Details

sample25.0ms

Algorithm

intervals

Results

4.0ms	247×	body	80	nan
4.0ms	47×	body	1280	valid
3.0ms	39×	body	640	valid
2.0ms	134×	body	80	valid
1.0ms	21×	body	320	valid
1.0ms	15×	body	160	valid

simplify5.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 29.1b

Counts

2 → 1

localize5.0ms

Local error

Found 1 expressions with local error:

4.5b	(- (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))

series74.0ms

Counts

1 → 3

Calls

1 calls:

74.0ms

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

simplify48.0ms

Algorithm

egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 3 (45.0ms)

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

prune43.0ms

Filtered

22 candidates to 14 candidates (63.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	19	3	22
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	20	3	23

Merged error: 0.2b

Counts

23 → 3

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)))

rewrite19.0ms

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))
10.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series206.0ms

Counts

2 → 6

Calls

2 calls:

64.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
142.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify38.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 2 (31.0ms)

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

prune115.0ms

Filtered

61 candidates to 39 candidates (63.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	55	6	61
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	56	8	64

Merged error: 0.0b

Counts

64 → 8

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)))
0.2b	(/ 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))))

rewrite103.0ms

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))))
32.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series808.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
164.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
343.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
142.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify143.0ms

Algorithm

egg-herbie

Counts

457 → 457

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	1033	8864
1	4120	7704
2	5001	7681

prune504.0ms

Filtered

457 candidates to 146 candidates (31.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	450	7	457
Fresh	5	1	6
Picked	1	0	1
Done	0	1	1
Total	456	9	465

Merged error: 0.0b

Counts

465 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

21584×	`sqrt-prod`
15024×	`*-un-lft-identity`
14958×	`times-frac`
5512×	`distribute-lft-out`
5380×	`add-sqr-sqrt`
5378×	`add-cube-cbrt`
586×	`sqrt-div`
555×	`associate-/l*`
292×	`associate-/r/`
147×	`flip3-+` `flip-+`
146×	`div-inv`
33×	`associate-/r*`
20×	`add-exp-log` `add-cbrt-cube`
10×	`cbrt-undiv` `div-exp`
6×	`pow1`
4×	`sqrt-pow1` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`rem-sqrt-square` `pow1/2` `associate-/l/`

Counts

4 → 5792

Calls

4 calls:

9.0ms	(sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
13.0ms	(/ 1.0 (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
198.0ms	(/ (/ (/ 1.0 (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
41.0ms	(/ (/ 1.0 (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))

series1.5s

Counts

4 → 12

Calls

4 calls:

333.0ms	(sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
445.0ms	(/ 1.0 (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
146.0ms	(/ (/ (/ 1.0 (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
564.0ms	(/ (/ 1.0 (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify1.7s

Algorithm

egg-herbie

Counts

5804 → 5804

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5001	220216

prune8.1s

Filtered

5804 candidates to 1919 candidates (33.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	5803	1	5804
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	5803	10	5813

Merged error: 0b

Counts

5813 → 10

regimes83.0ms

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

sample664.0ms

Algorithm

intervals

Results

148.0ms	1743×	body	1280	valid
138.0ms	8133×	body	80	nan
82.0ms	1238×	body	640	valid
76.0ms	4096×	body	80	valid
32.0ms	612×	body	320	valid
10.0ms	311×	body	160	valid