Details

sample34.0ms

Algorithm

intervals

Results

9.0ms	274×	body	80	nan
5.0ms	50×	body	640	valid
5.0ms	39×	body	1280	valid
3.0ms	135×	body	80	valid
2.0ms	24×	body	320	valid
0.0ms	8×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	6
1	14	6
2	14	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: 18.8b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1.0 (sqrt (+ x 1.0)))
0.3b	(/ 1.0 (sqrt x))
3.2b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

9×	`frac-sub`
8×	`frac-2neg` `clear-num`
4×	`div-inv`
2×	`sqrt-div` `associate-/r/`
1×	`sub-neg` `flip3--` `flip3-+` `flip--` `flip-+` `distribute-lft-out--`

Counts

3 → 22

Calls

3 calls:

3.0ms	(/ 1.0 (sqrt (+ x 1.0)))
2.0ms	(/ 1.0 (sqrt x))
6.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series265.0ms

Counts

3 → 9

Calls

3 calls:

82.0ms	(/ 1.0 (sqrt (+ x 1.0)))
39.0ms	(/ 1.0 (sqrt x))
144.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify35.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	313	324
1	1058	282
2	5001	260

prune81.0ms

Filtered

31 candidates to 25 candidates (80.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	26	5	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	27	5	32

Merged error: 18.6b

Counts

32 → 5

localize14.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (+ (- (sqrt (+ x 1.0))) (sqrt x)) (* (- (sqrt x)) (/ (sqrt (+ x 1.0)) 1.0)))
0.2b	(* (- (sqrt x)) (/ (sqrt (+ x 1.0)) 1.0))
3.2b	(+ (- (sqrt (+ x 1.0))) (sqrt x))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

10×	`associate-*r/`
6×	`associate-/r/` `associate-/l/`
5×	`clear-num`
4×	`flip3-+` `sqrt-div` `associate-/r*` `flip-+`
3×	`frac-2neg` `div-inv`
2×	`neg-sub0` `associate-+l-` `neg-mul-1` `associate-r` `associate-l` `un-div-inv` `*-commutative`
1×	`+-commutative` `distribute-lft-neg-out` `div-sub`

Counts

3 → 30

Calls

3 calls:

9.0ms	(/ (+ (- (sqrt (+ x 1.0))) (sqrt x)) (* (- (sqrt x)) (/ (sqrt (+ x 1.0)) 1.0)))
5.0ms	(* (- (sqrt x)) (/ (sqrt (+ x 1.0)) 1.0))
4.0ms	(+ (- (sqrt (+ x 1.0))) (sqrt x))

series454.0ms

Counts

3 → 9

Calls

3 calls:

293.0ms	(/ (+ (- (sqrt (+ x 1.0))) (sqrt x)) (* (- (sqrt x)) (/ (sqrt (+ x 1.0)) 1.0)))
79.0ms	(* (- (sqrt x)) (/ (sqrt (+ x 1.0)) 1.0))
82.0ms	(+ (- (sqrt (+ x 1.0))) (sqrt x))

simplify39.0ms

Algorithm

egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	349	376
1	1285	328
2	5001	313

prune116.0ms

Filtered

39 candidates to 35 candidates (89.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	37	2	39
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	39	5	44

Merged error: 0.3b

Counts

44 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (- (sqrt (+ x 1.0))) (sqrt x))
0.2b	(/ (+ 1.0 (- x x)) (- (- (sqrt (+ x 1.0))) (sqrt x)))
0.2b	(* (- (sqrt x)) (/ (sqrt (+ x 1.0)) 1.0))
0.2b	(/ (/ (+ 1.0 (- x x)) (- (- (sqrt (+ x 1.0))) (sqrt x))) (* (- (sqrt x)) (/ (sqrt (+ x 1.0)) 1.0)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

18×	`associate-/r/`
13×	`associate-/l/`
12×	`times-frac` `div-inv`
10×	`associate-*r/`
7×	`flip3--` `clear-num` `flip--`
5×	`neg-mul-1` `frac-2neg` `associate-r` `associate-l` `*-commutative`
4×	`flip3-+` `sqrt-div` `associate-/r*` `flip-+`
3×	`div-sub` `associate-/l*`
2×	`associate-+r-` `un-div-inv`
1×	`distribute-lft-neg-out` `associate--l-` `neg-sub0` `sub-neg`

Counts

4 → 57

Calls

4 calls:

