Details

sample34.0ms

Algorithm

intervals

Results

7.0ms	58×	body	1280	valid
7.0ms	45×	body	640	valid
6.0ms	230×	body	80	nan
3.0ms	124×	body	80	valid
1.0ms	16×	body	320	valid
1.0ms	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: 31.8b

Counts

2 → 1

localize5.0ms

Local error

Found 1 expressions with local error:

3.6b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite8.0ms

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))

simplify47.0ms

Algorithm

egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 3 (44.0ms)

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

prune37.0ms

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))
12.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series202.0ms

Counts

2 → 6

Calls

2 calls:

66.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
136.0ms	(/ 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

prune113.0ms

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

localize8.0ms

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)))))

rewrite81.0ms

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:

9.0ms	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
9.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
9.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
37.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

series801.0ms

Counts

4 → 12

Calls

4 calls:

345.0ms	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
143.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
144.0ms	(/ 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)))))

simplify113.0ms

Algorithm

egg-herbie

Counts

262 → 262

Iterations

Useful iterations: 2 (79.0ms)

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

prune430.0ms

Filtered

262 candidates to 136 candidates (51.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	257	5	262
Fresh	4	2	6
Picked	1	0	1
Done	0	1	1
Total	262	8	270

Merged error: 0.0b

Counts

270 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.1b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(* (pow (sqrt (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))) 3) (sqrt (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))))
0.4b	(pow (sqrt (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))) 3)

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

437×	`sqrt-prod`
249×	`*-un-lft-identity`
182×	`add-sqr-sqrt`
144×	`times-frac`
92×	`distribute-lft-out`
88×	`add-cube-cbrt`
76×	`unpow-prod-down` `cube-prod`
66×	`associate-l`
40×	`unswap-sqr`
30×	`associate-r`
14×	`add-exp-log` `associate-/r/`
12×	`associate-/r*`
11×	`add-cbrt-cube`
10×	`sqrt-div`
8×	`pow1`
7×	`flip3-+` `flip-+` `div-inv`
6×	`associate-/l*` `sqr-pow`
5×	`pow-pow`
4×	`sqrt-pow1` `add-log-exp`
3×	`cube-div` `pow-unpow` `prod-exp`
2×	`cbrt-undiv` `cube-mult` `pow-to-exp` `frac-2neg` `pow1/2` `unpow3` `div-exp` `pow-exp` `clear-num`
1×	`frac-times` `pow-plus` `associate-r/` `associate-l/` `*-commutative` `pow-prod-up` `sqrt-pow2` `cbrt-unprod` `rem-cube-cbrt`

Counts

4 → 318

Calls

4 calls:

9.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
12.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
53.0ms	(* (pow (sqrt (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))) 3) (sqrt (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))))
19.0ms	(pow (sqrt (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))) 3)

series1.3s

Counts

4 → 12

Calls

4 calls:

145.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
139.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
168.0ms	(* (pow (sqrt (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))) 3) (sqrt (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))))
833.0ms	(pow (sqrt (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))) 3)

simplify150.0ms

Algorithm

egg-herbie

Counts

330 → 330

Iterations

Useful iterations: 2 (101.0ms)

Iter	Nodes	Cost
0	952	4971
1	4242	4523
2	5001	4248

prune571.0ms

Filtered

330 candidates to 142 candidates (43.0%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	328	2	330
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	329	9	338

Merged error: 0b

Counts

338 → 9

regimes42.0ms

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

sample922.0ms

Algorithm

intervals

Results

226.0ms	1744×	body	1280	valid
211.0ms	8056×	body	80	nan
123.0ms	1248×	body	640	valid
112.0ms	4118×	body	80	valid
46.0ms	596×	body	320	valid
14.0ms	294×	body	160	valid