Details

sample17.0ms

Algorithm

intervals

Results

6.0ms	256×	body	80	valid
2.0ms	83×	body	80	nan

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	7	3
1	7	3

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: 23.3b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) y)
21.8b	(sqrt (+ (* x x) y))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt`
4×	`add-log-exp`
3×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
2×	`add-exp-log` `expm1-log1p-u` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
1×	`+-commutative` `rem-sqrt-square` `fma-def` `sqrt-pow1` `pow1/2` `sum-log` `hypot-def`

Counts

2 → 32

Calls

2 calls:

4.0ms	(+ (* x x) y)
4.0ms	(sqrt (+ (* x x) y))

series63.0ms

Counts

2 → 6

Calls

2 calls:

19.0ms	(+ (* x x) y)
44.0ms	(sqrt (+ (* x x) y))

simplify54.0ms

Algorithm

egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 3 (50.0ms)

Iter	Nodes	Cost
0	153	160
1	518	146
2	1716	138
3	5002	137

prune74.0ms

Filtered

38 candidates to 32 candidates (84.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	36	2	38
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	36	3	39

Merged error: 0b

Counts

39 → 3

localize4.0ms

Local error

Found 1 expressions with local error:

0.0b	(fma 1/2 (/ y x) x)

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

1.0ms

(fma 1/2 (/ y x) x)

series36.0ms

Counts

1 → 3

Calls

1 calls:

36.0ms

(fma 1/2 (/ y x) x)

simplify81.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	21	44
1	48	39
2	156	39
3	585	39
4	2784	39
5	5001	39

prune20.0ms

Filtered

13 candidates to 10 candidates (76.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	13	0	13
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	13	3	16

Merged error: 0b

Counts

16 → 3

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (* 1/2 (/ y x)))
0.0b	(* 1/2 (/ y x))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
13×	`associate-r`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`times-frac`
7×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `add-log-exp`
3×	`fma-def` `associate-l`
2×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `flip3-+` `associate-r/` `div-exp` `pow-prod-down` `sum-log` `-commutative` `flip-+` `div-inv`

Counts

2 → 50

Calls

2 calls:

3.0ms	(+ x (* 1/2 (/ y x)))
7.0ms	(* 1/2 (/ y x))

series44.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(+ x (* 1/2 (/ y x)))
18.0ms	(* 1/2 (/ y x))

simplify108.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	230	213
1	988	194
2	4421	194
3	5001	194

prune80.0ms

Filtered

56 candidates to 42 candidates (75.0%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	56	0	56
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	56	3	59

Merged error: 0b

Counts

59 → 3

regimes114.0ms

Accuracy

97.4% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 21.8b

bsearch46.0ms

Steps

Iters	Range		Point
6	6.876338848371802e+44	4.895029231506205e+45	4.8328616978417944e+45
8	-9.054381491912354e+157	-1.2405689363353731e+154	-1.324355824971499e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	9
1	30	9
2	32	9
3	32	9

end0.0ms

sample452.0ms

Algorithm

intervals

Results

208.0ms	8000×	body	80	valid
70.0ms	2691×	body	80	nan