4.0ms	(- (- (sqrt (+ x 1.0))) (sqrt x))
7.0ms	(/ (+ 1.0 (- x x)) (- (- (sqrt (+ x 1.0))) (sqrt x)))
5.0ms	(* (- (sqrt x)) (/ (sqrt (+ x 1.0)) 1.0))
13.0ms	(/ (/ (+ 1.0 (- x x)) (- (- (sqrt (+ x 1.0))) (sqrt x))) (* (- (sqrt x)) (/ (sqrt (+ x 1.0)) 1.0)))

series843.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(- (- (sqrt (+ x 1.0))) (sqrt x))
148.0ms	(/ (+ 1.0 (- x x)) (- (- (sqrt (+ x 1.0))) (sqrt x)))
79.0ms	(* (- (sqrt x)) (/ (sqrt (+ x 1.0)) 1.0))
533.0ms	(/ (/ (+ 1.0 (- x x)) (- (- (sqrt (+ x 1.0))) (sqrt x))) (* (- (sqrt x)) (/ (sqrt (+ x 1.0)) 1.0)))

simplify67.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	580	964
1	2438	791
2	5001	751

prune252.0ms

Filtered

69 candidates to 61 candidates (88.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	63	6	69
Fresh	1	2	3
Picked	1	0	1
Done	1	0	1
Total	66	8	74

Merged error: 0.1b

Counts

74 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (- (sqrt (+ x 1.0))) (sqrt x))
0.1b	(/ (/ 1.0 (* (sqrt (+ x 1.0)) (sqrt x))) (- (- (sqrt (+ x 1.0))) (sqrt x)))
0.2b	(/ 1.0 (* (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(* (sqrt (+ x 1.0)) (sqrt x))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

6×	`sqrt-div` `associate-*l/` `associate-/r/`
5×	`associate-/l/`
4×	`associate-/r*`
3×	`frac-2neg` `flip3-+` `clear-num` `-commutative` `flip-+` `div-inv` `associate-/l`
2×	`flip3--` `pow1/2` `flip--`
1×	`associate--l-` `neg-sub0` `sub-neg` `sqrt-unprod` `pow-prod-down`

Counts

4 → 30

Calls

4 calls:

7.0ms	(- (- (sqrt (+ x 1.0))) (sqrt x))
14.0ms	(/ (/ 1.0 (* (sqrt (+ x 1.0)) (sqrt x))) (- (- (sqrt (+ x 1.0))) (sqrt x)))
7.0ms	(/ 1.0 (* (sqrt (+ x 1.0)) (sqrt x)))
7.0ms	(* (sqrt (+ x 1.0)) (sqrt x))

series743.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(- (- (sqrt (+ x 1.0))) (sqrt x))
507.0ms	(/ (/ 1.0 (* (sqrt (+ x 1.0)) (sqrt x))) (- (- (sqrt (+ x 1.0))) (sqrt x)))
90.0ms	(/ 1.0 (* (sqrt (+ x 1.0)) (sqrt x)))
63.0ms	(* (sqrt (+ x 1.0)) (sqrt x))

simplify38.0ms

Algorithm

egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	412	399
1	1408	346
2	5002	317

prune124.0ms

Filtered

42 candidates to 37 candidates (88.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	40	2	42
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	42	8	50

Merged error: 0.1b

Counts

50 → 8

regimes39.0ms

Accuracy

0% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 0.8b

bsearch0.0ms

simplify8.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	33
1	47	33
2	51	33
3	76	33
4	99	33
5	108	33
6	126	33
7	136	33
8	145	33
9	154	33
10	162	33
11	170	33
12	177	33
13	179	33
14	187	33
15	187	33

end0.0ms

sample854.0ms

Algorithm

intervals

Results

183.0ms	1867×	body	640	valid
182.0ms	7959×	body	80	nan
145.0ms	1126×	body	1280	valid
107.0ms	4097×	body	80	valid
42.0ms	595×	body	320	valid
15.0ms	315×	body	160	valid

Iter	Nodes	Cost
0	35	33
1	47	33
2	51	33
3	76	33
4	99	33
5	108	33
6	126	33
7	136	33
8	145	33
9	154	33
10	162	33
11	170	33
12	177	33
13	179	33
14	187	33
15	187	33

Iter	Nodes	Cost
0	35	33
1	47	33
2	51	33
3	76	33
4	99	33
5	108	33
6	126	33
7	136	33
8	145	33
9	154	33
10	162	33
11	170	33
12	177	33
13	179	33
14	187	33
15	187	33

Iter	Nodes	Cost
0	35	33
1	47	33
2	51	33
3	76	33
4	99	33
5	108	33
6	126	33
7	136	33
8	145	33
9	154	33
10	162	33
11	170	33
12	177	33
13	179	33
14	187	33
15	187	33