Details

sample25.0ms

Algorithm

intervals

Results

5.0ms	59×	body	1280	valid
4.0ms	229×	body	80	nan
3.0ms	127×	body	80	valid
2.0ms	36×	body	640	valid
1.0ms	21×	body	320	valid
0.0ms	13×	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

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: 30.9b

Counts

2 → 1

localize8.0ms

Local error

Found 1 expressions with local error:

4.9b	(- (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))

series70.0ms

Counts

1 → 3

Calls

1 calls:

70.0ms

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

simplify54.0ms

Algorithm

egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 3 (47.0ms)

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

prune42.0ms

Filtered

22 candidates to 14 candidates (63.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	20	2	22
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	21	2	23

Merged error: 0.1b

Counts

23 → 2

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))
13.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series203.0ms

Counts

2 → 6

Calls

2 calls:

66.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
137.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify39.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 2 (32.0ms)

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

prune130.0ms

Filtered

61 candidates to 39 candidates (63.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	54	7	61
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	55	8	63

Merged error: 0.0b

Counts

63 → 8

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
0.1b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.1b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.3b	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

297×	`*-un-lft-identity`
274×	`sqrt-prod`
157×	`times-frac`
119×	`add-sqr-sqrt`
116×	`distribute-lft-out`
88×	`add-cube-cbrt`
41×	`swap-sqr`
27×	`associate-r` `associate-l`
20×	`pow1`
14×	`associate-/r/`
12×	`associate-/r*`
10×	`add-exp-log` `add-cbrt-cube`
9×	`sqrt-pow1` `pow1/2` `unswap-sqr`
7×	`flip3-+` `flip-+` `div-inv`
6×	`associate-/l*`
5×	`sqrt-div` `pow-prod-up`
4×	`add-log-exp`
3×	`pow-prod-down` `pow-sqr`
2×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `div-exp` `clear-num`
1×	`pow2` `frac-times` `pow-plus` `sqrt-unprod` `associate-r/` `associate-l/` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 250

Calls

4 calls:

13.0ms	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
10.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
10.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
35.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

series813.0ms

Counts

4 → 12

Calls

4 calls:

355.0ms	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
148.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
140.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
169.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify118.0ms

Algorithm

egg-herbie

Counts

262 → 262

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	647	2845
1	3152	2529
2	5002	2489

prune523.0ms

Filtered

262 candidates to 135 candidates (51.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	256	6	262
Fresh	6	0	6
Picked	0	1	1
Done	0	1	1
Total	262	8	270

Merged error: 0.0b

Counts

270 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

100×	`*-un-lft-identity`
82×	`sqrt-prod`
46×	`times-frac`
40×	`distribute-lft-out`
34×	`add-sqr-sqrt`
30×	`add-cube-cbrt`
15×	`associate-/r*`
11×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `sqrt-div` `associate-/r/`
4×	`flip3-+` `flip-+` `associate-/l*` `add-log-exp`
3×	`cbrt-undiv` `rem-sqrt-square` `div-exp` `div-inv`
2×	`frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`
1×	`sqrt-undiv` `sqrt-unprod` `associate-*l/` `prod-exp` `cbrt-unprod` `associate-/l/`

Counts

4 → 132

Calls

4 calls:

11.0ms	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
8.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
10.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
27.0ms	(/ (* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt 1.0)) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series851.0ms

Counts

4 → 12

Calls

4 calls:

361.0ms	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
169.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
148.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
172.0ms	(/ (* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt 1.0)) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify82.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	693	1805
1	2963	1644
2	5001	1576

prune365.0ms

Filtered

144 candidates to 89 candidates (61.8%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	141	3	144
Fresh	2	3	5
Picked	0	1	1
Done	0	2	2
Total	143	9	152

Merged error: 0.0b

Counts

152 → 9

regimes43.0ms

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

sample681.0ms

Algorithm

intervals

Results

152.0ms	1742×	body	1280	valid
130.0ms	7833×	body	80	nan
93.0ms	1315×	body	640	valid
81.0ms	4034×	body	80	valid
31.0ms	591×	body	320	valid
11.0ms	318×	body	160	valid