Details

sample22.0ms

Algorithm

intervals

Results

7.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify60.0ms

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: 17.3b

localize9.0ms

Local error

Found 2 expressions with local error:

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

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

series81.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify43.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 2 (38.0ms)

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: 0.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(cbrt (pow (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) 3))
0.0b	(pow (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) 3)
17.1b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

24×	`cbrt-prod`
18×	`unpow-prod-down` `cube-prod`
16×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
15×	`add-exp-log` `times-frac` `add-cbrt-cube`
10×	`associate-/r/`
9×	`flip3-+` `flip-+`
8×	`associate-/l/`
6×	`add-log-exp`
5×	`pow1` `div-inv`
4×	`cbrt-undiv` `frac-times` `div-exp`
3×	`pow-unpow` `flip3--` `pow-exp` `associate-/r*` `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 → 116

Calls

4 calls:

8.0ms	(+ (* x x) (* y y))
12.0ms	(cbrt (pow (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) 3))
23.0ms	(pow (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) 3)
30.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series219.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(+ (* x x) (* y y))
72.0ms	(cbrt (pow (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) 3))
67.0ms	(pow (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) 3)
56.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify74.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	494	1238
1	2872	1167
2	5001	1161

prune250.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize10.0ms

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)))
17.0b	(/ (+ (pow x 2) (pow y 2)) (+ x y))

rewrite136.0ms

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:

16.0ms	(+ (pow x 2) (pow y 2))
50.0ms	(/ (- x y) (/ (+ (pow x 2) (pow y 2)) (+ x y)))
55.0ms	(/ (+ (pow x 2) (pow y 2)) (+ x y))

series135.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (pow x 2) (pow y 2))
52.0ms	(/ (- x y) (/ (+ (pow x 2) (pow y 2)) (+ x y)))
55.0ms	(/ (+ (pow x 2) (pow y 2)) (+ x y))

simplify96.0ms

Algorithm

egg-herbie

Counts

246 → 246

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	762	2924
1	3418	2840
2	5002	2838

prune397.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.3b

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: 0.3b

regimes78.0ms

Accuracy

73.6% (5.1b remaining)

Error of 5.5b against oracle of 0.4b and baseline of 19.9b

bsearch69.0ms

Steps

Iters	Range	Point
7	1.268274377264742e-180	2.016704920243041e-178	1.981429660423225e-178
5	-5.484858039329347e-151	-2.078490583145916e-151	-3.224969964239895e-151
9	-6.735794998768675e+156	-1.8797925544767705e+149	-1.9550884380039752e+149

Iters

Range

Point

1.268274377264742e-180

2.016704920243041e-178

1.981429660423225e-178

-5.484858039329347e-151

-2.078490583145916e-151

-3.224969964239895e-151

-6.735794998768675e+156

-1.8797925544767705e+149

-1.9550884380039752e+149

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	18
1	31	18

end0.0ms

sample529.0ms

Algorithm

intervals

Results

232.0ms	8000×	body	80	valid
113.0ms	8000×	pre	80	true