Details

sample20.0ms

Algorithm

intervals

Results

8.0ms	256×	body	80	valid
4.0ms	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: 19.3b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite16.0ms

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:

4.0ms	(+ (* x x) (* y y))
11.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series91.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(+ (* x x) (* y y))
64.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify41.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 2 (37.0ms)

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

prune112.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (- x y) (sqrt (+ (* x x) (* y y)))) (/ (+ x y) (sqrt (+ (* x x) (* y y)))))
0.0b	(/ (+ x y) (sqrt (+ (* x x) (* y y))))
18.6b	(sqrt (+ (* x x) (* y y)))
18.6b	(sqrt (+ (* x x) (* y y)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-sqr-sqrt`
93×	`*-un-lft-identity`
90×	`times-frac`
55×	`add-cube-cbrt`
54×	`sqrt-prod`
36×	`associate-l`
30×	`associate-r`
18×	`add-exp-log` `add-cbrt-cube`
13×	`distribute-lft-out`
10×	`sqrt-div`
9×	`unswap-sqr`
8×	`pow1`
6×	`flip3-+` `associate-/r*` `associate-/r/` `flip-+` `distribute-lft-out--` `difference-of-squares`
5×	`cbrt-undiv` `div-exp`
4×	`prod-exp` `cbrt-unprod` `associate-/l*` `add-log-exp`
3×	`div-inv`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l/`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 175

Calls

4 calls:

32.0ms	(* (/ (- x y) (sqrt (+ (* x x) (* y y)))) (/ (+ x y) (sqrt (+ (* x x) (* y y)))))
8.0ms	(/ (+ x y) (sqrt (+ (* x x) (* y y))))
3.0ms	(sqrt (+ (* x x) (* y y)))
3.0ms	(sqrt (+ (* x x) (* y y)))

series223.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (/ (- x y) (sqrt (+ (* x x) (* y y)))) (/ (+ x y) (sqrt (+ (* x x) (* y y)))))
84.0ms	(/ (+ x y) (sqrt (+ (* x x) (* y y))))
34.0ms	(sqrt (+ (* x x) (* y y)))
39.0ms	(sqrt (+ (* x x) (* y y)))

simplify68.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	579	2358
1	2429	2169
2	5001	2080

prune371.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (pow x 2) (pow y 2))
0.0b	(/ (- x y) (/ (+ (pow x 2) (pow y 2)) (+ x y)))
18.7b	(/ (+ (pow x 2) (pow y 2)) (+ x y))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

347×	`*-un-lft-identity`
270×	`times-frac`
155×	`add-sqr-sqrt`
101×	`add-cube-cbrt`
96×	`distribute-lft-out`
60×	`unpow-prod-down`
30×	`associate-/r*`
27×	`distribute-lft-out--` `difference-of-squares`
15×	`associate-/r/`
10×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
9×	`flip3-+` `flip-+`
8×	`div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp` `associate-/l/`
3×	`pow1`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `flip3--` `div-sub` `sum-log` `flip--`

Counts

3 → 237

Calls

3 calls:

7.0ms	(+ (pow x 2) (pow y 2))
18.0ms	(/ (- x y) (/ (+ (pow x 2) (pow y 2)) (+ x y)))
11.0ms	(/ (+ (pow x 2) (pow y 2)) (+ x y))

series153.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (pow x 2) (pow y 2))
67.0ms	(/ (- x y) (/ (+ (pow x 2) (pow y 2)) (+ x y)))
59.0ms	(/ (+ (pow x 2) (pow y 2)) (+ x y))

simplify101.0ms

Algorithm

egg-herbie

Counts

246 → 246

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	762	2924
1	3415	2840
2	5001	2838

prune402.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

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

prune0.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.1b

regimes50.0ms

Accuracy

76.1% (4.8b remaining)

Error of 5.2b against oracle of 0.4b and baseline of 20.5b

bsearch86.0ms

Steps

Iters	Range	Point
9	1.9839035781685802e-168	4.3404891581481784e-161	3.4833472832353795e-161
8	-6.46348463023251e-162	-1.5121105300358365e-165	-6.149327853551763e-162
8	-6.117858652932295e+22	-5.950199898746248e+18	-6.0195069609054914e+22

Iters

Range

Point

1.9839035781685802e-168

4.3404891581481784e-161

3.4833472832353795e-161

-6.46348463023251e-162

-1.5121105300358365e-165

-6.149327853551763e-162

-6.117858652932295e+22

-5.950199898746248e+18

-6.0195069609054914e+22

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	20
1	34	20

end0.0ms

sample489.0ms

Algorithm

intervals

Results

242.0ms	8000×	body	80	valid
107.0ms	8000×	pre	80	true