Details

sample23.0ms

Algorithm

intervals

Results

4.0ms	55×	body	1280	valid
4.0ms	272×	body	80	nan
3.0ms	46×	body	640	valid
2.0ms	125×	body	80	valid
1.0ms	19×	body	320	valid
0.0ms	11×	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: 31.1b

Counts

2 → 1

localize5.0ms

Local error

Found 1 expressions with local error:

2.9b	(- (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))

simplify48.0ms

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

prune46.0ms

Filtered

22 candidates to 14 candidates (63.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	18	4	22
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	19	4	23

Merged error: 0.2b

Counts

23 → 4

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)))

rewrite18.0ms

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

series209.0ms

Counts

2 → 6

Calls

2 calls:

68.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
140.0ms	(/ 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

prune131.0ms

Filtered

61 candidates to 39 candidates (63.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	52	9	61
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	54	11	65

Merged error: 0.0b

Counts

65 → 11

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))))

rewrite100.0ms

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:

7.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
8.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
10.0ms	(/ 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))))

series787.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
160.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
327.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
141.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify141.0ms

Algorithm

egg-herbie

Counts

457 → 457

Iterations

Useful iterations: 2 (68.0ms)

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

prune554.0ms

Filtered

457 candidates to 145 candidates (31.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	448	9	457
Fresh	9	0	9
Picked	1	0	1
Done	0	1	1
Total	458	10	468

Merged error: 0b

Counts

468 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

300×	`sqrt-prod`
292×	`sqrt-div`
234×	`*-un-lft-identity`
168×	`times-frac`
102×	`add-sqr-sqrt`
92×	`distribute-lft-out`
90×	`associate-/r/`
74×	`flip3-+` `flip-+`
71×	`add-cube-cbrt`
48×	`frac-times`
33×	`sqrt-pow1`
28×	`pow1`
24×	`associate-r/` `associate-l/`
22×	`swap-sqr`
20×	`add-exp-log` `add-cbrt-cube`
18×	`associate-/l*`
17×	`pow1/2`
12×	`associate-r` `associate-l` `div-inv`
10×	`associate-/r*`
9×	`pow-prod-up` `unswap-sqr`
7×	`cbrt-undiv` `div-exp`
5×	`pow-prod-down` `pow-sqr`
4×	`add-log-exp`
3×	`prod-exp` `cbrt-unprod`
2×	`frac-2neg` `clear-num`
1×	`pow2` `rem-sqrt-square` `pow-plus` `sqrt-unprod` `rem-square-sqrt` `*-commutative` `associate-/l/`

Counts

4 → 321

Calls

4 calls:

10.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
23.0ms	(/ 1.0 (* (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))))
35.0ms	(/ (/ 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))))
28.0ms	(* (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))

series791.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
325.0ms	(/ 1.0 (* (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))))
141.0ms	(/ (/ 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))))
162.0ms	(* (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify94.0ms

Algorithm

egg-herbie

Counts

333 → 333

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1016	7831
1	5002	6864

prune625.0ms

Filtered

333 candidates to 148 candidates (44.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	330	3	333
Fresh	4	4	8
Picked	0	1	1
Done	0	1	1
Total	334	9	343

Merged error: 0b

Counts

343 → 9

regimes38.0ms

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

sample626.0ms

Algorithm

intervals

Results

139.0ms	1658×	body	1280	valid
125.0ms	8076×	body	80	nan
82.0ms	1241×	body	640	valid
73.0ms	4128×	body	80	valid
31.0ms	636×	body	320	valid
11.0ms	337×	body	160	valid