Details

sample25.0ms

Algorithm

intervals

Results

4.0ms	49×	body	1280	valid
4.0ms	233×	body	80	nan
3.0ms	37×	body	640	valid
2.0ms	130×	body	80	valid
1.0ms	23×	body	320	valid
1.0ms	17×	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: 29.5b

localize7.0ms

Local error

Found 1 expressions with local error:

3.7b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite9.0ms

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:

8.0ms

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

series67.0ms

Counts

1 → 3

Calls

1 calls:

67.0ms

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

simplify53.0ms

Algorithm

egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 3 (46.0ms)

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

prune43.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.1b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 55

Calls

2 calls:

7.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
12.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series202.0ms

Counts

2 → 6

Calls

2 calls:

66.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
136.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify36.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	295	535
1	1077	482
2	5001	453

prune124.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.0b	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.1b	(/ 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))))

rewrite92.0ms

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:

8.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
8.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
11.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
28.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series798.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
162.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
332.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
144.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify138.0ms

Algorithm

egg-herbie

Counts

457 → 457

Iterations

Useful iterations: 2 (63.0ms)

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

prune608.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite3.2s

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:

19.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
11.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
30.0ms	(/ (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))))
335.0ms	(/ (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)))))))

series1.3s

Counts

4 → 12

Calls

4 calls:

334.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
336.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
488.0ms	(/ (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))))
167.0ms	(/ (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)))))))

simplify5.0s

Algorithm

egg-herbie

Counts

12729 → 12729

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	6268	571651

prune25.0s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes42.0ms

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

sample677.0ms

Algorithm

intervals

Results

151.0ms	1696×	body	1280	valid
134.0ms	8115×	body	80	nan
84.0ms	1203×	body	640	valid
81.0ms	4149×	body	80	valid
33.0ms	607×	body	320	valid
12.0ms	345×	body	160	valid