Details

sample20.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 20.6b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
20.3b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

8×	`associate-/l/`
5×	`flip3-+` `flip-+`
4×	`frac-times`
3×	`flip3--` `flip--`
2×	`associate-r/` `associate-l/` `associate-/r/` `associate-/l*`
1×	`+-commutative` `frac-2neg` `clear-num` `*-commutative` `div-inv`

Counts

2 → 18

Calls

2 calls:

4.0ms	(+ (* x x) (* y y))
9.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series88.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(+ (* x x) (* y y))
62.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify86.0ms

Algorithm

egg-herbie

Counts

24 → 24

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	169	148
1	859	142
2	3711	134
3	5001	134

prune61.0ms

Filtered

24 candidates to 21 candidates (87.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	21	3	24
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	21	4	25

Merged error: 0.3b

Counts

25 → 4

localize12.0ms

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)))
19.5b	(/ (+ (pow x 2) (pow y 2)) (- x y))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

9×	`associate-/r/`
6×	`associate-/l/`
4×	`flip3-+` `flip-+`
3×	`frac-2neg` `clear-num` `associate-/r*` `div-inv`
2×	`flip3--` `flip--`
1×	`+-commutative`

Counts

3 → 23

Calls

3 calls:

3.0ms	(+ (pow x 2) (pow y 2))
7.0ms	(/ (+ x y) (/ (+ (pow x 2) (pow y 2)) (- x y)))
5.0ms	(/ (+ (pow x 2) (pow y 2)) (- x y))

series145.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ (pow x 2) (pow y 2))
61.0ms	(/ (+ x y) (/ (+ (pow x 2) (pow y 2)) (- x y)))
58.0ms	(/ (+ (pow x 2) (pow y 2)) (- x y))

simplify81.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 3 (76.0ms)

Iter	Nodes	Cost
0	140	162
1	515	160
2	1970	154
3	5002	153

prune77.0ms

Filtered

32 candidates to 24 candidates (75.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	29	3	32
Fresh	2	0	2
Picked	1	0	1
Done	0	1	1
Total	32	4	36

Merged error: 0.3b

Counts

36 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow x 2) (pow y 2))
0.0b	(* (/ (/ (+ (pow x 2) (pow y 2)) (- x y)) (+ x y)) (+ x y))
0.0b	(/ (+ x y) (* (/ (/ (+ (pow x 2) (pow y 2)) (- x y)) (+ x y)) (+ x y)))
19.5b	(/ (+ (pow x 2) (pow y 2)) (- x y))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

53×	`associate-/r/`
46×	`associate-/l/`
44×	`frac-times`
35×	`flip3-+` `flip-+`
22×	`associate-*l/`
18×	`associate-/l*`
14×	`frac-2neg` `clear-num`
10×	`div-inv`
7×	`flip3--` `flip--`
6×	`associate-l`
5×	`associate-/r*`
4×	`associate-*r/`
3×	`+-commutative`
2×	`distribute-rgt-in` `distribute-lft-in` `*-commutative`

Counts

4 → 98

Calls

4 calls:

4.0ms	(+ (pow x 2) (pow y 2))
11.0ms	(* (/ (/ (+ (pow x 2) (pow y 2)) (- x y)) (+ x y)) (+ x y))
14.0ms	(/ (+ x y) (* (/ (/ (+ (pow x 2) (pow y 2)) (- x y)) (+ x y)) (+ x y)))
6.0ms	(/ (+ (pow x 2) (pow y 2)) (- x y))

series211.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (pow x 2) (pow y 2))
62.0ms	(* (/ (/ (+ (pow x 2) (pow y 2)) (- x y)) (+ x y)) (+ x y))
61.0ms	(/ (+ x y) (* (/ (/ (+ (pow x 2) (pow y 2)) (- x y)) (+ x y)) (+ x y)))
62.0ms	(/ (+ (pow x 2) (pow y 2)) (- x y))

simplify142.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	601	1015
1	4363	893
2	5001	893

prune337.0ms

Filtered

110 candidates to 94 candidates (85.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	110	4	114

Merged error: 0.3b

Counts

114 → 4

localize4.0ms

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)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	2	2
Total	4	4

Merged error: 0.3b

Counts

4 → 4

regimes83.0ms

Accuracy

76.8% (4.6b remaining)

Error of 5.2b against oracle of 0.6b and baseline of 20.6b

bsearch74.0ms

Steps

Iters	Range	Point
8	4.6392126302617956e-172	3.3746055148489886e-168	3.3216144882269104e-168
5	-7.101451878346312e-157	-3.155267202466709e-157	-4.654600319030996e-157
9	-1.2994787762702041e+157	-1.865346764731705e+152	-1.1011563348006714e+153

Iters

Range

Point

4.6392126302617956e-172

3.3746055148489886e-168

3.3216144882269104e-168

-7.101451878346312e-157

-3.155267202466709e-157

-4.654600319030996e-157

-1.2994787762702041e+157

-1.865346764731705e+152

-1.1011563348006714e+153

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	18
1	33	18
2	33	18

end0.0ms

sample476.0ms

Algorithm

intervals

Results

227.0ms	8000×	body	80	valid
111.0ms	8000×	pre	80	true