Details

sample17.0ms

Algorithm

intervals

Results

8.0ms

256×

body

valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	16	7
1	27	7
2	33	7
3	34	7
4	34	7

prune2.0ms

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: 37.6b

Counts

2 → 1

localize12.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
34.7b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

313×	`*-un-lft-identity`
160×	`distribute-lft-out`
104×	`associate-l`
85×	`times-frac`
46×	`sqrt-prod`
44×	`add-sqr-sqrt`
41×	`add-cube-cbrt`
28×	`associate-/l*`
24×	`swap-sqr`
22×	`sqrt-div`
6×	`associate-/r*`
4×	`add-exp-log` `add-cbrt-cube` `associate-/l/`
3×	`pow1`
2×	`expm1-log1p-u` `rem-sqrt-square` `frac-2neg` `flip3-+` `clear-num` `flip-+` `log1p-expm1-u` `div-inv` `add-log-exp`
1×	`cbrt-undiv` `sqrt-pow1` `pow1/2` `div-exp`

Counts

2 → 156

Calls

2 calls:

33.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
31.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series218.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
169.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify155.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	276	1542
1	1058	1377
2	4500	1355
3	5001	1355

prune246.0ms

Filtered

162 candidates to 64 candidates (39.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	156	6	162
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	157	6	163

Merged error: 17.4b

Counts

163 → 6

localize11.0ms

Local error

Found 2 expressions with local error:

0.4b	(* (+ (+ (* x x) (* y y)) (* z z)) (/ 1 3.0))
34.7b	(sqrt (* (+ (+ (* x x) (* y y)) (* z z)) (/ 1 3.0)))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

104×	`*-un-lft-identity`
54×	`associate-l`
53×	`add-sqr-sqrt`
40×	`distribute-lft-out`
36×	`frac-times`
35×	`sqrt-prod`
32×	`sqrt-div`
31×	`add-cube-cbrt`
26×	`associate-r`
24×	`times-frac`
20×	`flip3-+` `flip-+` `associate-/l*`
18×	`associate-r/` `associate-/r`
11×	`add-exp-log`
9×	`unswap-sqr`
8×	`clear-num`
7×	`pow1` `add-cbrt-cube`
6×	`frac-2neg` `swap-sqr` `un-div-inv`
4×	`rem-sqrt-square` `associate-*l/` `prod-exp`
2×	`expm1-log1p-u` `sqrt-pow1` `div-exp` `pow-prod-down` `*-commutative` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`
1×	`cbrt-undiv` `rec-exp` `pow1/2` `1-exp`

Counts

2 → 162

Calls

2 calls:

35.0ms	(* (+ (+ (* x x) (* y y)) (* z z)) (/ 1 3.0))
42.0ms	(sqrt (* (+ (+ (* x x) (* y y)) (* z z)) (/ 1 3.0)))

series228.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(* (+ (+ (* x x) (* y y)) (* z z)) (/ 1 3.0))
173.0ms	(sqrt (* (+ (+ (* x x) (* y y)) (* z z)) (/ 1 3.0)))

simplify91.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	477	1990
1	2240	1826
2	5001	1751

prune355.0ms

Filtered

168 candidates to 87 candidates (51.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	166	2	168
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	168	6	174

Merged error: 17.4b

Counts

174 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ 1 3.0))))
0.4b	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ 1 3.0))
34.8b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
34.8b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite219.0ms

Algorithm

rewrite-expression-head

Rules

312×	`sqrt-div`
237×	`*-un-lft-identity`
188×	`sqrt-prod`
175×	`add-sqr-sqrt`
136×	`frac-times`
119×	`associate-l`
100×	`distribute-lft-out`
75×	`flip3-+` `flip-+`
70×	`associate-r`
68×	`associate-*r/`
56×	`unswap-sqr`
53×	`add-cube-cbrt`
40×	`associate-/l*`
38×	`times-frac`
36×	`associate-/r*`
17×	`swap-sqr`
16×	`clear-num`
15×	`pow1` `add-exp-log`
12×	`frac-2neg` `un-div-inv`
11×	`add-cbrt-cube`
10×	`associate-*l/` `hypot-def`
6×	`sqrt-pow1` `pow-prod-down`
5×	`prod-exp` `*-commutative`
4×	`expm1-log1p-u` `pow1/2` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-unprod`
2×	`rem-sqrt-square` `div-exp` `div-inv`
1×	`cbrt-undiv` `rec-exp` `sqrt-unprod` `1-exp`

Counts

4 → 354

Calls

4 calls:

93.0ms	(* (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ 1 3.0))))
40.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ 1 3.0))
26.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
27.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series497.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(* (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ 1 3.0))))
111.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ 1 3.0))
104.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
107.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify130.0ms

Algorithm

egg-herbie

Counts

366 → 366

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	779	7233
1	2358	6951
2	5002	6807

prune955.0ms

Filtered

366 candidates to 185 candidates (50.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	366	0	366
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	366	6	372

Merged error: 17.4b

Counts

372 → 6

localize11.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
34.8b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

325×	`*-un-lft-identity`
166×	`sqrt-prod`
160×	`distribute-lft-out`
104×	`associate-l`
102×	`times-frac`
64×	`add-sqr-sqrt`
53×	`add-cube-cbrt`
25×	`swap-sqr`
17×	`associate-/l*`
6×	`associate-/r*`
5×	`hypot-def`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
3×	`pow1`
2×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `rem-sqrt-square` `sqrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `*-commutative` `div-inv` `unswap-sqr`

Counts

2 → 175

Calls

2 calls:

35.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
29.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series358.0ms

Counts

2 → 6

Calls

2 calls:

246.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
112.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify90.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 3 (68.0ms)

Iter	Nodes	Cost
0	229	2038
1	628	1971
2	1982	1967
3	5001	1954

prune229.0ms

Filtered

181 candidates to 59 candidates (32.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	177	4	181
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	178	9	187

Merged error: 13.4b

Counts

187 → 9

regimes403.0ms

Accuracy

82.2% (2.6b remaining)

Error of 16.2b against oracle of 13.6b and baseline of 28.4b

bsearch81.0ms

Steps

Iters	Range		Point
7	8.598898606995893e+135	3.265227753953506e+137	3.2268796450835897e+137
9	-3.245969229886643e+141	-4.4608468462434657e+133	-3.168263711041591e+141

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	12
1	33	12
2	33	12

end0.0ms

sample438.0ms

Algorithm

intervals

Results

271.0ms

8000×

body

valid