Details

sample16.0ms

Algorithm

intervals

Results

8.0ms

256×

body

valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	5
1	22	5
2	26	5
3	29	5
4	30	5
5	30	5

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: 0.0b

Counts

2 → 1

localize6.0ms

Local error

Found 1 expressions with local error:

5.5b	(/ y (+ 1.0 (/ (* x y) 2.0)))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
12×	`times-frac`
10×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`associate-/r*` `distribute-lft-out`
3×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
2×	`associate-/r/`
1×	`pow1` `cbrt-undiv` `expm1-log1p-u` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 35

Calls

1 calls:

6.0ms

(/ y (+ 1.0 (/ (* x y) 2.0)))

series63.0ms

Counts

1 → 3

Calls

1 calls:

63.0ms

(/ y (+ 1.0 (/ (* x y) 2.0)))

simplify142.0ms

Algorithm

egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 3 (137.0ms)

Iter	Nodes	Cost
0	214	293
1	824	273
2	4306	265
3	5001	264

prune71.0ms

Filtered

38 candidates to 28 candidates (73.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	35	3	38
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	36	3	39

Merged error: 0.0b

Counts

39 → 3

localize8.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ 1 (/ (+ 1.0 (/ (* x y) 2.0)) y))
5.4b	(/ (+ 1.0 (/ (* x y) 2.0)) y)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

108×	`times-frac`
92×	`*-un-lft-identity`
60×	`add-sqr-sqrt` `add-cube-cbrt`
19×	`associate-/r*`
16×	`distribute-lft-out`
15×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`div-exp`
7×	`associate-/l*`
6×	`div-inv`
4×	`cbrt-undiv`
3×	`pow1`
2×	`expm1-log1p-u` `rec-exp` `frac-2neg` `1-exp` `clear-num` `log1p-expm1-u` `associate-/l/` `add-log-exp`
1×	`pow-flip` `flip3-+` `associate-/r/` `flip-+` `inv-pow`

Counts

2 → 125

Calls

2 calls:

12.0ms	(/ 1 (/ (+ 1.0 (/ (* x y) 2.0)) y))
7.0ms	(/ (+ 1.0 (/ (* x y) 2.0)) y)

series112.0ms

Counts

2 → 6

Calls

2 calls:

63.0ms	(/ 1 (/ (+ 1.0 (/ (* x y) 2.0)) y))
48.0ms	(/ (+ 1.0 (/ (* x y) 2.0)) y)

simplify69.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	452	1205
1	2119	1085
2	5001	966

prune152.0ms

Filtered

131 candidates to 68 candidates (51.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	130	4	134

Merged error: 0b

Counts

134 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (+ 1.0 (/ (* x y) 2.0))) y)
0.2b	(/ (/ 1 (sqrt (+ 1.0 (/ (* x y) 2.0)))) (/ (sqrt (+ 1.0 (/ (* x y) 2.0))) y))
1.4b	(sqrt (+ 1.0 (/ (* x y) 2.0)))
1.4b	(sqrt (+ 1.0 (/ (* x y) 2.0)))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

1830×	`times-frac`
1114×	`*-un-lft-identity`
784×	`add-sqr-sqrt`
778×	`add-cube-cbrt`
672×	`sqrt-prod`
168×	`distribute-lft-out`
58×	`sqrt-div`
56×	`div-inv`
53×	`associate-/r/`
34×	`associate-/l*`
29×	`flip3-+` `flip-+`
28×	`add-exp-log` `associate-/r*`
18×	`add-cbrt-cube`
17×	`div-exp`
9×	`cbrt-undiv`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l/`
2×	`rem-sqrt-square` `rec-exp` `frac-2neg` `sqrt-pow1` `pow1/2` `1-exp` `clear-num` `hypot-def`

Counts

4 → 838

Calls

4 calls:

