Details

sample27.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 49.996948%

Guaranteed chance to sample good point: 99.993897%

Results

6.0ms	47×	body	1280	valid
6.0ms	57×	body	640	valid
3.0ms	116×	body	80	valid
2.0ms	27×	body	320	valid
0.0ms	9×	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

prune3.0ms

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: 33.5b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
3.8b	(- (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 → 35

Calls

2 calls:

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

series17.0ms

Counts

2 → 6

Calls

2 calls:

7.0ms	(sqrt (+ x 1.0))
10.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify35.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	282	318
1	1037	308
2	5001	297

prune81.0ms

Filtered

31 candidates to 41 candidates (-32.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	36	5	41
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	37	5	42

Merged error: 0.2b

Counts

42 → 5

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 80

Calls

3 calls:

3.0ms	(sqrt (+ x 1.0))
7.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
12.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series21.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(sqrt (+ x 1.0))
5.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
12.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify68.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	514	800
1	2206	753
2	5001	721

prune156.0ms

Filtered

59 candidates to 89 candidates (-50.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	82	7	89
Fresh	4	0	4
Picked	0	1	1
Done	0	0	0
Total	86	8	94

Merged error: 0.0b

Counts

94 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.3b	(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

597×	`*-un-lft-identity`
420×	`sqrt-prod`
256×	`distribute-lft-out`
247×	`times-frac`
130×	`add-sqr-sqrt`
99×	`add-cube-cbrt`
71×	`swap-sqr`
33×	`associate-r` `associate-l`
20×	`pow1`
14×	`associate-/r/`
12×	`associate-/r*`
10×	`add-exp-log` `add-cbrt-cube`
9×	`sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `unswap-sqr`
8×	`associate-/l*`
7×	`div-inv`
5×	`sqrt-div` `pow-prod-up`
4×	`associate-/l/` `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 → 316

Calls

4 calls:

12.0ms	(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
12.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
12.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
45.0ms	(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))

series51.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
9.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
9.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
12.0ms	(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify167.0ms

Algorithm

egg-herbie

Counts

328 → 328

Iterations

Useful iterations: 2 (128.0ms)

Iter	Nodes	Cost
0	827	3986
1	4668	3471
2	5002	3447

prune605.0ms

Filtered

151 candidates to 328 candidates (-117.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	324	4	328
Fresh	3	3	6
Picked	1	0	1
Done	0	1	1
Total	328	8	336

Merged error: 0.0b

Counts

336 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
0.1b	(sqrt (pow (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) 4))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.5b	(pow (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) 4)

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

222×	`*-un-lft-identity`
197×	`sqrt-prod`
98×	`times-frac`
93×	`distribute-lft-out`
69×	`unpow-prod-down`
61×	`add-sqr-sqrt`
53×	`add-cube-cbrt`
8×	`associate-/r/`
7×	`pow1` `add-exp-log` `rem-sqrt-square`
6×	`associate-/r*` `add-cbrt-cube`
5×	`flip3-+` `flip-+`
4×	`div-inv` `associate-/l*` `add-log-exp`
3×	`pow-unpow` `pow-pow` `sqrt-pow1` `pow1/2` `sqr-pow`
2×	`associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `sqrt-div` `div-exp` `pow-exp` `clear-num` `sqrt-pow2`

Counts

4 → 193

Calls

4 calls:

12.0ms	(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
20.0ms	(sqrt (pow (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) 4))
12.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
15.0ms	(pow (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) 4)

series82.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
12.0ms	(sqrt (pow (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) 4))
13.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
36.0ms	(pow (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) 4)

simplify134.0ms

Algorithm

egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 2 (107.0ms)

Iter	Nodes	Cost
0	1021	2939
1	4574	2581
2	5001	2479

prune388.0ms

Filtered

116 candidates to 205 candidates (-76.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	204	1	205
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	205	8	213

Merged error: 0.0b

Counts

213 → 8

regimes55.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	6
1	16	6
2	16	6

end0.0ms

sample679.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 49.996948%

Guaranteed chance to sample good point: 99.993897%

Results

228.0ms	1754×	body	1280	valid
128.0ms	1266×	body	640	valid
114.0ms	4001×	body	80	valid
53.0ms	642×	body	320	valid
17.0ms	337×	body	160	valid

Details

sample27.0ms

simplify5.0ms

prune3.0ms

localize5.0ms

rewrite12.0ms

series17.0ms

simplify35.0ms

prune81.0ms

localize7.0ms

rewrite25.0ms

series21.0ms

simplify68.0ms

prune156.0ms

localize10.0ms

rewrite111.0ms

series51.0ms

simplify167.0ms

prune605.0ms

localize12.0ms

rewrite70.0ms

series82.0ms

simplify134.0ms

prune388.0ms

regimes55.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample679.0ms

Profiling