Details

analyze71.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	50%	50%	2
0%	50%	50%	3
0%	50%	50%	4
6.2%	43.7%	50%	5
9.4%	28.1%	62.5%	6
12.5%	25%	62.5%	7
15.6%	15.6%	68.8%	8
16.8%	14.4%	68.8%	9
18.5%	8.8%	72.7%	10
19.2%	7.7%	73.1%	11
20.1%	4.6%	75.2%	12
20.5%	4%	75.5%	13
21%	2.4%	76.6%	14

sample45.0ms

Algorithm

intervals

Results

13.0ms

256×

body

valid

simplify141.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (140.0ms)

Iter	Nodes	Cost
0	4908	20
1	4908	20

prune10.0ms

Filtered

1 candidates to 1 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: 0.1b

Counts

2 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- a (/ 1.0 3.0)) 9.0)
0.1b	(* (- a (/ 1.0 3.0)) (+ (/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0))) 1))
0.1b	(sqrt (* (- a (/ 1.0 3.0)) 9.0))
0.2b	(/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
17×	`add-cube-cbrt`
14×	`times-frac`
12×	`associate-l`
11×	`pow1`
10×	`add-exp-log` `add-cbrt-cube`
8×	`associate-*l/`
7×	`associate-r`
6×	`flip3--` `flip--`
5×	`sqrt-prod`
4×	`frac-times` `sqrt-div` `associate-/r*` `add-log-exp` `difference-of-squares`
3×	`flip3-+` `pow-prod-down` `flip-+` `associate-/l*`
2×	`sqrt-pow1` `associate-r/` `prod-exp` `associate-/r/` `-commutative` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`
1×	`cbrt-undiv` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow1/2` `div-exp` `clear-num` `div-inv` `distribute-lft-out`

Counts

4 → 101

Calls

4 calls:

9.0ms	(* (- a (/ 1.0 3.0)) 9.0)
25.0ms	(* (- a (/ 1.0 3.0)) (+ (/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0))) 1))
8.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9.0))
10.0ms	(/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0)))

series36.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (- a (/ 1.0 3.0)) 9.0)
12.0ms	(* (- a (/ 1.0 3.0)) (+ (/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0))) 1))
6.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9.0))
15.0ms	(/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0)))

simplify36.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5787	1905

prune262.0ms

Filtered

90 candidates to 113 candidates (-25.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	107	6	113
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	109	6	115

Merged error: 0b

Counts

115 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- a (/ 1.0 3.0)))
0.1b	(* (- a (/ 1.0 3.0)) (+ (/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0)) 1))
0.2b	(/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))
0.2b	(/ rand (sqrt (- a (/ 1.0 3.0))))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

441×	`times-frac`
343×	`add-sqr-sqrt`
261×	`*-un-lft-identity`
258×	`sqrt-prod`
205×	`add-cube-cbrt`
54×	`difference-of-squares`
36×	`associate-/l*`
27×	`distribute-lft-out--`
18×	`sqrt-div`
16×	`associate-/r/`
15×	`associate-/r*`
13×	`add-exp-log` `add-cbrt-cube`
12×	`flip3--` `flip--`
9×	`div-inv`
7×	`pow1`
6×	`associate-l`
4×	`cbrt-undiv` `frac-times` `div-exp` `associate-r` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`frac-2neg` `associate-r/` `associate-l/` `clear-num`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `associate-/l/` `distribute-lft-out` `unswap-sqr`

Counts

4 → 355

Calls

4 calls:

6.0ms	(sqrt (- a (/ 1.0 3.0)))
74.0ms	(* (- a (/ 1.0 3.0)) (+ (/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0)) 1))
18.0ms	(/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))
9.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))

series52.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(sqrt (- a (/ 1.0 3.0)))
13.0ms	(* (- a (/ 1.0 3.0)) (+ (/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0)) 1))
24.0ms	(/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))
11.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))

simplify97.0ms

Algorithm

egg-herbie

Counts

367 → 367

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4988	7942
1	4988	7942

prune860.0ms

Filtered

219 candidates to 367 candidates (-67.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	367	0	367
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	367	6	373

Merged error: 0b

Counts

373 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- a (/ 1.0 3.0)) 9.0)
0.1b	(sqrt (* (- a (/ 1.0 3.0)) 9.0))
0.2b	(/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0)))
9.3b	(* (- a (/ 1.0 3.0)) (/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
27×	`times-frac`
24×	`add-cube-cbrt`
21×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
12×	`associate-l`
11×	`pow1`
10×	`associate-*l/`
8×	`sqrt-prod`
6×	`flip3--` `sqrt-div` `flip--`
4×	`associate-/r*` `associate-/r/` `add-log-exp` `difference-of-squares`
3×	`pow-prod-down` `prod-exp` `cbrt-unprod` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `sqrt-pow1` `div-exp` `*-commutative` `div-inv` `distribute-lft-out--`
1×	`frac-2neg` `pow1/2` `associate-*r/` `clear-num`

