Details

sample30.0ms

Algorithm

intervals

Results

8.0ms	256×	body	80	valid
7.0ms	230×	body	80	nan

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	22	7
1	44	7
2	63	7
3	70	7
4	71	7
5	71	7

prune3.0ms

Filtered

1 candidates to 0 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: 18.5b

Counts

2 → 1

localize14.0ms

Local error

Found 3 expressions with local error:

0.6b	(+ (* x y) (* x z))
1.6b	(+ (+ (* x y) (* x z)) (* y z))
17.5b	(sqrt (+ (+ (* x y) (* x z)) (* y z)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

5×	`*-commutative`
4×	`fma-def`
3×	`+-commutative` `flip3-+` `flip-+`
2×	`associate-+l+` `distribute-rgt-out` `sqrt-div` `distribute-lft-out`
1×	`pow1/2`

Counts

3 → 17

Calls

3 calls:

5.0ms	(+ (* x y) (* x z))
8.0ms	(+ (+ (* x y) (* x z)) (* y z))
8.0ms	(sqrt (+ (+ (* x y) (* x z)) (* y z)))

series173.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(+ (* x y) (* x z))
22.0ms	(+ (+ (* x y) (* x z)) (* y z))
115.0ms	(sqrt (+ (+ (* x y) (* x z)) (* y z)))

simplify74.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 3 (70.0ms)

Iter	Nodes	Cost
0	192	148
1	649	134
2	2437	125
3	5002	124

prune72.0ms

Filtered

26 candidates to 18 candidates (69.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	24	2	26
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	24	3	27

Merged error: 18.5b

Counts

27 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

10.1b	(- (* (+ (* x y) (* x z)) (+ (* x y) (* x z))) (* (* y z) (* y z)))
11.3b	(/ (sqrt (- (* (+ (* x y) (* x z)) (+ (* x y) (* x z))) (* (* y z) (* y z)))) (sqrt (- (+ (* x y) (* x z)) (* y z))))
12.1b	(sqrt (- (+ (* x y) (* x z)) (* y z)))
13.8b	(sqrt (- (* (+ (* x y) (* x z)) (+ (* x y) (* x z))) (* (* y z) (* y z))))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

179×	`*-commutative`
80×	`prod-diff`
56×	`swap-sqr`
54×	`distribute-rgt-out` `distribute-lft-out`
38×	`associate-r` `associate-l`
12×	`difference-of-squares`
10×	`fma-neg`
8×	`sqrt-div` `sqrt-prod`
5×	`flip3--` `flip--`
4×	`associate--l+` `associate-/l*`
2×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `pow1/2` `associate-/r/` `associate-/l/`
1×	`sub-neg` `sqrt-undiv` `frac-2neg` `clear-num` `div-inv`

Counts

4 → 124

Calls

4 calls:

24.0ms	(- (* (+ (* x y) (* x z)) (+ (* x y) (* x z))) (* (* y z) (* y z)))
29.0ms	(/ (sqrt (- (* (+ (* x y) (* x z)) (+ (* x y) (* x z))) (* (* y z) (* y z)))) (sqrt (- (+ (* x y) (* x z)) (* y z))))
8.0ms	(sqrt (- (+ (* x y) (* x z)) (* y z)))
26.0ms	(sqrt (- (* (+ (* x y) (* x z)) (+ (* x y) (* x z))) (* (* y z) (* y z))))

series621.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(- (* (+ (* x y) (* x z)) (+ (* x y) (* x z))) (* (* y z) (* y z)))
234.0ms	(/ (sqrt (- (* (+ (* x y) (* x z)) (+ (* x y) (* x z))) (* (* y z) (* y z)))) (sqrt (- (+ (* x y) (* x z)) (* y z))))
113.0ms	(sqrt (- (+ (* x y) (* x z)) (* y z)))
197.0ms	(sqrt (- (* (+ (* x y) (* x z)) (+ (* x y) (* x z))) (* (* y z) (* y z))))

simplify75.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	433	1921
1	1508	1565
2	5002	1551

prune409.0ms

Filtered

136 candidates to 37 candidates (27.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	133	3	136
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	134	5	139

