Details

analyze76.0ms

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

sample23.0ms

Algorithm

intervals

Results

14.0ms	256×	body	80	valid
0.0ms	8×	body	80	nan
0.0ms	6×	body	80	invalid

simplify144.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (143.0ms)

Iter	Nodes	Cost
0	4908	20
1	4908	20

prune9.0ms

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:

0.0b	(* (- a (/ 1.0 3.0)) 9.0)
0.1b	(* (- a (/ 1.0 3.0)) (+ (/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0))) 1))
0.2b	(/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0)))
0.4b	(sqrt (* (- a (/ 1.0 3.0)) 9.0))

rewrite53.0ms

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)
24.0ms	(* (- a (/ 1.0 3.0)) (+ (/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0))) 1))
10.0ms	(/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0)))
7.0ms	(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))
14.0ms	(/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0)))
6.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9.0))

simplify38.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5787	1905

prune259.0ms

Filtered

92 candidates to 113 candidates (-22.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	106	7	113
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	108	7	115

Merged error: 0b

Counts

115 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- a (/ 1.0 3.0)) 9.0)
0.2b	(/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0)))
0.4b	(sqrt (* (- a (/ 1.0 3.0)) 9.0))
7.6b	(* (- a (/ 1.0 3.0)) (/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0))))

rewrite48.0ms

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)
9.0ms	(/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0)))
7.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9.0))
19.0ms	(* (- a (/ 1.0 3.0)) (/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0))))

series40.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (- a (/ 1.0 3.0)) 9.0)
14.0ms	(/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0)))
5.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9.0))
17.0ms	(* (- a (/ 1.0 3.0)) (/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0))))

simplify34.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5015	2084

prune272.0ms

Filtered

101 candidates to 125 candidates (-23.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	122	3	125
Fresh	4	2	6
Picked	0	1	1
Done	0	0	0
Total	126	6	132

Merged error: 0b

Counts

132 → 6

localize11.0ms

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))))
0.3b	(/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))

rewrite122.0ms

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)))
68.0ms	(* (- a (/ 1.0 3.0)) (+ (/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0)) 1))
9.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))
17.0ms	(/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))

series48.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(sqrt (- a (/ 1.0 3.0)))
18.0ms	(* (- a (/ 1.0 3.0)) (+ (/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0)) 1))
10.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))
16.0ms	(/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))

simplify87.0ms

Algorithm

egg-herbie

Counts

367 → 367

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4988	7942
1	4988	7942

prune765.0ms

Filtered

219 candidates to 367 candidates (-67.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	367	0	367
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	367	6	373

Merged error: 0b

Counts

373 → 6

localize11.0ms

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)))
0.3b	(* (/ (- 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))))

rewrite100.0ms

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:

25.0ms	(+ (* (/ (- a (/ 1.0 3.0)) (sqrt (- a (/ 1.0 3.0)))) (/ rand (sqrt 9.0))) (- a (/ 1.0 3.0)))
6.0ms	(sqrt (- a (/ 1.0 3.0)))
40.0ms	(* (/ (- a (/ 1.0 3.0)) (sqrt (- a (/ 1.0 3.0)))) (/ rand (sqrt 9.0)))
15.0ms	(/ (- a (/ 1.0 3.0)) (sqrt (- a (/ 1.0 3.0))))

series45.0ms

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)))
9.0ms	(/ (- a (/ 1.0 3.0)) (sqrt (- a (/ 1.0 3.0))))

simplify61.0ms

Algorithm

egg-herbie

Counts

249 → 249

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5763	4727

prune564.0ms

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

regimes122.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	19
1	33	19

end0.0ms

sample611.0ms

Algorithm

intervals

Results

442.0ms	8000×	body	80	valid
15.0ms	250×	body	80	nan
15.0ms	270×	body	80	invalid

Details

analyze76.0ms

sample23.0ms

simplify144.0ms

prune9.0ms

localize10.0ms

rewrite53.0ms

series36.0ms

simplify38.0ms

prune259.0ms

localize10.0ms

rewrite48.0ms

series40.0ms

simplify34.0ms

prune272.0ms

localize11.0ms

rewrite122.0ms

series48.0ms

simplify87.0ms

prune765.0ms

localize11.0ms

rewrite100.0ms

series45.0ms

simplify61.0ms

prune564.0ms

regimes122.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample611.0ms

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