Details

analyze75.0ms

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

sample22.0ms

Algorithm

intervals

Results

13.0ms	256×	body	80	valid
1.0ms	10×	body	80	invalid
0.0ms	10×	body	80	nan

simplify141.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (140.0ms)

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)))
0.6b	(sqrt (* (- a (/ 1.0 3.0)) 9.0))

rewrite54.0ms

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)
23.0ms	(* (- 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)))
10.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9.0))

series37.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (- a (/ 1.0 3.0)) 9.0)
14.0ms	(* (- 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))

simplify33.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5787	1905

prune266.0ms

Filtered

92 candidates to 113 candidates (-22.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	105	8	113
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	106	9	115

Merged error: 0b

Counts

115 → 9

localize11.0ms

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)))
0.6b	(sqrt (* (- a (/ 1.0 3.0)) 9.0))
8.3b	(* (- 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)
10.0ms	(/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0)))
7.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9.0))
20.0ms	(* (- a (/ 1.0 3.0)) (/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0))))

series37.0ms

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

simplify33.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5015	2084

prune275.0ms

Filtered

101 candidates to 125 candidates (-23.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	123	2	125
Fresh	4	4	8
Picked	0	1	1
Done	0	0	0
Total	127	7	134

Merged error: 0b

Counts

134 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- a (/ 1.0 3.0)) (+ (/ 1 (/ (sqrt (* (- a (/ 1.0 3.0)) 9.0)) rand)) 1))
0.2b	(/ (sqrt (* (- a (/ 1.0 3.0)) 9.0)) rand)
0.6b	(/ 1 (/ (sqrt (* (- a (/ 1.0 3.0)) 9.0)) rand))
0.6b	(sqrt (* (- a (/ 1.0 3.0)) 9.0))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 167

Calls

4 calls:

31.0ms	(* (- a (/ 1.0 3.0)) (+ (/ 1 (/ (sqrt (* (- a (/ 1.0 3.0)) 9.0)) rand)) 1))
10.0ms	(/ (sqrt (* (- a (/ 1.0 3.0)) 9.0)) rand)
14.0ms	(/ 1 (/ (sqrt (* (- a (/ 1.0 3.0)) 9.0)) rand))
7.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9.0))

series57.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(* (- a (/ 1.0 3.0)) (+ (/ 1 (/ (sqrt (* (- a (/ 1.0 3.0)) 9.0)) rand)) 1))
20.0ms	(/ (sqrt (* (- a (/ 1.0 3.0)) 9.0)) rand)
19.0ms	(/ 1 (/ (sqrt (* (- a (/ 1.0 3.0)) 9.0)) rand))
5.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9.0))

simplify48.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5715	3468

prune354.0ms

Filtered

129 candidates to 179 candidates (-38.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	177	2	179
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	180	6	186

Merged error: 0b

Counts

186 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- a (/ 1.0 3.0)) (+ (/ (/ 1 (sqrt (* (- a (/ 1.0 3.0)) 9.0))) (/ 1 rand)) 1))
0.3b	(/ (/ 1 (sqrt (* (- a (/ 1.0 3.0)) 9.0))) (/ 1 rand))
0.3b	(/ 1 (sqrt (* (- a (/ 1.0 3.0)) 9.0)))
0.6b	(sqrt (* (- a (/ 1.0 3.0)) 9.0))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

586×	`times-frac`
267×	`add-sqr-sqrt`
264×	`*-un-lft-identity`
260×	`add-cube-cbrt`
50×	`add-exp-log`
47×	`sqrt-prod`
35×	`div-inv`
34×	`div-exp` `associate-*l/`
32×	`sqrt-div`
31×	`associate-/r/`
21×	`associate-/l*`
20×	`add-cbrt-cube`
19×	`flip3--` `flip--`
17×	`associate-/r*`
13×	`pow1`
9×	`cbrt-undiv` `rec-exp` `1-exp`
6×	`associate-l`
4×	`frac-times` `pow-flip` `sqrt-pow1` `associate-r` `add-log-exp`
3×	`flip3-+` `pow-prod-down` `flip-+`
2×	`frac-2neg` `pow1/2` `associate-*r/` `clear-num` `difference-of-squares`
1×	`distribute-rgt-in` `distribute-lft-in` `prod-exp` `*-commutative` `cbrt-unprod` `associate-/l/` `distribute-lft-out` `distribute-lft-out--` `inv-pow` `unswap-sqr`

Counts

4 → 382

Calls

4 calls:

79.0ms	(* (- a (/ 1.0 3.0)) (+ (/ (/ 1 (sqrt (* (- a (/ 1.0 3.0)) 9.0))) (/ 1 rand)) 1))
20.0ms	(/ (/ 1 (sqrt (* (- a (/ 1.0 3.0)) 9.0))) (/ 1 rand))
10.0ms	(/ 1 (sqrt (* (- a (/ 1.0 3.0)) 9.0)))
8.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9.0))

series40.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(* (- a (/ 1.0 3.0)) (+ (/ (/ 1 (sqrt (* (- a (/ 1.0 3.0)) 9.0))) (/ 1 rand)) 1))
16.0ms	(/ (/ 1 (sqrt (* (- a (/ 1.0 3.0)) 9.0))) (/ 1 rand))
7.0ms	(/ 1 (sqrt (* (- a (/ 1.0 3.0)) 9.0)))
5.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9.0))

simplify266.0ms

Algorithm

egg-herbie

Counts

394 → 394

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5006	9036

prune743.0ms

Filtered

204 candidates to 394 candidates (-93.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	394	0	394
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	394	6	400

Merged error: 0b

Counts

400 → 6

regimes142.0ms

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	34	24
1	34	24

end0.0ms

sample609.0ms

Algorithm

intervals

Results

441.0ms	8000×	body	80	valid
16.0ms	270×	body	80	invalid
13.0ms	262×	body	80	nan

Details

analyze75.0ms

sample22.0ms

simplify141.0ms

prune9.0ms

localize10.0ms

rewrite54.0ms

series37.0ms

simplify33.0ms

prune266.0ms

localize11.0ms

rewrite51.0ms

series37.0ms

simplify33.0ms

prune275.0ms

localize11.0ms

rewrite68.0ms

series57.0ms

simplify48.0ms

prune354.0ms

localize15.0ms

rewrite143.0ms

series40.0ms

simplify266.0ms

prune743.0ms

regimes142.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample609.0ms

Profiling