Details

sample25.0ms

Algorithm

intervals

Results

5.0ms	65×	body	1280	valid
4.0ms	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

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: 32.4b

localize5.0ms

Local error

Found 2 expressions with local error:

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

rewrite27.0ms

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))
22.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series103.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(sqrt (+ x 1.0))
73.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify63.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 3 (53.0ms)

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

localize6.0ms

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)))

rewrite49.0ms

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

series251.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(sqrt (+ x 1.0))
71.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
143.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify44.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (37.0ms)

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

prune176.0ms

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))))

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)))
25.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
25.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
76.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series828.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
173.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
335.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
139.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify137.0ms

Algorithm

egg-herbie

Counts

457 → 457

Iterations

Useful iterations: 2 (64.0ms)

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

prune573.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize9.0ms

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

rewrite182.0ms

Algorithm

rewrite-expression-head

Rules

2446×	`times-frac`
1949×	`*-un-lft-identity`
1343×	`sqrt-prod`
975×	`add-sqr-sqrt`
974×	`add-cube-cbrt`
557×	`distribute-lft-out`
65×	`div-inv`
40×	`associate-/r*`
22×	`associate-/l*`
20×	`add-exp-log`
15×	`add-cbrt-cube`
13×	`div-exp`
8×	`cbrt-undiv`
5×	`add-log-exp`
4×	`pow1`
2×	`flip3-+` `sqrt-div` `1-exp` `flip-+`
1×	`+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `sum-log` `associate-/r/` `associate-/l/`

Counts

3 → 994

Calls

3 calls:

4.0ms	(sqrt (+ x 1.0))
17.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
55.0ms	(/ (/ (sqrt 1.0) 1) (/ (+ (sqrt (+ x 1.0)) (sqrt x)) (sqrt 1.0)))

series279.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(sqrt (+ x 1.0))
70.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
178.0ms	(/ (/ (sqrt 1.0) 1) (/ (+ (sqrt (+ x 1.0)) (sqrt x)) (sqrt 1.0)))

simplify202.0ms

Algorithm

egg-herbie

Counts

1003 → 1003

Iterations

Useful iterations: 1 (51.0ms)

Iter	Nodes	Cost
0	2666	19020
1	5002	16999

prune774.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes39.0ms

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	15	9
1	15	9

end0.0ms

sample677.0ms

Algorithm

intervals

Results

150.0ms	1747×	body	1280	valid
142.0ms	7958×	body	80	nan
89.0ms	1295×	body	640	valid
78.0ms	4026×	body	80	valid
32.0ms	652×	body	320	valid
10.0ms	280×	body	160	valid