Details

sample27.0ms

Algorithm

intervals

Results

7.0ms	47×	body	1280	valid
5.0ms	276×	body	80	nan
3.0ms	155×	body	80	valid
2.0ms	22×	body	640	valid
1.0ms	21×	body	320	valid
0.0ms	11×	body	160	valid

simplify6.0ms

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: 23.8b

localize5.0ms

Local error

Found 1 expressions with local error:

3.0b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite22.0ms

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:

22.0ms

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

series76.0ms

Counts

1 → 3

Calls

1 calls:

76.0ms

(- (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

prune48.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

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)))

rewrite41.0ms

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:

16.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
23.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series219.0ms

Counts

2 → 6

Calls

2 calls:

70.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
148.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify35.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 2 (29.0ms)

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

prune129.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

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

rewrite216.0ms

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:

26.0ms	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
23.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
25.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
124.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

series824.0ms

Counts

4 → 12

Calls

4 calls:

356.0ms	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
149.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
142.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
177.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify109.0ms

Algorithm

egg-herbie

Counts

262 → 262

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	647	2850
1	3301	2529
2	5001	2489

prune524.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize8.0ms

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)))
0.2b	(/ 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))))

rewrite183.0ms

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:

21.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
22.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
27.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
74.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series839.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
170.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
345.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
154.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify135.0ms

Algorithm

egg-herbie

Counts

457 → 457

Iterations

Useful iterations: 2 (65.0ms)

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

prune556.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes38.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	13
1	11	13

end0.0ms

sample693.0ms

Algorithm

intervals

Results

159.0ms	1749×	body	1280	valid
146.0ms	8072×	body	80	nan
85.0ms	1145×	body	640	valid
83.0ms	4152×	body	80	valid
34.0ms	655×	body	320	valid
11.0ms	299×	body	160	valid