Details

sample24.0ms

Algorithm

intervals

Results

4.0ms	56×	body	1280	valid
4.0ms	233×	body	80	nan
3.0ms	42×	body	640	valid
2.0ms	131×	body	80	valid
1.0ms	18×	body	320	valid
0.0ms	9×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.0b

localize5.0ms

Local error

Found 1 expressions with local error:

2.2b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `sqrt-prod`
4×	`difference-of-squares`
3×	`distribute-lft-out--` `add-log-exp`
1×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out`

Counts

1 → 19

Calls

1 calls:

44.0ms

(- (sqrt (+ x 1.0)) (sqrt x))

series62.0ms

Counts

1 → 3

Calls

1 calls:

62.0ms

(- (sqrt (+ x 1.0)) (sqrt x))

simplify51.0ms

Algorithm

egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 3 (44.0ms)

Iter	Nodes	Cost
0	132	175
1	400	159
2	1559	153
3	5001	149

prune39.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 1 expressions with local error:

0.1b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 41

Calls

1 calls:

46.0ms

(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series133.0ms

Counts

1 → 3

Calls

1 calls:

133.0ms

(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify32.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	249	412
1	918	375
2	5001	348

prune85.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.1b	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

rewrite292.0ms

Algorithm

rewrite-expression-head

Rules

742×	`*-un-lft-identity`
700×	`sqrt-prod`
594×	`times-frac`
280×	`distribute-lft-out`
254×	`add-sqr-sqrt`
252×	`add-cube-cbrt`
36×	`associate-/l*`
28×	`sqrt-div`
24×	`associate-/r/`
18×	`associate-/r*`
14×	`flip3-+` `flip-+`
12×	`div-inv`
11×	`add-exp-log` `add-cbrt-cube`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`
1×	`associate-/l/`

Counts

4 → 445

Calls

4 calls:

39.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
40.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
46.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
127.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series753.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
153.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
309.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
138.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify136.0ms

Algorithm

egg-herbie

Counts

457 → 457

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	1033	8862
1	4120	7704
2	5001	7681

prune555.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b	(/ (sqrt (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (/ (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))))
0.2b	(/ (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))))

rewrite3.5s

Algorithm

rewrite-expression-head

Rules

56169×	`sqrt-prod`
42381×	`times-frac`
38028×	`*-un-lft-identity`
14256×	`add-sqr-sqrt` `add-cube-cbrt`
13584×	`distribute-lft-out`
1391×	`sqrt-div`
1389×	`associate-/r/`
714×	`div-inv`
676×	`flip3-+` `flip-+`
383×	`associate-/r*`
51×	`associate-/l*`
15×	`add-exp-log` `add-cbrt-cube`
6×	`cbrt-undiv` `div-exp`
4×	`pow1` `frac-2neg` `clear-num` `add-log-exp`
3×	`sqrt-undiv` `associate-/l/`

Counts

4 → 12717

Calls

4 calls:

46.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
47.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
490.0ms	(/ (sqrt (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (/ (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))))
123.0ms	(/ (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))))

series1.2s

Counts

4 → 12

Calls

4 calls:

311.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
314.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
157.0ms	(/ (sqrt (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (/ (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))))
452.0ms	(/ (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))))

simplify4.5s

Algorithm

egg-herbie

Counts

12729 → 12729

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	6268	572364

prune27.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes37.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	5
1	9	5

end0.0ms

sample688.0ms

Algorithm

intervals

Results

139.0ms	8007×	body	80	nan
139.0ms	1741×	body	1280	valid
78.0ms	1258×	body	640	valid
74.0ms	4058×	body	80	valid
30.0ms	638×	body	320	valid
10.0ms	305×	body	160	valid