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	47×	body	1280	valid
5.0ms	46×	body	640	valid
3.0ms	127×	body	80	valid
2.0ms	23×	body	320	valid
1.0ms	13×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	71	7
1	71	7

prune6.0ms

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: 31.1b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
4.6b	(- (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))
10.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify44.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4975	520
1	4975	520

prune69.0ms

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: 0.2b

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

rewrite23.0ms

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:

5.0ms	(sqrt (+ x 1.0))
7.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
9.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series18.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(sqrt (+ x 1.0))
5.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
9.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify25.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	5038	1051

prune147.0ms

Filtered

59 candidates to 80 candidates (-35.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	73	7	80
Fresh	1	0	1
Picked	0	1	1
Done	1	0	1
Total	75	8	83

Merged error: 0.0b

Counts

83 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
0.1b	(/ 1 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))
0.1b	(/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))
0.3b	(* (/ 1 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))) (/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

184×	`*-un-lft-identity`
161×	`sqrt-prod`
130×	`times-frac`
120×	`add-sqr-sqrt`
73×	`add-cube-cbrt`
60×	`distribute-lft-out`
33×	`associate-r` `associate-l`
32×	`add-exp-log`
20×	`add-cbrt-cube`
18×	`associate-/r*`
15×	`unswap-sqr`
11×	`div-exp`
10×	`sqrt-div`
9×	`pow1`
8×	`prod-exp` `associate-/r/`
6×	`cbrt-undiv` `associate-/l*`
5×	`flip3-+` `flip-+`
4×	`cbrt-unprod` `div-inv` `add-log-exp`
3×	`rec-exp` `pow-flip` `1-exp`
2×	`frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`
1×	`frac-times` `rem-sqrt-square` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `inv-pow`

Counts

4 → 235

Calls

4 calls:

8.0ms	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
11.0ms	(/ 1 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))
13.0ms	(/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))
40.0ms	(* (/ 1 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))) (/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))))

series55.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
17.0ms	(/ 1 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))
18.0ms	(/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))
9.0ms	(* (/ 1 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))) (/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))))

simplify58.0ms

Algorithm

egg-herbie

Counts

247 → 247

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5044	4518

prune462.0ms

Filtered

128 candidates to 247 candidates (-93.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	243	4	247
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	246	9	255

Merged error: 0.0b

Counts

255 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
0.1b	(/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))
0.1b	(pow (+ (sqrt (+ 1.0 x)) (sqrt x)) -1/2)
0.3b	(* (pow (+ (sqrt (+ 1.0 x)) (sqrt x)) -1/2) (/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

113×	`*-un-lft-identity`
91×	`sqrt-prod`
65×	`add-sqr-sqrt`
60×	`times-frac`
43×	`add-cube-cbrt`
40×	`distribute-lft-out`
33×	`associate-r`
20×	`add-exp-log`
15×	`unpow-prod-down`
11×	`add-cbrt-cube`
10×	`associate-l`
9×	`associate-/r*` `unswap-sqr`
6×	`pow1` `sqrt-div` `prod-exp`
5×	`sqr-pow`
4×	`div-exp` `associate-/r/` `add-log-exp`
3×	`pow-to-exp` `pow-unpow` `flip3-+` `pow-exp` `flip-+` `associate-/l*`
2×	`cbrt-undiv` `cbrt-unprod` `div-inv`
1×	`rem-sqrt-square` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `clear-num` `-commutative`

Counts

4 → 160

Calls

4 calls:

7.0ms	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
11.0ms	(/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))
8.0ms	(pow (+ (sqrt (+ 1.0 x)) (sqrt x)) -1/2)
31.0ms	(* (pow (+ (sqrt (+ 1.0 x)) (sqrt x)) -1/2) (/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))))

series240.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
206.0ms	(/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))
14.0ms	(pow (+ (sqrt (+ 1.0 x)) (sqrt x)) -1/2)
10.0ms	(* (pow (+ (sqrt (+ 1.0 x)) (sqrt x)) -1/2) (/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))))

simplify50.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4978	3461
1	4978	3461

prune349.0ms

Filtered

103 candidates to 172 candidates (-67.0%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	170	2	172
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	171	10	181

Merged error: 0b

Counts

181 → 10

regimes69.0ms

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

sample644.0ms

Algorithm

intervals

Results

240.0ms	1759×	body	1280	valid
125.0ms	1213×	body	640	valid
115.0ms	4075×	body	80	valid
52.0ms	641×	body	320	valid
16.0ms	312×	body	160	valid
0.0ms	2×	body	80	nan

Details

analyze2.0ms

sample22.0ms

simplify4.0ms

prune6.0ms

localize5.0ms

rewrite12.0ms

series13.0ms

simplify44.0ms

prune69.0ms

localize6.0ms

rewrite23.0ms

series18.0ms

simplify25.0ms

prune147.0ms

localize10.0ms

rewrite84.0ms

series55.0ms

simplify58.0ms

prune462.0ms

localize14.0ms

rewrite65.0ms

series240.0ms

simplify50.0ms

prune349.0ms

regimes69.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample644.0ms

Profiling