Details

sample43.0ms

Algorithm

intervals

Results

12.0ms	256×	body	80	valid
10.0ms	234×	body	80	nan

simplify21.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

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

prune4.0ms

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: 16.4b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x y) (* x z))
0.6b	(+ (+ (* x y) (* x z)) (* y z))
15.6b	(sqrt (+ (+ (* x y) (* x z)) (* y z)))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

84×	`*-un-lft-identity`
52×	`distribute-lft-out`
45×	`associate-l`
24×	`fma-def`
20×	`add-sqr-sqrt`
13×	`sqrt-prod`
12×	`add-cube-cbrt`
10×	`add-log-exp`
7×	`associate-r`
5×	`*-commutative`
4×	`pow1` `sum-log`
3×	`add-exp-log` `+-commutative` `expm1-log1p-u` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
2×	`associate-+l+` `distribute-rgt-out` `sqrt-div` `hypot-def` `unswap-sqr`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

3 → 101

Calls

3 calls:

16.0ms	(+ (* x y) (* x z))
30.0ms	(+ (+ (* x y) (* x z)) (* y z))
36.0ms	(sqrt (+ (+ (* x y) (* x z)) (* y z)))

series220.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(+ (* x y) (* x z))
35.0ms	(+ (+ (* x y) (* x z)) (* y z))
143.0ms	(sqrt (+ (+ (* x y) (* x z)) (* y z)))

simplify160.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 3 (151.0ms)

Iter	Nodes	Cost
0	291	511
1	1033	462
2	4363	453
3	5001	452

prune260.0ms

Filtered

110 candidates to 69 candidates (62.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	103	7	110
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	103	8	111

Merged error: 15.6b

Counts

111 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (+ (* x y) (* x z)) (* y z))
0.6b	(+ (+ (* x y) (* x z)) (* y z))
15.6b	(sqrt (+ (+ (* x y) (* x z)) (* y z)))
15.6b	(sqrt (+ (+ (* x y) (* x z)) (* y z)))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

140×	`*-un-lft-identity`
88×	`distribute-lft-out`
68×	`associate-l`
26×	`sqrt-prod`
24×	`add-sqr-sqrt` `fma-def`
14×	`add-log-exp`
12×	`add-cube-cbrt`
6×	`pow1` `sum-log`
4×	`add-exp-log` `+-commutative` `expm1-log1p-u` `associate-+l+` `flip3-+` `sqrt-div` `associate-r` `*-commutative` `add-cbrt-cube` `flip-+` `hypot-def` `log1p-expm1-u`
2×	`rem-sqrt-square` `distribute-rgt-out` `sqrt-pow1` `pow1/2` `unswap-sqr`

Counts

4 → 134

Calls

4 calls:

25.0ms	(+ (+ (* x y) (* x z)) (* y z))
24.0ms	(+ (+ (* x y) (* x z)) (* y z))
28.0ms	(sqrt (+ (+ (* x y) (* x z)) (* y z)))
24.0ms	(sqrt (+ (+ (* x y) (* x z)) (* y z)))

series272.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(+ (+ (* x y) (* x z)) (* y z))
21.0ms	(+ (+ (* x y) (* x z)) (* y z))
112.0ms	(sqrt (+ (+ (* x y) (* x z)) (* y z)))
117.0ms	(sqrt (+ (+ (* x y) (* x z)) (* y z)))

simplify119.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 3 (103.0ms)

Iter	Nodes	Cost
0	203	842
1	732	754
2	3298	738
3	5001	736

prune394.0ms

Filtered

146 candidates to 82 candidates (56.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	144	2	146
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	145	9	154

Merged error: 15.6b

Counts

154 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

11.6b	(cbrt (+ (* x y) (* x z)))
11.6b	(cbrt (+ (* x y) (* x z)))
15.6b	(sqrt (fma (* (cbrt (+ (* x y) (* x z))) (cbrt (+ (* x y) (* x z)))) (cbrt (+ (* x y) (* x z))) (* y z)))
15.6b	(sqrt (+ (+ (* x y) (* x z)) (* y z)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

