Details

analyze24.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
25%	74.9%	0.1%	4
37.5%	62.4%	0.1%	5
62.4%	37.5%	0.1%	6
87.4%	12.5%	0.1%	7
87.4%	12.5%	0.1%	8
93.7%	6.2%	0.1%	9
93.7%	6.2%	0.1%	10
96.8%	3.1%	0.1%	11
96.8%	3.1%	0.1%	12
98.3%	1.6%	0.1%	13
98.3%	1.6%	0.1%	14

sample12.0ms

Algorithm

intervals

Results

5.0ms

256×

body

valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	3
1	9	3
2	9	3

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: 0.0b

Counts

2 → 1

localize4.0ms

Local error

Found 1 expressions with local error:

0.0b	(/ (+ x y) (- x y))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

34×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
20×	`times-frac`
12×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`associate-/r*` `distribute-lft-out--` `difference-of-squares`
4×	`associate-/l*`
3×	`add-exp-log` `add-cbrt-cube`
2×	`associate-/r/` `associate-/l/`
1×	`pow1` `cbrt-undiv` `flip3--` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip--` `flip-+` `div-inv` `add-log-exp`

Counts

1 → 45

Calls

1 calls:

7.0ms

(/ (+ x y) (- x y))

series13.0ms

Counts

1 → 3

Calls

1 calls:

13.0ms

(/ (+ x y) (- x y))

simplify45.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	169	288
1	510	274
2	1421	270
3	5001	270

prune44.0ms

Filtered

32 candidates to 48 candidates (-50.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	45	3	48
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	45	4	49

Merged error: 0.0b

Counts

49 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (+ x y) (- x y)))
0.0b	(* (sqrt (/ (+ x y) (- x y))) (sqrt (/ (+ x y) (- x y))))
0.0b	(/ (+ x y) (- x y))
0.0b	(/ (+ x y) (- x y))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

316×	`*-un-lft-identity`
191×	`times-frac`
188×	`sqrt-prod`
187×	`add-sqr-sqrt`
88×	`add-cube-cbrt`
55×	`distribute-lft-out`
53×	`swap-sqr`
46×	`distribute-lft-out--`
34×	`difference-of-squares`
29×	`associate-r` `associate-l`
20×	`pow1`
14×	`associate-/r/`
10×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
9×	`sqrt-pow1` `pow1/2` `unswap-sqr`
8×	`associate-/l*`
7×	`flip3--` `flip--` `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` `flip3-+` `div-exp` `clear-num` `flip-+`
1×	`pow2` `frac-times` `pow-plus` `sqrt-unprod` `associate-r/` `associate-l/` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 276

Calls

4 calls:

8.0ms	(sqrt (/ (+ x y) (- x y)))
30.0ms	(* (sqrt (/ (+ x y) (- x y))) (sqrt (/ (+ x y) (- x y))))
7.0ms	(/ (+ x y) (- x y))
8.0ms	(/ (+ x y) (- x y))

series45.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(sqrt (/ (+ x y) (- x y)))
10.0ms	(* (sqrt (/ (+ x y) (- x y))) (sqrt (/ (+ x y) (- x y))))
8.0ms	(/ (+ x y) (- x y))
9.0ms	(/ (+ x y) (- x y))

simplify81.0ms

Algorithm

egg-herbie

Counts

288 → 288

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	360	2069
1	1654	1954
2	5002	1914

prune168.0ms

Filtered

157 candidates to 288 candidates (-83.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	287	1	288
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	288	4	292

Merged error: 0.0b

Counts

292 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (exp (sqrt (/ (+ x y) (- x y)))))
0.0b	(* (sqrt (/ (+ x y) (- x y))) (log (exp (sqrt (/ (+ x y) (- x y))))))
0.0b	(/ (+ x y) (- x y))
0.0b	(/ (+ x y) (- x y))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

161×	`*-un-lft-identity`
114×	`add-sqr-sqrt`
101×	`times-frac`
80×	`sqrt-prod`
63×	`add-cube-cbrt`
60×	`log-pow`
58×	`exp-prod`
33×	`associate-r`
29×	`associate-l`
27×	`distribute-lft-out`
22×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `associate-/r*` `associate-/r/` `add-cbrt-cube`
9×	`log-prod`
8×	`pow1` `associate-/l*`
5×	`flip3--` `flip--` `div-inv`
4×	`associate-/l/` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `unswap-sqr`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+`
1×	`sqrt-div` `rem-log-exp` `pow-prod-down` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod`

