Details

sample21.0ms

Algorithm

intervals

Results

8.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify86.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	23	6
1	52	6
2	117	6
3	240	6
4	478	6
5	947	6
6	1844	6
7	5001	6

prune7.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 18.1b

Counts

2 → 2

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
18.2b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

290×	`*-un-lft-identity`
120×	`times-frac`
116×	`associate-l`
94×	`distribute-lft-out`
88×	`add-sqr-sqrt`
50×	`add-cube-cbrt`
39×	`associate-r`
37×	`swap-sqr`
15×	`fma-def` `associate-/l*`
10×	`*-commutative` `unswap-sqr`
9×	`distribute-lft-out--` `difference-of-squares`
8×	`associate-/r*` `associate-/l/`
7×	`add-exp-log` `add-cbrt-cube`
5×	`flip3-+` `flip-+`
4×	`frac-times` `add-log-exp`
3×	`flip3--` `flip--`
2×	`pow1` `cbrt-undiv` `expm1-log1p-u` `associate-r/` `div-exp` `associate-l/` `associate-/r/` `log1p-expm1-u`
1×	`+-commutative` `frac-2neg` `prod-exp` `clear-num` `sum-log` `cbrt-unprod` `div-inv`

Counts

2 → 202

Calls

2 calls:

17.0ms	(+ (* x x) (* y y))
36.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series106.0ms

Counts

2 → 6

Calls

2 calls:

32.0ms	(+ (* x x) (* y y))
74.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify96.0ms

Algorithm

egg-herbie

Counts

208 → 208

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	566	1845
1	2906	1681
2	5002	1656

prune222.0ms

Filtered

208 candidates to 95 candidates (54.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	202	6	208
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	204	6	210

Merged error: 0.0b

Counts

210 → 6

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (+ x y) (hypot x y))
0.0b	(/ (- x y) (hypot x y))
0.0b	(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

178×	`*-un-lft-identity`
156×	`frac-times`
145×	`add-sqr-sqrt`
132×	`associate-/l*`
93×	`add-cube-cbrt`
87×	`associate-/r*`
58×	`times-frac` `associate-/l/`
30×	`clear-num`
29×	`frac-2neg`
22×	`distribute-lft-out`
20×	`distribute-lft-out--` `difference-of-squares`
19×	`add-exp-log` `associate-l` `add-cbrt-cube`
16×	`associate-r`
15×	`flip3-+` `flip-+`
14×	`flip3--` `flip--`
13×	`associate-*l/`
12×	`associate-*r/`
6×	`cbrt-undiv` `div-exp`
5×	`pow1`
4×	`prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
3×	`expm1-log1p-u` `un-div-inv` `log1p-expm1-u` `add-log-exp`
1×	`div-sub` `pow-prod-down` `*-commutative`

Counts

3 → 317

Calls

3 calls:

6.0ms	(/ (+ x y) (hypot x y))
7.0ms	(/ (- x y) (hypot x y))
25.0ms	(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))

series311.0ms

Counts

3 → 9

Calls

3 calls:

101.0ms	(/ (+ x y) (hypot x y))
100.0ms	(/ (- x y) (hypot x y))
110.0ms	(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))

simplify78.0ms

Algorithm

egg-herbie

Counts

326 → 326

Iterations

Useful iterations: 1 (41.0ms)

Iter	Nodes	Cost
0	1315	3088
1	5001	2987

prune473.0ms

Filtered

326 candidates to 201 candidates (38.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	324	2	326
Fresh	5	0	5
Picked	1	0	1
Done	0	0	0
Total	330	2	332

Merged error: 0b

Counts

332 → 2

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x y) (* (hypot x y) (/ (hypot x y) (+ x y))))
0.0b	(/ (hypot x y) (+ x y))
0.0b	(* (hypot x y) (/ (hypot x y) (+ x y)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

243×	`times-frac`
228×	`*-un-lft-identity`
207×	`add-sqr-sqrt`
126×	`associate-r`
114×	`add-cube-cbrt`
40×	`associate-/r*`
29×	`distribute-lft-out--` `difference-of-squares`
28×	`associate-/r/`
27×	`distribute-lft-out`
21×	`associate-l`
20×	`associate-*r/`
19×	`add-exp-log` `add-cbrt-cube`
16×	`associate-/l*`
14×	`unswap-sqr`
9×	`div-inv`
8×	`flip3-+` `flip-+`
7×	`*-commutative`
6×	`cbrt-undiv` `div-exp` `clear-num`
5×	`pow1`
4×	`frac-2neg` `prod-exp` `un-div-inv` `cbrt-unprod`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`associate-/l/`
1×	`flip3--` `div-sub` `pow-prod-down` `flip--`

