Details

analyze2.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

sample26.0ms

Algorithm

intervals

Results

9.0ms	66×	body	1280	valid
7.0ms	33×	body	640	valid
3.0ms	133×	body	80	valid
1.0ms	13×	body	320	valid
1.0ms	11×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	71	7
1	71	7

prune2.0ms

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: 29.3b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
3.3b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-log-exp` `difference-of-squares`
3×	`pow1` `add-cube-cbrt` `distribute-lft-out--`
2×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `distribute-lft-out`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip--` `flip-+`

Counts

2 → 34

Calls

2 calls:

3.0ms	(sqrt (+ x 1.0))
8.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series13.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(sqrt (+ x 1.0))
9.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify46.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4975	520
1	4975	520

prune67.0ms

Filtered

30 candidates to 40 candidates (-33.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	38	2	40
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	38	3	41

Merged error: 0.1b

Counts

41 → 3

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.1b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

52×	`*-un-lft-identity`
24×	`sqrt-prod`
21×	`distribute-lft-out`
18×	`times-frac`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
6×	`associate-/r*`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`sqrt-div` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 71

Calls

3 calls:

3.0ms	(sqrt (+ x 1.0))
7.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
11.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series18.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(sqrt (+ x 1.0))
6.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
9.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify26.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5038	1051

prune139.0ms

Filtered

59 candidates to 80 candidates (-35.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	73	7	80
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	74	9	83

Merged error: 0.0b

Counts

83 → 9

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite82.0ms

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:

10.0ms	(sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x))))
10.0ms	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
12.0ms	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
35.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))))

series71.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x))))
14.0ms	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
9.0ms	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
12.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))))

simplify96.0ms

Algorithm

egg-herbie

Counts

262 → 262

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4952	4249
1	4952	4249

prune447.0ms

Filtered

140 candidates to 262 candidates (-87.1%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	261	1	262
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	262	9	271

Merged error: 0.0b

Counts

271 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite95.0ms

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:

11.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
8.0ms	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
12.0ms	(/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))
29.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series65.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
10.0ms	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
26.0ms	(/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))
18.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify127.0ms

Algorithm

egg-herbie

Counts

457 → 457

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5073	11200

prune517.0ms

Filtered

149 candidates to 457 candidates (-206.7%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	456	1	457
Fresh	1	4	5
Picked	0	1	1
Done	0	3	3
Total	457	9	466

Merged error: 0.0b

Counts

466 → 9

regimes99.0ms

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	9
1	9	9

end0.0ms

sample592.0ms

Algorithm

intervals

Results

217.0ms	1722×	body	1280	valid
121.0ms	1270×	body	640	valid
107.0ms	4096×	body	80	valid
44.0ms	618×	body	320	valid
14.0ms	294×	body	160	valid
0.0ms	2×	body	80	nan

Details

analyze2.0ms

sample26.0ms

simplify5.0ms

prune2.0ms

localize5.0ms

rewrite12.0ms

series13.0ms

simplify46.0ms

prune67.0ms

localize6.0ms

rewrite24.0ms

series18.0ms

simplify26.0ms

prune139.0ms

localize9.0ms

rewrite82.0ms

series71.0ms

simplify96.0ms

prune447.0ms

localize13.0ms

rewrite95.0ms

series65.0ms

simplify127.0ms

prune517.0ms

regimes99.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample592.0ms

Profiling