Details

sample20.0ms

Algorithm

intervals

Results

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

simplify59.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	7
1	48	7
2	104	7
3	196	7
4	359	7
5	686	7
6	1355	7
7	5001	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
19.8b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite41.0ms

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` `associate-r/` `div-exp` `associate-l/` `associate-/r/`
1×	`+-commutative` `frac-2neg` `prod-exp` `clear-num` `sum-log` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

2 → 42

Calls

2 calls:

8.0ms	(+ (* x x) (* y y))
32.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series92.0ms

Counts

2 → 6

Calls

2 calls:

31.0ms	(+ (* x x) (* y y))
61.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify42.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	308	388
1	1848	330
2	5001	322

prune111.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.8b

localize0.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify2.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0

prune6.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.8b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(/ 1 (/ (+ (* x x) (* y y)) (* (- x y) (+ x y))))
19.8b	(/ (+ (* x x) (* y y)) (* (- x y) (+ x y)))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

60×	`times-frac`
41×	`associate-/r/`
29×	`add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
20×	`frac-times`
17×	`flip3-+` `add-cbrt-cube` `flip-+`
16×	`associate-/r*`
15×	`flip3--` `flip--`
14×	`div-exp`
10×	`associate-r/` `associate-l/`
7×	`cbrt-undiv`
6×	`div-inv` `associate-/l*`
5×	`add-log-exp`
4×	`pow1` `prod-exp`
3×	`rec-exp` `1-exp`
2×	`frac-2neg` `clear-num` `cbrt-unprod` `associate-/l/`
1×	`+-commutative` `pow-flip` `sum-log` `inv-pow`

Counts

3 → 130

Calls

3 calls:

8.0ms	(+ (* x x) (* y y))
41.0ms	(/ 1 (/ (+ (* x x) (* y y)) (* (- x y) (+ x y))))
39.0ms	(/ (+ (* x x) (* y y)) (* (- x y) (+ x y)))

series153.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(+ (* x x) (* y y))
65.0ms	(/ 1 (/ (+ (* x x) (* y y)) (* (- x y) (+ x y))))
61.0ms	(/ (+ (* x x) (* y y)) (* (- x y) (+ x y)))

simplify91.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	604	1641
1	3913	1448
2	5001	1367

prune231.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow x 2) (pow y 2))
0.0b	(pow (/ (* (- x y) (+ x y)) (+ (pow x 2) (pow y 2))) 3)
0.0b	(cbrt (pow (/ (* (- x y) (+ x y)) (+ (pow x 2) (pow y 2))) 3))
19.8b	(/ (* (- x y) (+ x y)) (+ (pow x 2) (pow y 2)))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

44×	`*-un-lft-identity`
36×	`unpow-prod-down`
28×	`cbrt-prod`
25×	`times-frac`
22×	`cube-prod`
16×	`add-sqr-sqrt` `add-cube-cbrt`
15×	`add-exp-log` `add-cbrt-cube`
14×	`distribute-lft-out`
10×	`associate-/r/`
9×	`flip3-+` `flip-+`
8×	`associate-/l/`
6×	`add-log-exp`
5×	`pow1` `associate-/r*` `div-inv`
4×	`cbrt-undiv` `frac-times` `div-exp`
3×	`pow-unpow` `flip3--` `pow-exp` `flip--` `rem-cube-cbrt`
2×	`cube-div` `cube-mult` `unpow3` `associate-r/` `associate-l/` `prod-exp` `cbrt-unprod` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `cbrt-div` `pow-pow` `frac-2neg` `pow1/3` `clear-num` `sum-log` `rem-cbrt-cube` `associate-/l*`

Counts

4 → 130

Calls

4 calls:

17.0ms	(+ (pow x 2) (pow y 2))
39.0ms	(pow (/ (* (- x y) (+ x y)) (+ (pow x 2) (pow y 2))) 3)
28.0ms	(cbrt (pow (/ (* (- x y) (+ x y)) (+ (pow x 2) (pow y 2))) 3))
47.0ms	(/ (* (- x y) (+ x y)) (+ (pow x 2) (pow y 2)))

series254.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(+ (pow x 2) (pow y 2))
78.0ms	(pow (/ (* (- x y) (+ x y)) (+ (pow x 2) (pow y 2))) 3)
81.0ms	(cbrt (pow (/ (* (- x y) (+ x y)) (+ (pow x 2) (pow y 2))) 3))
65.0ms	(/ (* (- x y) (+ x y)) (+ (pow x 2) (pow y 2)))

simplify71.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	493	1309
1	2760	1228
2	5002	1222

prune280.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.8b

regimes79.0ms

Accuracy

79.1% (4.5b remaining)

Error of 4.9b against oracle of 0.5b and baseline of 21.8b

bsearch78.0ms

Steps

Iters	Range	Point
9	1.5213384114896885e-175	3.62313754533445e-170	3.565272236996636e-170
7	-7.037677722153121e-161	-2.982283826009562e-163	-1.7529668527424618e-161
8	-3.66318343323661e+154	-2.4612156793354082e+151	-5.916052332961235e+153

Iters

Range

Point

1.5213384114896885e-175

3.62313754533445e-170

3.565272236996636e-170

-7.037677722153121e-161

-2.982283826009562e-163

-1.7529668527424618e-161

-3.66318343323661e+154

-2.4612156793354082e+151

-5.916052332961235e+153

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	16
1	29	16

end0.0ms

sample493.0ms

Algorithm

intervals

Results

224.0ms	8000×	body	80	valid
94.0ms	8000×	pre	80	true