7.0ms	(/ (sqrt (+ 1.0 (/ (* x y) 2.0))) y)
28.0ms	(/ (/ 1 (sqrt (+ 1.0 (/ (* x y) 2.0)))) (/ (sqrt (+ 1.0 (/ (* x y) 2.0))) y))
5.0ms	(sqrt (+ 1.0 (/ (* x y) 2.0)))
5.0ms	(sqrt (+ 1.0 (/ (* x y) 2.0)))

series385.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(/ (sqrt (+ 1.0 (/ (* x y) 2.0))) y)
65.0ms	(/ (/ 1 (sqrt (+ 1.0 (/ (* x y) 2.0)))) (/ (sqrt (+ 1.0 (/ (* x y) 2.0))) y))
99.0ms	(sqrt (+ 1.0 (/ (* x y) 2.0)))
100.0ms	(sqrt (+ 1.0 (/ (* x y) 2.0)))

simplify402.0ms

Algorithm

egg-herbie

Counts

850 → 850

Iterations

Useful iterations: 1 (53.0ms)

Iter	Nodes	Cost
0	2628	18992
1	5002	17342

prune924.0ms

Filtered

850 candidates to 292 candidates (34.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	850	0	850
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	850	4	854

Merged error: 0b

Counts

854 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (* x y) 2.0) (/ (* x y) 2.0))
1.2b	(- (* (/ (* x y) 2.0) (/ (* x y) 2.0)) (* 1.0 (/ (* x y) 2.0)))
2.9b	(/ y (+ (pow 1.0 3) (pow (/ (* x y) 2.0) 3)))
19.4b	(* (/ y (+ (pow 1.0 3) (pow (/ (* x y) 2.0) 3))) (+ (* 1.0 1.0) (- (* (/ (* x y) 2.0) (/ (* x y) 2.0)) (* 1.0 (/ (* x y) 2.0)))))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

110×	`*-un-lft-identity`
67×	`times-frac`
47×	`add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
40×	`add-cube-cbrt` `associate-l`
35×	`distribute-lft-out`
28×	`unpow-prod-down` `cube-prod`
17×	`prod-exp` `cbrt-unprod`
14×	`cbrt-undiv` `div-exp`
13×	`pow1`
10×	`associate-r/` `associate-r*`
9×	`associate-/r*`
7×	`swap-sqr` `sum-cubes`
6×	`div-inv` `add-log-exp`
4×	`expm1-log1p-u` `frac-times` `flip3-+` `associate-*l/` `associate-/r/` `flip-+` `log1p-expm1-u`
3×	`frac-sub` `associate-/l*` `unswap-sqr`
2×	`pow-prod-down` `*-commutative` `sub-div`
1×	`pow2` `distribute-rgt-in` `sub-neg` `flip3--` `distribute-rgt-out--` `frac-2neg` `distribute-lft-in` `pow-plus` `fma-neg` `diff-log` `prod-diff` `clear-num` `pow-sqr` `pow-prod-up` `flip--`

Counts

4 → 195

Calls

4 calls:

10.0ms	(* (/ (* x y) 2.0) (/ (* x y) 2.0))
14.0ms	(- (* (/ (* x y) 2.0) (/ (* x y) 2.0)) (* 1.0 (/ (* x y) 2.0)))
16.0ms	(/ y (+ (pow 1.0 3) (pow (/ (* x y) 2.0) 3)))
30.0ms	(* (/ y (+ (pow 1.0 3) (pow (/ (* x y) 2.0) 3))) (+ (* 1.0 1.0) (- (* (/ (* x y) 2.0) (/ (* x y) 2.0)) (* 1.0 (/ (* x y) 2.0)))))

series348.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (/ (* x y) 2.0) (/ (* x y) 2.0))
78.0ms	(- (* (/ (* x y) 2.0) (/ (* x y) 2.0)) (* 1.0 (/ (* x y) 2.0)))
62.0ms	(/ y (+ (pow 1.0 3) (pow (/ (* x y) 2.0) 3)))
168.0ms	(* (/ y (+ (pow 1.0 3) (pow (/ (* x y) 2.0) 3))) (+ (* 1.0 1.0) (- (* (/ (* x y) 2.0) (/ (* x y) 2.0)) (* 1.0 (/ (* x y) 2.0)))))

simplify54.0ms

Algorithm

egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	990	2403
1	5001	2078

prune440.0ms

Filtered

207 candidates to 128 candidates (61.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	207	0	207
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	207	4	211

Merged error: 0b

Counts

211 → 4

regimes36.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	6
1	15	6

end0.0ms

sample391.0ms

Algorithm

intervals

Results

261.0ms	7998×	body	80	valid
0.0ms	1×	body	1280	valid
0.0ms	1×	body	640	valid