Counts

4 → 214

Calls

4 calls:

10.0ms	(log (exp (sqrt (/ (+ x y) (- x y)))))
34.0ms	(* (sqrt (/ (+ x y) (- x y))) (log (exp (sqrt (/ (+ x y) (- x y))))))
8.0ms	(/ (+ x y) (- x y))
12.0ms	(/ (+ x y) (- x y))

series47.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(log (exp (sqrt (/ (+ x y) (- x y)))))
10.0ms	(* (sqrt (/ (+ x y) (- x y))) (log (exp (sqrt (/ (+ x y) (- x y))))))
8.0ms	(/ (+ x y) (- x y))
12.0ms	(/ (+ x y) (- x y))

simplify101.0ms

Algorithm

egg-herbie

Counts

226 → 226

Iterations

Useful iterations: 3 (81.0ms)

Iter	Nodes	Cost
0	388	1636
1	980	1512
2	2672	1466
3	5001	1460

prune207.0ms

Filtered

150 candidates to 226 candidates (-50.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	226	0	226
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	226	4	230

Merged error: 0.0b

Counts

230 → 4

localize7.0ms

Local error

Found 2 expressions with local error:

0.1b	(* (sqrt (+ x y)) (/ (sqrt (+ x y)) (- x y)))
0.1b	(/ (sqrt (+ x y)) (- x y))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

96×	`*-un-lft-identity`
88×	`add-sqr-sqrt`
74×	`times-frac`
53×	`sqrt-prod`
42×	`add-cube-cbrt`
41×	`associate-r`
15×	`distribute-lft-out--` `difference-of-squares`
12×	`distribute-lft-out`
9×	`add-exp-log` `add-cbrt-cube`
7×	`associate-l` `associate-/l*`
6×	`sqrt-div` `unswap-sqr`
5×	`associate-/r*`
4×	`pow1` `associate-/r/`
3×	`flip3-+` `flip-+`
2×	`cbrt-undiv` `frac-times` `flip3--` `div-exp` `associate-*l/` `prod-exp` `flip--` `cbrt-unprod` `div-inv` `associate-/l/` `add-log-exp`
1×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

2 → 135

Calls

2 calls:

23.0ms	(* (sqrt (+ x y)) (/ (sqrt (+ x y)) (- x y)))
8.0ms	(/ (sqrt (+ x y)) (- x y))

series25.0ms

Counts

2 → 6

Calls

2 calls:

13.0ms	(* (sqrt (+ x y)) (/ (sqrt (+ x y)) (- x y)))
12.0ms	(/ (sqrt (+ x y)) (- x y))

simplify54.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	374	1195
1	1564	1085
2	5001	1024

prune101.0ms

Filtered

81 candidates to 141 candidates (-74.1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	141	0	141
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	141	4	145

Merged error: 0.0b

Counts

145 → 4

regimes136.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	3
1	6	3

end0.0ms

analyze25.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
25%	74.9%	0.1%	4
37.5%	62.4%	0.1%	5
62.4%	37.5%	0.1%	6
87.4%	12.5%	0.1%	7
87.4%	12.5%	0.1%	8
93.7%	6.2%	0.1%	9
93.7%	6.2%	0.1%	10
96.8%	3.1%	0.1%	11
96.8%	3.1%	0.1%	12
98.3%	1.6%	0.1%	13
98.3%	1.6%	0.1%	14

sample311.0ms

Algorithm

intervals

Results

183.0ms

8000×

body

valid

Details

analyze24.0ms

sample12.0ms

simplify5.0ms

prune2.0ms

localize4.0ms

rewrite9.0ms

series13.0ms

simplify45.0ms

prune44.0ms

localize9.0ms

rewrite75.0ms

series45.0ms

simplify81.0ms

prune168.0ms

localize12.0ms

rewrite75.0ms

series47.0ms

simplify101.0ms

prune207.0ms

localize7.0ms

rewrite38.0ms

series25.0ms

simplify54.0ms

prune101.0ms

regimes136.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze25.0ms

sample311.0ms

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