Details

sample19.0ms

Algorithm

intervals

Results

9.0ms

256×

body

valid

simplify12.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.6b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.0b	(+ (* x x) (* y y))
0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
35.9b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
20×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
13×	`sqrt-prod`
11×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `fma-def` `sum-log` `log1p-expm1-u`
3×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`+-commutative` `rem-sqrt-square` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `associate-+l+` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-exp` `clear-num`

Counts

4 → 90

Calls

4 calls:

7.0ms	(+ (+ (* x x) (* y y)) (* z z))
4.0ms	(+ (* x x) (* y y))
9.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
6.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series313.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(+ (+ (* x x) (* y y)) (* z z))
31.0ms	(+ (* x x) (* y y))
59.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
182.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify50.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	345	852
1	1445	759
2	5001	739

prune332.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 17.6b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma y y (* z z))
0.1b	(* 0.3333333333333333 (fma x x (fma y y (* z z))))
35.9b	(sqrt (* 0.3333333333333333 (fma x x (fma y y (* z z)))))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

8×	`pow1`
7×	`add-sqr-sqrt`
5×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
3×	`expm1-log1p-u` `associate-r` `associate-l` `fma-udef` `log1p-expm1-u` `add-log-exp`
2×	`sqrt-pow1` `pow-prod-down`
1×	`distribute-rgt-in` `distribute-lft-in` `pow1/2` `prod-exp` `sqrt-prod` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

3 → 45

Calls

3 calls:

1.0ms	(fma y y (* z z))
4.0ms	(* 0.3333333333333333 (fma x x (fma y y (* z z))))
3.0ms	(sqrt (* 0.3333333333333333 (fma x x (fma y y (* z z)))))

series531.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(fma y y (* z z))
63.0ms	(* 0.3333333333333333 (fma x x (fma y y (* z z))))
425.0ms	(sqrt (* 0.3333333333333333 (fma x x (fma y y (* z z)))))

simplify90.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	137	274
1	541	235
2	2831	235
3	5001	235

prune141.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 17.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.0b	(+ (* x x) (* y y))
0.4b	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
35.8b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

45×	`sqrt-prod`
36×	`add-sqr-sqrt` `times-frac`
34×	`add-cube-cbrt` `*-un-lft-identity`
11×	`add-log-exp`
6×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
5×	`pow1`
4×	`expm1-log1p-u` `fma-def` `flip3-+` `sqrt-div` `sum-log` `flip-+` `log1p-expm1-u`
2×	`+-commutative` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `associate-+l+` `sqrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `hypot-def` `div-inv`

Counts

4 → 115

Calls

4 calls:

7.0ms	(+ (+ (* x x) (* y y)) (* z z))
5.0ms	(+ (* x x) (* y y))
10.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
6.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series425.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(+ (+ (* x x) (* y y)) (* z z))
30.0ms	(+ (* x x) (* y y))
239.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
112.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify54.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	348	1348
1	1426	1262
2	5002	1230

prune365.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 11.4b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.4b	(/ (hypot (sqrt (+ (* x x) (* y y))) z) (sqrt 3.0))
28.4b	(sqrt (+ (* x x) (* y y)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
15×	`sqrt-prod`
6×	`associate-/r*`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1`
3×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
2×	`flip3-+` `sqrt-div` `flip-+`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `sqrt-undiv` `hypot-udef` `fma-def` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `sum-log` `hypot-def` `div-inv`

Counts

3 → 74

Calls

3 calls:

4.0ms	(+ (* x x) (* y y))
4.0ms	(/ (hypot (sqrt (+ (* x x) (* y y))) z) (sqrt 3.0))
4.0ms	(sqrt (+ (* x x) (* y y)))

series374.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(+ (* x x) (* y y))
302.0ms	(/ (hypot (sqrt (+ (* x x) (* y y))) z) (sqrt 3.0))
38.0ms	(sqrt (+ (* x x) (* y y)))

simplify96.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 3 (87.0ms)

Iter	Nodes	Cost
0	249	728
1	912	678
2	3040	660
3	5002	659

prune255.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

regimes308.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	5

end0.0ms

sample460.0ms

Algorithm

intervals

Results

276.0ms

8000×

body

valid