Details

sample21.0ms

Algorithm

intervals

Results

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

simplify70.0ms

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: 17.0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
17.1b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

8×	`associate-/l/`
7×	`add-exp-log` `add-cbrt-cube`
5×	`flip3-+` `flip-+`
4×	`add-sqr-sqrt` `frac-times` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
3×	`flip3--` `times-frac` `associate-/r*` `flip--`
2×	`pow1` `cbrt-undiv` `expm1-log1p-u` `associate-r/` `div-exp` `associate-l/` `associate-/r/` `log1p-expm1-u`
1×	`+-commutative` `fma-def` `frac-2neg` `prod-exp` `clear-num` `sum-log` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

2 → 47

Calls

2 calls:

11.0ms	(+ (* x x) (* y y))
27.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series82.0ms

Counts

2 → 6

Calls

2 calls:

28.0ms	(+ (* x x) (* y y))
53.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify46.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	322	380
1	1875	324
2	5001	308

prune118.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(/ (hypot x y) (+ x y))
0.0b	(/ (- x y) (/ (hypot x y) (+ x y)))
16.9b	(sqrt (+ (* x x) (* y y)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

174×	`times-frac`
163×	`*-un-lft-identity`
120×	`add-sqr-sqrt`
81×	`add-cube-cbrt`
22×	`associate-/r*` `distribute-lft-out`
19×	`distribute-lft-out--` `difference-of-squares`
15×	`associate-/r/`
11×	`add-exp-log` `add-cbrt-cube`
9×	`flip3-+` `flip-+`
8×	`div-inv` `associate-/l*`
6×	`add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`sqrt-prod`
2×	`frac-2neg` `sqrt-div` `clear-num` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `flip3--` `fma-def` `sqrt-pow1` `pow1/2` `div-sub` `sum-log` `flip--` `hypot-def`

Counts

4 → 200

Calls

4 calls:

8.0ms	(+ (* x x) (* y y))
11.0ms	(/ (hypot x y) (+ x y))
31.0ms	(/ (- x y) (/ (hypot x y) (+ x y)))
8.0ms	(sqrt (+ (* x x) (* y y)))

series219.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(+ (* x x) (* y y))
81.0ms	(/ (hypot x y) (+ x y))
78.0ms	(/ (- x y) (/ (hypot x y) (+ x y)))
36.0ms	(sqrt (+ (* x x) (* y y)))

simplify94.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	753	1885
1	3494	1809
2	5001	1803

prune483.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 3 expressions with local error:

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

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

1059×	`times-frac`
757×	`*-un-lft-identity`
593×	`add-sqr-sqrt`
411×	`add-cube-cbrt`
103×	`associate-/l*`
91×	`distribute-lft-out--` `difference-of-squares`
82×	`distribute-lft-out`
59×	`associate-/r/`
33×	`div-inv`
27×	`flip3-+` `flip-+`
25×	`associate-/r*`
19×	`add-exp-log` `add-cbrt-cube`
10×	`cbrt-undiv` `div-exp`
3×	`pow1` `expm1-log1p-u` `frac-2neg` `div-sub` `clear-num` `log1p-expm1-u` `associate-/l/` `add-log-exp`
1×	`flip3--` `flip--`

Counts

3 → 571

Calls

3 calls:

51.0ms	(/ (/ (- x y) (/ (hypot x y) (+ x y))) (hypot x y))
14.0ms	(/ (hypot x y) (+ x y))
28.0ms	(/ (- x y) (/ (hypot x y) (+ x y)))

series241.0ms

Counts

3 → 9

Calls

3 calls:

81.0ms	(/ (/ (- x y) (/ (hypot x y) (+ x y))) (hypot x y))
80.0ms	(/ (hypot x y) (+ x y))
81.0ms	(/ (- x y) (/ (hypot x y) (+ x y)))

simplify109.0ms

Algorithm

egg-herbie

Counts

580 → 580

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1752	8207
1	5001	7913

prune1.3s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize7.0ms

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	(/ (- x y) (hypot x y))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

894×	`times-frac`
603×	`*-un-lft-identity`
475×	`add-sqr-sqrt`
353×	`add-cube-cbrt`
64×	`distribute-lft-out`
61×	`distribute-lft-out--` `difference-of-squares`
43×	`associate-/r/`
42×	`div-inv`
27×	`associate-/l*`
25×	`associate-/r*`
21×	`flip3-+` `flip-+`
19×	`add-exp-log` `add-cbrt-cube`
10×	`cbrt-undiv` `div-exp`
3×	`pow1` `expm1-log1p-u` `frac-2neg` `div-sub` `clear-num` `log1p-expm1-u` `associate-/l/` `add-log-exp`
1×	`flip3--` `flip--`

Counts

3 → 477

Calls

3 calls:

36.0ms	(/ (/ (- x y) (hypot x y)) (/ (hypot x y) (+ x y)))
11.0ms	(/ (hypot x y) (+ x y))
19.0ms	(/ (- x y) (hypot x y))

series237.0ms

Counts

3 → 9

Calls

3 calls:

78.0ms	(/ (/ (- x y) (hypot x y)) (/ (hypot x y) (+ x y)))
78.0ms	(/ (hypot x y) (+ x y))
81.0ms	(/ (- x y) (hypot x y))

simplify100.0ms

Algorithm

egg-herbie

Counts

486 → 486

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1827	7457
1	5001	7286

prune918.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes25.0ms

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	9	7
1	9	7

end0.0ms

sample503.0ms

Algorithm

intervals

Results

214.0ms	8000×	body	80	valid
102.0ms	8000×	pre	80	true