

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	16	9
1	16	9

end0.0ms

sample1.7s

Algorithm

intervals

Results

703.0ms	1683×	body	1280	valid
361.0ms	1394×	body	640	valid
288.0ms	4955×	body	80	valid
128.0ms	701×	body	320	valid
50.0ms	369×	body	160	valid