Details

sample15.0ms

Algorithm

intervals

Results

5.0ms	256×	body	80	valid
1.0ms	84×	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: 22.8b

Counts

2 → 1

localize4.0ms

Local error

Found 1 expressions with local error:

21.2b

(sqrt (+ (* x x) y))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 18

Calls

1 calls:

4.0ms

(sqrt (+ (* x x) y))

series44.0ms

Counts

1 → 3

Calls

1 calls:

44.0ms

(sqrt (+ (* x x) y))

simplify155.0ms

Algorithm

egg-herbie

Counts

21 → 21

Iterations

Useful iterations: 3 (41.0ms)

Iter	Nodes	Cost
0	126	102
1	378	95
2	1147	92
3	4567	90
4	5001	90

prune52.0ms

Filtered

21 candidates to 19 candidates (90.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	19	2	21
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	19	3	22

Merged error: 0b

Counts

22 → 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)

series33.0ms

Counts

1 → 3

Calls

1 calls:

33.0ms

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

simplify79.0ms

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

prune27.0ms

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

localize5.0ms

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)))

series22.0ms

Counts

1 → 3

Calls

1 calls:

22.0ms

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

simplify122.0ms

Algorithm

egg-herbie

Counts

19 → 19

Iterations

Useful iterations: 1 (5.0ms)

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

prune38.0ms

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

regimes102.0ms

Accuracy

98.7% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 21.2b

bsearch45.0ms

Steps

Iters	Range		Point
7	7.443759268190367e+89	1.5340021636682078e+92	7.312923605803941e+91
9	-1.2994787762702041e+157	-1.865346764731705e+152	-1.3380532120724433e+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

sample357.0ms

Algorithm

intervals

Results

146.0ms	8000×	body	80	valid
46.0ms	2700×	body	80	nan