Counts

4 → 113

Calls

4 calls:

9.0ms	(* (- a (/ 1.0 3.0)) 9.0)
7.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9.0))
10.0ms	(/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0)))
21.0ms	(* (- a (/ 1.0 3.0)) (/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0))))

series41.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (- a (/ 1.0 3.0)) 9.0)
6.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9.0))
15.0ms	(/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0)))
18.0ms	(* (- a (/ 1.0 3.0)) (/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0))))

simplify32.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5015	2084

prune304.0ms

Filtered

101 candidates to 125 candidates (-23.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	124	1	125
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	125	6	131

Merged error: 0b

Counts

131 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (/ (- a (/ 1.0 3.0)) (sqrt (- a (/ 1.0 3.0)))) (/ rand (sqrt 9.0))) (- a (/ 1.0 3.0)))
0.0b	(sqrt (- a (/ 1.0 3.0)))
0.4b	(* (/ (- a (/ 1.0 3.0)) (sqrt (- a (/ 1.0 3.0)))) (/ rand (sqrt 9.0)))
0.5b	(/ (- a (/ 1.0 3.0)) (sqrt (- a (/ 1.0 3.0))))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

260×	`add-sqr-sqrt`
171×	`times-frac`
130×	`*-un-lft-identity`
99×	`sqrt-prod`
66×	`difference-of-squares`
64×	`add-cube-cbrt`
60×	`associate-l`
33×	`distribute-lft-out--`
22×	`associate-r`
18×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
9×	`associate-/r*` `add-log-exp` `unswap-sqr`
7×	`flip3--` `flip--`
6×	`sqrt-div` `frac-add` `associate-/l*`
5×	`cbrt-undiv` `div-exp`
4×	`prod-exp` `associate-/r/` `cbrt-unprod`
3×	`frac-times` `associate-r/` `associate-l/` `div-inv`
2×	`sqrt-pow1` `pow1/2` `sum-log` `associate-/l/` `pow-div`
1×	`+-commutative` `associate-+r-` `sub-neg` `rem-sqrt-square` `associate-+r+` `frac-2neg` `flip3-+` `diff-log` `div-sub` `pow-prod-down` `clear-num` `*-commutative` `flip-+`

Counts

4 → 237

Calls

4 calls:

30.0ms	(+ (* (/ (- a (/ 1.0 3.0)) (sqrt (- a (/ 1.0 3.0)))) (/ rand (sqrt 9.0))) (- a (/ 1.0 3.0)))
7.0ms	(sqrt (- a (/ 1.0 3.0)))
38.0ms	(* (/ (- a (/ 1.0 3.0)) (sqrt (- a (/ 1.0 3.0)))) (/ rand (sqrt 9.0)))
18.0ms	(/ (- a (/ 1.0 3.0)) (sqrt (- a (/ 1.0 3.0))))

series41.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ (* (/ (- a (/ 1.0 3.0)) (sqrt (- a (/ 1.0 3.0)))) (/ rand (sqrt 9.0))) (- a (/ 1.0 3.0)))
4.0ms	(sqrt (- a (/ 1.0 3.0)))
17.0ms	(* (/ (- a (/ 1.0 3.0)) (sqrt (- a (/ 1.0 3.0)))) (/ rand (sqrt 9.0)))
5.0ms	(/ (- a (/ 1.0 3.0)) (sqrt (- a (/ 1.0 3.0))))

simplify62.0ms

Algorithm

egg-herbie

Counts

249 → 249

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5763	4727

prune578.0ms

Filtered

170 candidates to 249 candidates (-46.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	248	1	249
Fresh	2	1	3
Picked	1	0	1
Done	0	2	2
Total	251	4	255

Merged error: 0b

Counts

255 → 4

regimes136.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	19
1	33	19

end0.0ms

sample1.2s

Algorithm

intervals

Results

411.0ms

8000×

body

valid

Details

analyze71.0ms

sample45.0ms

simplify141.0ms

prune10.0ms

localize10.0ms

rewrite55.0ms

series36.0ms

simplify36.0ms

prune262.0ms

localize12.0ms

rewrite134.0ms

series52.0ms

simplify97.0ms

prune860.0ms

localize11.0ms

rewrite51.0ms

series41.0ms

simplify32.0ms

prune304.0ms

localize12.0ms

rewrite106.0ms

series41.0ms

simplify62.0ms

prune578.0ms

regimes136.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.2s

Profiling