Details

sample33.0ms

Algorithm

intervals

Results

17.0ms	103×	body	1280	valid
4.0ms	121×	body	80	valid
3.0ms	23×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	3×	body	160	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	6
1	24	6
2	28	6
3	30	6
4	35	6
5	37	6
6	37	6

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: 15.3b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(/ 1.0 (hypot 1.0 x))
1.3b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

2×	`flip3-+` `sqrt-div` `associate-*r/` `sqrt-prod` `flip-+`
1×	`+-commutative` `sub-neg` `flip3--` `frac-2neg` `pow1/2` `clear-num` `*-commutative` `flip--` `div-inv`

Counts

4 → 15

Calls

4 calls:

3.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
3.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
2.0ms	(/ 1.0 (hypot 1.0 x))
2.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series197.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
76.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
6.0ms	(/ 1.0 (hypot 1.0 x))
88.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify100.0ms

Algorithm

egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 4 (96.0ms)

Iter	Nodes	Cost
0	112	181
1	263	178
2	949	176
3	3293	175
4	5002	173

prune53.0ms

Filtered

27 candidates to 15 candidates (55.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	25	2	27
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	25	3	28

Merged error: 14.9b

Counts

28 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
0.9b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

28×	`associate-*r/`
16×	`frac-sub`
11×	`clear-num`
10×	`flip3--` `flip--` `associate-/l/`
7×	`frac-2neg`
4×	`associate--l+` `un-div-inv`
3×	`sub-neg` `div-inv`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-/r/`
1×	`flip3-+` `div-sub` `flip-+`

Counts

4 → 38

Calls

4 calls:

11.0ms	(/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
2.0ms	(/ 1.0 (hypot 1.0 x))
2.0ms	(/ 1.0 (hypot 1.0 x))
8.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series218.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
6.0ms	(/ 1.0 (hypot 1.0 x))
6.0ms	(/ 1.0 (hypot 1.0 x))
39.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify45.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	306	516
1	1265	508
2	5002	501

prune146.0ms

Filtered

50 candidates to 34 candidates (68.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	47	3	50
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	49	4	53

Merged error: 14.8b

Counts

53 → 4

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x))
0.0b	(* (- (hypot 1.0 x)) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0)))
0.8b	(- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

20×	`distribute-rgt-in` `distribute-lft-in`
16×	`associate-+l+`
12×	`+-commutative` `associate--r+`
6×	`associate-r/` `associate-l/`
4×	`flip3--` `frac-sub` `flip--`
3×	`flip3-+` `associate-l` `flip-+`
2×	`*-commutative` `sqr-pow`
1×	`difference-cubes` `distribute-lft-neg-out` `neg-mul-1` `sub-neg` `frac-2neg` `clear-num` `div-inv` `difference-of-squares`

Counts

4 → 45

Calls

4 calls:

2.0ms	(/ 1.0 (hypot 1.0 x))
6.0ms	(* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x))
8.0ms	(* (- (hypot 1.0 x)) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0)))
15.0ms	(- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))

series92.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ 1.0 (hypot 1.0 x))
21.0ms	(* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x))
27.0ms	(* (- (hypot 1.0 x)) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0)))
37.0ms	(- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))

simplify56.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	416	582
1	1566	566
2	5001	566

prune426.0ms

Filtered

57 candidates to 37 candidates (64.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	55	2	57
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	56	5	61

Merged error: 14.8b

Counts

61 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (hypot 1.0 x))
0.0b	(/ (- 0.5 (* 0.5 (/ 1 (hypot 1.0 x)))) (+ (* (sqrt 0.5) (sqrt (+ (* 1.0 (/ 1 (hypot 1.0 x))) 1.0))) 1.0))
0.5b	(* (sqrt 0.5) (sqrt (+ (* 1.0 (/ 1 (hypot 1.0 x))) 1.0)))
0.9b	(- 0.5 (* 0.5 (/ 1 (hypot 1.0 x))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

2×	`flip3--` `frac-2neg` `flip3-+` `pow1/2` `sqrt-div` `associate-r/` `clear-num` `associate-/r/` `-commutative` `flip--` `flip-+` `div-inv` `associate-/l/`
1×	`sub-neg` `distribute-lft1-in` `sqrt-unprod` `div-sub` `associate-r` `pow-prod-down` `sqrt-prod` `inv-pow`

Counts

4 → 22

Calls

4 calls:

2.0ms	(/ 1 (hypot 1.0 x))
10.0ms	(/ (- 0.5 (* 0.5 (/ 1 (hypot 1.0 x)))) (+ (* (sqrt 0.5) (sqrt (+ (* 1.0 (/ 1 (hypot 1.0 x))) 1.0))) 1.0))
7.0ms	(* (sqrt 0.5) (sqrt (+ (* 1.0 (/ 1 (hypot 1.0 x))) 1.0)))
2.0ms	(- 0.5 (* 0.5 (/ 1 (hypot 1.0 x))))

series274.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ 1 (hypot 1.0 x))
162.0ms	(/ (- 0.5 (* 0.5 (/ 1 (hypot 1.0 x)))) (+ (* (sqrt 0.5) (sqrt (+ (* 1.0 (/ 1 (hypot 1.0 x))) 1.0))) 1.0))
74.0ms	(* (sqrt 0.5) (sqrt (+ (* 1.0 (/ 1 (hypot 1.0 x))) 1.0)))
33.0ms	(- 0.5 (* 0.5 (/ 1 (hypot 1.0 x))))

simplify74.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	167	284
1	512	280
2	2497	267
3	5001	267

prune79.0ms

Filtered

34 candidates to 21 candidates (61.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	33	1	34
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	35	4	39

Merged error: 14.8b

Counts

39 → 4

regimes211.0ms

Accuracy

0% (0.0b remaining)

Error of 14.6b against oracle of 14.6b and baseline of 14.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	31
1	26	31

end0.0ms

sample829.0ms

Algorithm

intervals

Results

484.0ms	2872×	body	1280	valid
121.0ms	4069×	body	80	valid
78.0ms	590×	body	640	valid
28.0ms	302×	body	320	valid
10.0ms	167×	body	160	valid