56×	`*-un-lft-identity`
34×	`distribute-lft-out`
29×	`associate-l`
24×	`cbrt-prod`
19×	`add-sqr-sqrt`
16×	`sqrt-prod`
12×	`add-cube-cbrt`
6×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `cbrt-div` `associate-r` `*-commutative` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`rem-sqrt-square` `distribute-rgt-out` `sqrt-pow1` `pow1/2` `pow1/3` `sqrt-div` `hypot-def`
1×	`unswap-sqr`

Counts

4 → 92

Calls

4 calls:

13.0ms	(cbrt (+ (* x y) (* x z)))
13.0ms	(cbrt (+ (* x y) (* x z)))
2.0ms	(sqrt (fma (* (cbrt (+ (* x y) (* x z))) (cbrt (+ (* x y) (* x z)))) (cbrt (+ (* x y) (* x z))) (* y z)))
28.0ms	(sqrt (+ (+ (* x y) (* x z)) (* y z)))

series756.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(cbrt (+ (* x y) (* x z)))
130.0ms	(cbrt (+ (* x y) (* x z)))
390.0ms	(sqrt (fma (* (cbrt (+ (* x y) (* x z))) (cbrt (+ (* x y) (* x z)))) (cbrt (+ (* x y) (* x z))) (* y z)))
114.0ms	(sqrt (+ (+ (* x y) (* x z)) (* y z)))

simplify67.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	505	1038
1	1805	980
2	5001	777

prune429.0ms

Filtered

104 candidates to 74 candidates (71.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	102	2	104
Fresh	2	4	6
Picked	0	1	1
Done	1	1	2
Total	105	8	113

Merged error: 15.6b

Counts

113 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(+ (* (* (cbrt x) (cbrt x)) (* (cbrt x) (+ y z))) (* y z))
15.6b	(sqrt (+ (* (* (cbrt x) (cbrt x)) (* (cbrt x) (+ y z))) (* y z)))

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

372×	`add-sqr-sqrt`
205×	`unswap-sqr`
107×	`cbrt-prod`
76×	`fma-def`
57×	`associate-l`
56×	`hypot-def`
47×	`*-un-lft-identity`
27×	`associate-r`
24×	`swap-sqr`
21×	`add-cube-cbrt`
13×	`distribute-lft-out`
12×	`*-commutative`
9×	`sqrt-prod`
8×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
6×	`add-log-exp`
5×	`pow1` `+-commutative`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
2×	`flip3-+` `pow1/3` `sqrt-div` `flip-+`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `sum-log`

Counts

4 → 208

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
71.0ms	(+ (* (* (cbrt x) (cbrt x)) (* (cbrt x) (+ y z))) (* y z))
71.0ms	(sqrt (+ (* (* (cbrt x) (cbrt x)) (* (cbrt x) (+ y z))) (* y z)))

series579.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(cbrt x)
188.0ms	(cbrt x)
60.0ms	(+ (* (* (cbrt x) (cbrt x)) (* (cbrt x) (+ y z))) (* y z))
145.0ms	(sqrt (+ (* (* (cbrt x) (cbrt x)) (* (cbrt x) (+ y z))) (* y z)))

simplify228.0ms

Algorithm

egg-herbie

Counts

220 → 220

Iterations

Useful iterations: 3 (213.0ms)

Iter	Nodes	Cost
0	298	731
1	1006	654
2	4950	586
3	5001	583

prune681.0ms

Filtered

220 candidates to 165 candidates (75.0%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	214	6	220
Fresh	2	3	5
Picked	1	0	1
Done	0	2	2
Total	217	11	228

Merged error: 10.2b

Counts

228 → 11

regimes648.0ms

Accuracy

50.2% (3.6b remaining)

Error of 15.7b against oracle of 12.2b and baseline of 19.3b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	24
1	36	24

end0.0ms

sample818.0ms

Algorithm

intervals

Results

252.0ms	8000×	body	80	valid
241.0ms	7991×	body	80	nan