Details

sample17.0ms

Algorithm

intervals

Results

6.0ms	256×	body	80	valid
2.0ms	93×	body	80	nan

simplify4.0ms

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: 21.8b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) y)
20.2b	(sqrt (+ (* x x) y))

rewrite8.0ms

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))

series57.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(+ (* x x) y)
39.0ms	(sqrt (+ (* x x) y))

simplify50.0ms

Algorithm

egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 3 (46.0ms)

Iter	Nodes	Cost
0	153	160
1	518	146
2	1716	138
3	5002	136

prune73.0ms

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

localize5.0ms

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)

series33.0ms

Counts

1 → 3

Calls

1 calls:

33.0ms

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

simplify76.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 1 (3.0ms)

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 1 expressions with local error:

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

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

3×	`fma-def` `add-log-exp`
2×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
1×	`pow1` `add-exp-log` `+-commutative` `expm1-log1p-u` `flip3-+` `sum-log` `add-cbrt-cube` `flip-+` `log1p-expm1-u`

Counts

1 → 16

Calls

1 calls:

3.0ms

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

series26.0ms

Counts

1 → 3

Calls

1 calls:

26.0ms

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

simplify117.0ms

Algorithm

egg-herbie

Counts

19 → 19

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	88	84
1	322	70
2	1253	70
3	4552	70
4	5001	70

prune29.0ms

Filtered

19 candidates to 16 candidates (84.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	19	0	19
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	19	3	22

Merged error: 0b

Counts

22 → 3

regimes115.0ms

Accuracy

97.5% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 21.0b

bsearch49.0ms

Steps

Iters	Range		Point
8	4.894072981317339e+56	3.636538464064539e+59	3.59902122559668e+59
8	-2.3864984321674706e+156	-2.2709498629311444e+153	-1.342254409532742e+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

sample447.0ms

Algorithm

intervals

Results

213.0ms	8000×	body	80	valid
64.0ms	2695×	body	80	nan