Details

sample24.0ms

Algorithm

intervals

Results

5.0ms	60×	body	1280	valid
4.0ms	243×	body	80	nan
3.0ms	139×	body	80	valid
2.0ms	36×	body	640	valid
1.0ms	15×	body	320	valid
0.0ms	6×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 28.2b

localize5.0ms

Local error

Found 1 expressions with local error:

1.7b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite22.0ms

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:

22.0ms

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

series77.0ms

Counts

1 → 3

Calls

1 calls:

76.0ms

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

simplify50.0ms

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

prune50.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite46.0ms

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:

17.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
28.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series216.0ms

Counts

2 → 6

Calls

2 calls:

66.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
150.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify41.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 2 (34.0ms)

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

prune140.0ms

Pruning

10 alts after pruning (9 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))))

rewrite186.0ms

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:

22.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
24.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
25.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
75.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series834.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
169.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
348.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
146.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify135.0ms

Algorithm

egg-herbie

Counts

457 → 457

Iterations

Useful iterations: 2 (65.0ms)

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

prune792.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize11.0ms

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 (pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 1))
0.2b	(/ (/ 1.0 (pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 1)) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

rewrite258.0ms

Algorithm

rewrite-expression-head

Rules

910×	`*-un-lft-identity`
816×	`times-frac`
800×	`sqrt-prod`
352×	`add-sqr-sqrt`
350×	`add-cube-cbrt`
320×	`distribute-lft-out`
306×	`unpow-prod-down`
46×	`associate-/l*`
34×	`sqr-pow`
22×	`associate-/r*`
19×	`add-exp-log`
12×	`div-inv`
11×	`add-cbrt-cube`
10×	`div-exp`
6×	`pow1` `sqrt-div`
4×	`cbrt-undiv` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`pow-to-exp` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-exp` `clear-num` `associate-/r/`
1×	`associate-/l/`

Counts

4 → 563

Calls

4 calls:

24.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
22.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
51.0ms	(/ 1.0 (pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 1))
113.0ms	(/ (/ 1.0 (pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 1)) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series803.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
161.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
328.0ms	(/ 1.0 (pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 1))
149.0ms	(/ (/ 1.0 (pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 1)) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify121.0ms

Algorithm

egg-herbie

Counts

575 → 575

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1371	12135
1	5002	9781

prune612.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

regimes46.0ms

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

sample661.0ms

Algorithm

intervals

Results

149.0ms	1762×	body	1280	valid
145.0ms	8106×	body	80	nan
77.0ms	1184×	body	640	valid
75.0ms	4134×	body	80	valid
34.0ms	586×	body	320	valid
11.0ms	334×	body	160	valid