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

sample22.0ms

Algorithm

intervals

Results

6.0ms	51×	body	1280	valid
4.0ms	44×	body	640	valid
3.0ms	128×	body	80	valid
2.0ms	23×	body	320	valid
0.0ms	10×	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

prune7.0ms

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: 30.5b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
3.4b	(- (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))

series14.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(sqrt (+ x 1.0))
10.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify47.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4975	520
1	4975	520

prune64.0ms

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

localize7.0ms

Local error

Found 3 expressions with local error:

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

rewrite22.0ms

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

series21.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(sqrt (+ x 1.0))
6.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
12.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify27.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5038	1051

prune134.0ms

Filtered

59 candidates to 80 candidates (-35.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	75	5	80
Fresh	1	0	1
Picked	0	1	1
Done	1	0	1
Total	77	6	83

Merged error: 0.0b

Counts

83 → 6

localize12.0ms

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)))
0.3b	(* (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))))
9.0ms	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
9.0ms	(/ 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)))))

series51.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x))))
9.0ms	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
9.0ms	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
13.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))))

simplify93.0ms

Algorithm

egg-herbie

Counts

262 → 262

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4952	4249
1	4952	4249

prune447.0ms

Filtered

142 candidates to 262 candidates (-84.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	258	4	262
Fresh	2	2	4
Picked	1	0	1
Done	0	1	1
Total	261	7	268

Merged error: 0b

Counts

268 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

157×	`sqrt-prod`
140×	`*-un-lft-identity`
74×	`times-frac`
57×	`add-sqr-sqrt` `unpow-prod-down`
52×	`distribute-lft-out`
49×	`add-cube-cbrt`
8×	`associate-/r/`
7×	`pow1` `add-exp-log` `rem-sqrt-square`
6×	`associate-/r*` `add-cbrt-cube`
4×	`flip3-+` `flip-+` `div-inv` `add-log-exp`
3×	`pow-unpow` `pow-pow` `sqrt-pow1` `pow1/2` `associate-/l*` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `sqrt-div` `div-exp` `pow-exp` `clear-num` `sqrt-pow2`

Counts

4 → 166

Calls

4 calls:

10.0ms	(sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x))))
14.0ms	(sqrt (pow (sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))) 4))
9.0ms	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
13.0ms	(pow (sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))) 4)

series78.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x))))
12.0ms	(sqrt (pow (sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))) 4))
9.0ms	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
36.0ms	(pow (sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))) 4)

simplify47.0ms

Algorithm

egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	4951	3069
1	4951	3069

prune298.0ms

Filtered

112 candidates to 178 candidates (-58.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	178	0	178
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	178	7	185

Merged error: 0b

Counts

185 → 7

regimes50.0ms

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

sample598.0ms

Algorithm

intervals

Results

206.0ms	1635×	body	1280	valid
119.0ms	1237×	body	640	valid
112.0ms	4168×	body	80	valid
51.0ms	647×	body	320	valid
15.0ms	313×	body	160	valid
0.0ms	1×	body	80	nan

Details

analyze2.0ms

sample22.0ms

simplify5.0ms

prune7.0ms

localize5.0ms

rewrite12.0ms

series14.0ms

simplify47.0ms

prune64.0ms

localize7.0ms

rewrite22.0ms

series21.0ms

simplify27.0ms

prune134.0ms

localize12.0ms

rewrite82.0ms

series51.0ms

simplify93.0ms

prune447.0ms

localize10.0ms

rewrite57.0ms

series78.0ms

simplify47.0ms

prune298.0ms

regimes50.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample598.0ms

Profiling