Details

sample26.0ms

Algorithm

intervals

Results

6.0ms	65×	body	1280	valid
5.0ms	256×	body	80	nan
3.0ms	47×	body	640	valid
2.0ms	120×	body	80	valid
1.0ms	14×	body	320	valid
0.0ms	10×	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: 32.4b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
2.8b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-log-exp` `difference-of-squares`
3×	`pow1` `add-cube-cbrt` `distribute-lft-out--`
2×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `distribute-lft-out`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip--` `flip-+`

Counts

2 → 35

Calls

2 calls:

4.0ms	(sqrt (+ x 1.0))
21.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series102.0ms

Counts

2 → 6

Calls

2 calls:

32.0ms	(sqrt (+ x 1.0))
70.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify60.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 3 (56.0ms)

Iter	Nodes	Cost
0	182	265
1	544	243
2	2020	233
3	5002	230

prune82.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize7.0ms

Local error

Found 3 expressions with local error:

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

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

52×	`*-un-lft-identity`
24×	`sqrt-prod`
21×	`distribute-lft-out`
18×	`times-frac`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
6×	`associate-/r*`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`sqrt-div` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 71

Calls

3 calls:

4.0ms	(sqrt (+ x 1.0))
19.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
23.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series236.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(sqrt (+ x 1.0))
60.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
141.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify39.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	341	624
1	1239	566
2	5001	533

prune171.0ms

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)))
0.1b	(/ 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))))

rewrite182.0ms

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)))
24.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
72.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series800.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
163.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
332.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
141.0ms	(/ (/ 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 (66.0ms)

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

prune583.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.2b	(/ (/ (sqrt 1.0) (sqrt (sqrt 1))) (/ (+ (sqrt (+ x 1.0)) (sqrt x)) (sqrt 1.0)))

rewrite448.0ms

Algorithm

rewrite-expression-head

Rules

6658×	`times-frac`
5807×	`sqrt-prod`
5129×	`*-un-lft-identity`
2643×	`add-sqr-sqrt`
2642×	`add-cube-cbrt`
1421×	`distribute-lft-out`
101×	`div-inv`
58×	`associate-/l*`
40×	`associate-/r*`
15×	`add-exp-log` `add-cbrt-cube`
8×	`cbrt-undiv` `div-exp`
5×	`add-log-exp`
4×	`pow1`
2×	`flip3-+` `sqrt-div` `flip-+`
1×	`+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `sum-log` `associate-/r/` `associate-/l/`

Counts

3 → 2468

Calls

3 calls:

4.0ms	(sqrt (+ x 1.0))
16.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
93.0ms	(/ (/ (sqrt 1.0) (sqrt (sqrt 1))) (/ (+ (sqrt (+ x 1.0)) (sqrt x)) (sqrt 1.0)))

series267.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(sqrt (+ x 1.0))
60.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
172.0ms	(/ (/ (sqrt 1.0) (sqrt (sqrt 1))) (/ (+ (sqrt (+ x 1.0)) (sqrt x)) (sqrt 1.0)))

simplify520.0ms

Algorithm

egg-herbie

Counts

2477 → 2477

Iterations

Useful iterations: 1 (91.0ms)

Iter	Nodes	Cost
0	4717	60347
1	5002	51594

prune1.7s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes41.0ms

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	17	11
1	17	11

end0.0ms

sample686.0ms

Algorithm

intervals

Results

156.0ms	1747×	body	1280	valid
145.0ms	7958×	body	80	nan
91.0ms	1295×	body	640	valid
78.0ms	4026×	body	80	valid
37.0ms	652×	body	320	valid
10.0ms	280×	body	160	valid