Merged error: 18.3b

Counts

139 → 5

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (* x y) (* x z))
0.9b	(- (+ (* x y) (* x z)) (* y z))
11.3b	(/ (fma x y (* x z)) (sqrt (- (+ (* x y) (* x z)) (* y z))))
12.1b	(sqrt (- (+ (* x y) (* x z)) (* y z)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-commutative`
4×	`distribute-rgt-out` `sqrt-div` `prod-diff` `distribute-lft-out`
3×	`flip3--` `flip--`
2×	`+-commutative` `fma-def` `fma-neg` `associate--l+` `associate-/r/`
1×	`sub-neg` `frac-2neg` `flip3-+` `pow1/2` `clear-num` `flip-+` `div-inv`

Counts

4 → 27

Calls

4 calls:

5.0ms	(+ (* x y) (* x z))
8.0ms	(- (+ (* x y) (* x z)) (* y z))
8.0ms	(/ (fma x y (* x z)) (sqrt (- (+ (* x y) (* x z)) (* y z))))
8.0ms	(sqrt (- (+ (* x y) (* x z)) (* y z)))

series369.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(+ (* x y) (* x z))
25.0ms	(- (+ (* x y) (* x z)) (* y z))
193.0ms	(/ (fma x y (* x z)) (sqrt (- (+ (* x y) (* x z)) (* y z))))
114.0ms	(sqrt (- (+ (* x y) (* x z)) (* y z)))

simplify104.0ms

Algorithm

egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 3 (99.0ms)

Iter	Nodes	Cost
0	253	262
1	827	236
2	3754	226
3	5001	225

prune113.0ms

Filtered

39 candidates to 26 candidates (66.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	38	1	39
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	39	5	44

Merged error: 18.2b

Counts

44 → 5

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (* x y) (* x z))
0.9b	(- (+ (* x y) (* x z)) (* y z))
11.3b	(/ (fma x y (* x z)) (pow (- (+ (* x y) (* x z)) (* y z)) 1/2))
16.7b	(pow (- (+ (* x y) (* x z)) (* y z)) 1/2)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-commutative`
4×	`distribute-rgt-out` `prod-diff` `distribute-lft-out`
2×	`+-commutative` `fma-def` `fma-neg` `associate--l+` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `flip3-+` `clear-num` `associate-/r*` `flip--` `flip-+` `div-inv` `unpow1/2`

Counts

4 → 26

Calls

4 calls:

5.0ms	(+ (* x y) (* x z))
8.0ms	(- (+ (* x y) (* x z)) (* y z))
6.0ms	(/ (fma x y (* x z)) (pow (- (+ (* x y) (* x z)) (* y z)) 1/2))
5.0ms	(pow (- (+ (* x y) (* x z)) (* y z)) 1/2)

series468.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(+ (* x y) (* x z))
25.0ms	(- (+ (* x y) (* x z)) (* y z))
194.0ms	(/ (fma x y (* x z)) (pow (- (+ (* x y) (* x z)) (* y z)) 1/2))
209.0ms	(pow (- (+ (* x y) (* x z)) (* y z)) 1/2)

simplify106.0ms

Algorithm

egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 3 (101.0ms)

Iter	Nodes	Cost
0	283	217
1	904	190
2	3994	180
3	5001	177

prune99.0ms

Filtered

38 candidates to 26 candidates (68.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	35	3	38
Fresh	3	0	3
Picked	0	1	1
Done	0	1	1
Total	38	5	43

Merged error: 18.1b

Counts

43 → 5

regimes172.0ms

Accuracy

0% (0.5b remaining)

Error of 19.8b against oracle of 19.3b and baseline of 19.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	7
1	17	7

end0.0ms

sample840.0ms

Algorithm

intervals

Results

267.0ms	8000×	body	80	valid
250.0ms	7925×	body	80	nan