Details

analyze135.0ms

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

sample37.0ms

Algorithm

intervals

Results

26.0ms	256×	body	80	valid
1.0ms	8×	body	80	nan
1.0ms	6×	body	80	invalid

simplify33.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	947	20
1	947	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

localize11.0ms

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

rewrite63.0ms

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:

18.0ms	(* (- a (/ 1.0 3.0)) 9.0)
22.0ms	(* (- a (/ 1.0 3.0)) (+ (/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0))) 1))
7.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9.0))
10.0ms	(/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0)))

series65.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (- a (/ 1.0 3.0)) 9.0)
22.0ms	(* (- a (/ 1.0 3.0)) (+ (/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0))) 1))
10.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9.0))
26.0ms	(/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0)))

simplify43.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5362	1905

prune438.0ms

Filtered

90 candidates to 113 candidates (-25.6%)

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: 0.0b

Counts

115 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (* (* (- a (/ 1.0 3.0)) (* (cbrt 9.0) (cbrt 9.0))) (cbrt 9.0)))
0.2b	(/ rand (sqrt (* (* (- a (/ 1.0 3.0)) (* (cbrt 9.0) (cbrt 9.0))) (cbrt 9.0))))
0.2b	(* (* (- a (/ 1.0 3.0)) (* (cbrt 9.0) (cbrt 9.0))) (cbrt 9.0))
0.3b	(* (- a (/ 1.0 3.0)) (* (cbrt 9.0) (cbrt 9.0)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

28×	`pow1`
22×	`add-sqr-sqrt`
20×	`add-exp-log`
18×	`*-un-lft-identity`
16×	`add-cube-cbrt`
15×	`pow-prod-down`
14×	`associate-*l/`
13×	`times-frac` `add-cbrt-cube`
9×	`prod-exp` `cbrt-unprod`
7×	`associate-r` `associate-l`
5×	`sqrt-prod`
4×	`flip3--` `sqrt-pow1` `sqrt-div` `associate-/r*` `flip--` `add-log-exp`
3×	`cbrt-prod` `associate-/l*`
2×	`associate-/r/` `*-commutative` `difference-of-squares`
1×	`cbrt-undiv` `frac-2neg` `pow1/2` `div-exp` `clear-num` `div-inv` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 98

Calls

4 calls:

13.0ms	(sqrt (* (* (- a (/ 1.0 3.0)) (* (cbrt 9.0) (cbrt 9.0))) (cbrt 9.0)))
16.0ms	(/ rand (sqrt (* (* (- a (/ 1.0 3.0)) (* (cbrt 9.0) (cbrt 9.0))) (cbrt 9.0))))
17.0ms	(* (* (- a (/ 1.0 3.0)) (* (cbrt 9.0) (cbrt 9.0))) (cbrt 9.0))
13.0ms	(* (- a (/ 1.0 3.0)) (* (cbrt 9.0) (cbrt 9.0)))

series55.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(sqrt (* (* (- a (/ 1.0 3.0)) (* (cbrt 9.0) (cbrt 9.0))) (cbrt 9.0)))
24.0ms	(/ rand (sqrt (* (* (- a (/ 1.0 3.0)) (* (cbrt 9.0) (cbrt 9.0))) (cbrt 9.0))))
12.0ms	(* (* (- a (/ 1.0 3.0)) (* (cbrt 9.0) (cbrt 9.0))) (cbrt 9.0))
11.0ms	(* (- a (/ 1.0 3.0)) (* (cbrt 9.0) (cbrt 9.0)))

simplify43.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4973	1442
1	4973	1442

prune229.0ms

Filtered

82 candidates to 110 candidates (-34.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	110	7	117

Merged error: 0.0b

Counts

117 → 7

localize12.0ms

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

rewrite64.0ms

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:

