Details

sample20.0ms

Algorithm

intervals

Results

7.0ms	256×	body	80	valid
3.0ms	256×	pre	80	true

simplify69.0ms

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

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 19.5b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(* (- x y) (+ x y))
19.6b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`add-exp-log` `add-cbrt-cube`
8×	`frac-times` `flip3-+` `flip-+` `associate-/l/`
7×	`add-cube-cbrt`
6×	`flip3--` `flip--`
5×	`pow1` `associate-l` `add-log-exp`
4×	`associate-r/` `associate-r` `associate-l/`
3×	`expm1-log1p-u` `times-frac` `associate-/r*` `log1p-expm1-u`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod`
1×	`+-commutative` `distribute-rgt-in` `fma-def` `frac-2neg` `distribute-lft-in` `pow-prod-down` `clear-num` `sum-log` `-commutative` `div-inv` `distribute-lft-out` `associate-/l` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

3 → 80

Calls

3 calls:

8.0ms	(+ (* x x) (* y y))
36.0ms	(* (- x y) (+ x y))
27.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series137.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(+ (* x x) (* y y))
42.0ms	(* (- x y) (+ x y))
65.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify64.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	435	575
1	2499	504
2	5001	494

prune193.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x y) (sqrt (+ (* x x) (* y y))))
0.0b	(* (/ (- x y) (hypot x y)) (/ (+ x y) (sqrt (+ (* x x) (* y y)))))
0.0b	(/ (- x y) (hypot x y))
19.1b	(sqrt (+ (* x x) (* y y)))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

96×	`*-un-lft-identity`
90×	`add-sqr-sqrt`
85×	`times-frac`
56×	`add-cube-cbrt`
32×	`sqrt-prod`
30×	`associate-r`
20×	`add-exp-log` `add-cbrt-cube`
19×	`associate-l`
13×	`distribute-lft-out`
9×	`associate-/r` `associate-/l`
7×	`pow1` `distribute-lft-out--` `difference-of-squares`
6×	`cbrt-undiv` `sqrt-div` `div-exp` `unswap-sqr`
4×	`expm1-log1p-u` `flip3-+` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+` `log1p-expm1-u` `div-inv` `associate-/l/` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `flip--` `hypot-def`

Counts

4 → 187

Calls

4 calls:

27.0ms	(/ (+ x y) (sqrt (+ (* x x) (* y y))))
74.0ms	(* (/ (- x y) (hypot x y)) (/ (+ x y) (sqrt (+ (* x x) (* y y)))))
16.0ms	(/ (- x y) (hypot x y))
8.0ms	(sqrt (+ (* x x) (* y y)))

series337.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(/ (+ x y) (sqrt (+ (* x x) (* y y))))
129.0ms	(* (/ (- x y) (hypot x y)) (/ (+ x y) (sqrt (+ (* x x) (* y y)))))
90.0ms	(/ (- x y) (hypot x y))
37.0ms	(sqrt (+ (* x x) (* y y)))

simplify71.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	637	1798
1	2710	1480
2	5001	1419

prune421.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (- x y) (hypot x y)) (/ 1 (/ (hypot x y) (+ x y))))
0.0b	(/ 1 (/ (hypot x y) (+ x y)))
0.0b	(/ (hypot x y) (+ x y))
0.0b	(/ (- x y) (hypot x y))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

251×	`times-frac`
194×	`*-un-lft-identity`
173×	`add-sqr-sqrt`
126×	`add-cube-cbrt`
64×	`add-exp-log`
59×	`associate-r`
34×	`add-cbrt-cube`
30×	`div-exp`
25×	`associate-/r*` `distribute-lft-out`
19×	`associate-l`
18×	`associate-/r/`
14×	`cbrt-undiv` `prod-exp`
12×	`div-inv`
11×	`associate-/l*`
10×	`unswap-sqr`
8×	`flip3-+` `flip-+`
7×	`pow1` `distribute-lft-out--` `difference-of-squares`
6×	`rec-exp` `1-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`associate-/l/`
1×	`frac-times` `flip3--` `pow-flip` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `un-div-inv` `*-commutative` `flip--` `inv-pow`

Counts

4 → 296

Calls

4 calls:

79.0ms	(* (/ (- x y) (hypot x y)) (/ 1 (/ (hypot x y) (+ x y))))
16.0ms	(/ 1 (/ (hypot x y) (+ x y)))
11.0ms	(/ (hypot x y) (+ x y))
16.0ms	(/ (- x y) (hypot x y))

series370.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(* (/ (- x y) (hypot x y)) (/ 1 (/ (hypot x y) (+ x y))))
92.0ms	(/ 1 (/ (hypot x y) (+ x y)))
90.0ms	(/ (hypot x y) (+ x y))
92.0ms	(/ (- x y) (hypot x y))

simplify106.0ms

Algorithm

egg-herbie

Counts

308 → 308

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	989	2718
1	4876	2404
2	5001	2404

prune615.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

283×	`times-frac`
236×	`*-un-lft-identity`
232×	`add-sqr-sqrt`
220×	`add-cube-cbrt`
169×	`prod-diff`
32×	`div-inv`
13×	`fma-neg`
10×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
9×	`associate-/l*`
6×	`add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
3×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
2×	`associate-/r/`
1×	`sub-neg` `flip3--` `distribute-rgt-out--` `flip3-+` `diff-log` `frac-sub` `flip--` `flip-+` `sub-div`

Counts

4 → 300

Calls

4 calls:

5.0ms	(/ x (hypot x y))
36.0ms	(- (/ x (hypot x y)) (/ y (hypot x y)))
11.0ms	(/ (hypot x y) (+ x y))
5.0ms	(/ y (hypot x y))

series372.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(/ x (hypot x y))
137.0ms	(- (/ x (hypot x y)) (/ y (hypot x y)))
94.0ms	(/ (hypot x y) (+ x y))
72.0ms	(/ y (hypot x y))

simplify89.0ms

Algorithm

egg-herbie

Counts

312 → 312

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	840	6327
1	2574	4562
2	5001	4172

prune470.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

regimes38.0ms

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	15	10
1	15	10

end0.0ms

sample511.0ms

Algorithm

intervals

Results

220.0ms	8000×	body	80	valid
107.0ms	8000×	pre	80	true