Counts

3 → 291

Calls

3 calls:

22.0ms	(/ (- x y) (* (hypot x y) (/ (hypot x y) (+ x y))))
5.0ms	(/ (hypot x y) (+ x y))
12.0ms	(* (hypot x y) (/ (hypot x y) (+ x y)))

series327.0ms

Counts

3 → 9

Calls

3 calls:

110.0ms	(/ (- x y) (* (hypot x y) (/ (hypot x y) (+ x y))))
111.0ms	(/ (hypot x y) (+ x y))
105.0ms	(* (hypot x y) (/ (hypot x y) (+ x y)))

simplify154.0ms

Algorithm

egg-herbie

Counts

300 → 300

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1019	3274
1	4758	3102
2	5001	3102

prune453.0ms

Filtered

300 candidates to 194 candidates (35.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	300	0	300
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	300	2	302

Merged error: 0b

Counts

302 → 2

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (hypot x y)) (sqrt (hypot x y)))
0.2b	(* (- (- x y)) (/ (+ x y) (sqrt (hypot x y))))
0.5b	(/ (+ x y) (sqrt (hypot x y)))
9.5b	(/ (* (- (- x y)) (/ (+ x y) (sqrt (hypot x y)))) (* (- (hypot x y)) (sqrt (hypot x y))))

rewrite260.0ms

Algorithm

rewrite-expression-head

Rules

1824×	`times-frac`
1332×	`add-sqr-sqrt`
1256×	`*-un-lft-identity`
1012×	`associate-r`
870×	`associate-l`
824×	`add-cube-cbrt`
566×	`sqrt-prod`
281×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
179×	`unswap-sqr`
165×	`distribute-lft-out`
82×	`associate-/l*`
77×	`neg-mul-1` `*-commutative`
65×	`associate-/r*`
64×	`associate-/l/` `distribute-neg-frac`
60×	`frac-times`
50×	`distribute-lft-out--` `difference-of-squares`
34×	`add-exp-log` `add-cbrt-cube`
32×	`flip3--` `flip--`
30×	`associate-*r/`
27×	`div-inv`
10×	`cbrt-undiv` `div-exp` `prod-exp` `clear-num` `cbrt-unprod`
8×	`pow1` `frac-2neg`
7×	`flip3-+` `flip-+`
6×	`un-div-inv`
4×	`expm1-log1p-u` `associate-*l/` `log1p-expm1-u` `add-log-exp`
3×	`distribute-lft-neg-out`
2×	`pow-prod-down`
1×	`distribute-frac-neg`

Counts

4 → 1491

Calls

4 calls:

6.0ms	(* (- (hypot x y)) (sqrt (hypot x y)))
24.0ms	(* (- (- x y)) (/ (+ x y) (sqrt (hypot x y))))
13.0ms	(/ (+ x y) (sqrt (hypot x y)))
66.0ms	(/ (* (- (- x y)) (/ (+ x y) (sqrt (hypot x y)))) (* (- (hypot x y)) (sqrt (hypot x y))))

series500.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(* (- (hypot x y)) (sqrt (hypot x y)))
155.0ms	(* (- (- x y)) (/ (+ x y) (sqrt (hypot x y))))
109.0ms	(/ (+ x y) (sqrt (hypot x y)))
116.0ms	(/ (* (- (- x y)) (/ (+ x y) (sqrt (hypot x y)))) (* (- (hypot x y)) (sqrt (hypot x y))))

simplify318.0ms

Algorithm

egg-herbie

Counts

1503 → 1503

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5001	29684

prune3.1s

Filtered

1503 candidates to 830 candidates (44.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	1503	0	1503
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	1503	2	1505

Merged error: 0b

Counts

1505 → 2

regimes29.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	7
1	10	7

end0.0ms

sample575.0ms

Algorithm

intervals

Results

272.0ms	8000×	body	80	valid
136.0ms	8000×	pre	80	true