30.0ms	(* (- a (/ 1.0 3.0)) (+ (/ 1 (/ (sqrt (* (- a (/ 1.0 3.0)) 9.0)) rand)) 1))
7.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9.0))
10.0ms	(/ (sqrt (* (- a (/ 1.0 3.0)) 9.0)) rand)
11.0ms	(/ 1 (/ (sqrt (* (- a (/ 1.0 3.0)) 9.0)) rand))

series61.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(* (- a (/ 1.0 3.0)) (+ (/ 1 (/ (sqrt (* (- a (/ 1.0 3.0)) 9.0)) rand)) 1))
6.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9.0))
25.0ms	(/ (sqrt (* (- a (/ 1.0 3.0)) 9.0)) rand)
18.0ms	(/ 1 (/ (sqrt (* (- a (/ 1.0 3.0)) 9.0)) rand))

simplify69.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4977	3408
1	4977	3408

prune363.0ms

Filtered

132 candidates to 179 candidates (-35.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	179	0	179
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	179	7	186

Merged error: 0.0b

Counts

186 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (* (- a (/ 1.0 3.0)) 9.0))
0.1b	(sqrt (* (- a (/ 1.0 3.0)) 9.0))
0.2b	(/ rand (sqrt (sqrt (* (- a (/ 1.0 3.0)) 9.0))))
0.3b	(/ (/ rand (sqrt (sqrt (* (- a (/ 1.0 3.0)) 9.0)))) (sqrt (sqrt (* (- a (/ 1.0 3.0)) 9.0))))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

378×	`times-frac`
282×	`sqrt-prod`
188×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
44×	`sqrt-div`
30×	`associate-/l*`
24×	`associate-*l/`
20×	`associate-/r/`
14×	`associate-/r*`
12×	`flip3--` `flip--`
11×	`add-exp-log` `add-cbrt-cube`
10×	`pow1` `div-inv`
4×	`cbrt-undiv` `sqrt-pow1` `div-exp` `add-log-exp`
2×	`frac-2neg` `pow1/2` `pow-prod-down` `clear-num`
1×	`associate-/l/`

Counts

4 → 311

Calls

4 calls:

7.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9.0))
7.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9.0))
11.0ms	(/ rand (sqrt (sqrt (* (- a (/ 1.0 3.0)) 9.0))))
27.0ms	(/ (/ rand (sqrt (sqrt (* (- a (/ 1.0 3.0)) 9.0)))) (sqrt (sqrt (* (- a (/ 1.0 3.0)) 9.0))))

series54.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9.0))
6.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9.0))
22.0ms	(/ rand (sqrt (sqrt (* (- a (/ 1.0 3.0)) 9.0))))
21.0ms	(/ (/ rand (sqrt (sqrt (* (- a (/ 1.0 3.0)) 9.0)))) (sqrt (sqrt (* (- a (/ 1.0 3.0)) 9.0))))

simplify86.0ms

Algorithm

egg-herbie

Counts

323 → 323

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5113	9398

prune827.0ms

Filtered

174 candidates to 323 candidates (-85.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	323	0	323
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	323	7	330

Merged error: 0.0b

Counts

330 → 7

regimes161.0ms

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 (0.0ms)

Iter	Nodes	Cost
0	23	27
1	23	27

end0.0ms

analyze74.0ms

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

sample654.0ms

Algorithm

intervals

Results

476.0ms	8000×	body	80	valid
17.0ms	294×	body	80	invalid
15.0ms	279×	body	80	nan

Details

analyze135.0ms

sample37.0ms

simplify33.0ms

prune9.0ms

localize11.0ms

rewrite63.0ms

series65.0ms

simplify43.0ms

prune438.0ms

localize14.0ms

rewrite62.0ms

series55.0ms

simplify43.0ms

prune229.0ms

localize12.0ms

rewrite64.0ms

series61.0ms

simplify69.0ms

prune363.0ms

localize13.0ms

rewrite68.0ms

series54.0ms

simplify86.0ms

prune827.0ms

regimes161.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze74.0ms

sample654.0ms

Profiling