Details

sample26.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify112.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

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

prune9.0ms

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: 20.7b

Counts

2 → 2

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
20.9b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite78.0ms

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:

21.0ms	(+ (* x x) (* y y))
44.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series123.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(+ (* x x) (* y y))
85.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify108.0ms

Algorithm

egg-herbie

Counts

208 → 208

Iterations

Useful iterations: 2 (81.0ms)

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

prune236.0ms

Filtered

208 candidates to 95 candidates (45.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	204	4	208
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	206	4	210

Merged error: 0.0b

Counts

210 → 4

localize12.0ms

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)))

rewrite62.0ms

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`
21×	`distribute-lft-out` `distribute-lft-out--`
20×	`difference-of-squares`
19×	`add-exp-log` `associate-r` `add-cbrt-cube`
16×	`associate-l`
15×	`flip3-+` `flip-+`
14×	`flip3--` `flip--`
13×	`associate-*r/`
12×	`associate-*l/`
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:

8.0ms	(/ (- x y) (hypot x y))
6.0ms	(/ (+ x y) (hypot x y))
28.0ms	(* (/ (+ x y) (hypot x y)) (/ (- x y) (hypot x y)))

series359.0ms

Counts

3 → 9

Calls

3 calls:

116.0ms	(/ (- x y) (hypot x y))
120.0ms	(/ (+ x y) (hypot x y))
122.0ms	(* (/ (+ x y) (hypot x y)) (/ (- x y) (hypot x y)))

simplify84.0ms

Algorithm

egg-herbie

Counts

326 → 326

Iterations

Useful iterations: 1 (45.0ms)

Iter	Nodes	Cost
0	1250	3089
1	5001	2980

prune479.0ms

Filtered

326 candidates to 201 candidates (61.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	324	2	326
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	327	3	330

Merged error: 0b

Counts

330 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

210×	`*-un-lft-identity`
183×	`add-sqr-sqrt`
156×	`frac-times`
132×	`associate-/l*`
113×	`add-cube-cbrt`
89×	`times-frac`
87×	`associate-/r*`
58×	`associate-/l/`
46×	`log-pow`
44×	`exp-prod`
38×	`associate-r`
32×	`associate-l`
30×	`clear-num`
29×	`frac-2neg`
24×	`distribute-lft-out` `distribute-lft-out--`
23×	`difference-of-squares`
21×	`add-exp-log`
20×	`add-cbrt-cube`
15×	`flip3-+` `flip-+`
14×	`flip3--` `flip--`
13×	`associate-*r/`
12×	`associate-*l/`
8×	`unswap-sqr`
7×	`pow1`
6×	`cbrt-undiv` `div-exp` `div-inv`
5×	`add-log-exp`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`log-prod` `un-div-inv`
2×	`rem-log-exp` `*-commutative`
1×	`exp-to-pow` `div-sub` `pow-prod-down`

Counts

4 → 377

Calls

4 calls:

20.0ms	(log (exp (* (/ (+ x y) (hypot x y)) (/ (- x y) (hypot x y)))))
7.0ms	(/ (- x y) (hypot x y))
6.0ms	(/ (+ x y) (hypot x y))
25.0ms	(* (/ (+ x y) (hypot x y)) (/ (- x y) (hypot x y)))

series401.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(log (exp (* (/ (+ x y) (hypot x y)) (/ (- x y) (hypot x y)))))
98.0ms	(/ (- x y) (hypot x y))
96.0ms	(/ (+ x y) (hypot x y))
103.0ms	(* (/ (+ x y) (hypot x y)) (/ (- x y) (hypot x y)))

simplify76.0ms

Algorithm

egg-herbie

Counts

389 → 389

Iterations

Useful iterations: 1 (37.0ms)

Iter	Nodes	Cost
0	1366	3553
1	5001	3420

prune731.0ms

Filtered

389 candidates to 248 candidates (63.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	389	0	389
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	389	3	392

Merged error: 0b

Counts

392 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (hypot x y) (+ x y))
0.0b	(* (/ (hypot x y) (+ x y)) (sqrt (hypot x y)))
0.0b	(/ (/ (- x y) (sqrt (hypot x y))) (* (/ (hypot x y) (+ x y)) (sqrt (hypot x y))))
0.5b	(/ (- x y) (sqrt (hypot x y)))

rewrite235.0ms

Algorithm

rewrite-expression-head

Rules

2688×	`times-frac`
1796×	`add-sqr-sqrt`
1664×	`*-un-lft-identity`
1012×	`add-cube-cbrt`
711×	`sqrt-prod`
648×	`associate-l`
216×	`associate-r`
212×	`distribute-lft-out--` `difference-of-squares`
144×	`unswap-sqr`
114×	`distribute-lft-out`
84×	`associate-/r/`
73×	`div-inv`
57×	`associate-/r*`
53×	`associate-/l*`
37×	`flip3-+` `flip-+`
36×	`*-commutative`
34×	`add-exp-log` `add-cbrt-cube`
20×	`associate-*l/` `associate-/l/`
14×	`cbrt-undiv` `div-exp`
6×	`pow1` `frac-2neg` `prod-exp` `clear-num` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`div-sub`
2×	`flip3--` `flip--`
1×	`pow-prod-down`

Counts

4 → 1386

Calls

4 calls:

6.0ms	(/ (hypot x y) (+ x y))
18.0ms	(* (/ (hypot x y) (+ x y)) (sqrt (hypot x y)))
48.0ms	(/ (/ (- x y) (sqrt (hypot x y))) (* (/ (hypot x y) (+ x y)) (sqrt (hypot x y))))
8.0ms	(/ (- x y) (sqrt (hypot x y)))

series431.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(/ (hypot x y) (+ x y))
121.0ms	(* (/ (hypot x y) (+ x y)) (sqrt (hypot x y)))
102.0ms	(/ (/ (- x y) (sqrt (hypot x y))) (* (/ (hypot x y) (+ x y)) (sqrt (hypot x y))))
107.0ms	(/ (- x y) (sqrt (hypot x y)))

simplify348.0ms

Algorithm

egg-herbie

Counts

1398 → 1398

Iterations

Useful iterations: 1 (83.0ms)

Iter	Nodes	Cost
0	4206	28655
1	5003	28083

prune2.2s

Filtered

1398 candidates to 611 candidates (43.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	1398	0	1398
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	1398	3	1401

Merged error: 0b

Counts

1401 → 3

regimes34.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	9
1	12	9

end0.0ms

sample485.0ms

Algorithm

intervals

Results

233.0ms	8000×	body	80	valid
112.0ms	8000×	pre	80	true