Details

sample32.0ms

Algorithm

intervals

Results

22.0ms

256×

body

valid

simplify14.0ms

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: 39.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
36.2b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite69.0ms

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:

3.0ms	(+ (* x x) (* y y))
13.0ms	(+ (+ (* x x) (* y y)) (* z z))
29.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
20.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series311.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(+ (* x x) (* y y))
39.0ms	(+ (+ (* x x) (* y y)) (* z z))
58.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
182.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify46.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (36.0ms)

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

prune356.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 21.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.3b	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
36.1b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
29×	`sqrt-prod`
18×	`*-un-lft-identity`
16×	`add-cube-cbrt` `associate-r`
13×	`times-frac`
11×	`add-log-exp`
9×	`pow1` `sqrt-div`
8×	`unswap-sqr`
6×	`add-exp-log` `associate-l` `add-cbrt-cube`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `fma-def` `sum-log` `log1p-expm1-u`
3×	`sqrt-pow1` `pow1/2` `pow-prod-down`
2×	`+-commutative` `frac-times` `associate-*l/`
1×	`rem-sqrt-square` `associate-+l+` `sqrt-unprod` `associate-r/` `prod-exp` `-commutative` `cbrt-unprod` `hypot-def` `div-inv`

Counts

4 → 101

Calls

4 calls:

3.0ms	(+ (* x x) (* y y))
13.0ms	(+ (+ (* x x) (* y y)) (* z z))
41.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
19.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series391.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(+ (* x x) (* y y))
48.0ms	(+ (+ (* x x) (* y y)) (* z z))
195.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
119.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify49.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	372	1017
1	1570	959
2	5001	931

prune351.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 17.8b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.3b	(* (hypot (sqrt (+ (* x x) (* y y))) z) (sqrt (/ 1 3.0)))
31.0b	(sqrt (+ (* x x) (* y y)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
19×	`sqrt-prod`
16×	`associate-r`
14×	`*-un-lft-identity`
13×	`add-cube-cbrt`
11×	`times-frac`
6×	`pow1`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`unswap-sqr`
3×	`expm1-log1p-u` `sqrt-div` `associate-l` `log1p-expm1-u`
2×	`flip3-+` `flip-+`
1×	`+-commutative` `rem-sqrt-square` `hypot-udef` `fma-def` `sqrt-pow1` `pow1/2` `sqrt-unprod` `associate-r/` `pow-prod-down` `prod-exp` `sum-log` `-commutative` `cbrt-unprod` `hypot-def` `div-inv`

Counts

3 → 70

Calls

3 calls:

3.0ms	(+ (* x x) (* y y))
11.0ms	(* (hypot (sqrt (+ (* x x) (* y y))) z) (sqrt (/ 1 3.0)))
4.0ms	(sqrt (+ (* x x) (* y y)))

series345.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(+ (* x x) (* y y))
270.0ms	(* (hypot (sqrt (+ (* x x) (* y y))) z) (sqrt (/ 1 3.0)))
42.0ms	(sqrt (+ (* x x) (* y y)))

simplify104.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 3 (97.0ms)

Iter	Nodes	Cost
0	282	602
1	1099	552
2	4023	531
3	5001	530

prune254.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 1 expressions with local error:

0.3b	(* (hypot (hypot x y) z) (sqrt (/ 1 3.0)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
16×	`associate-r` `sqrt-prod`
11×	`*-un-lft-identity` `times-frac`
10×	`add-cube-cbrt`
4×	`unswap-sqr`
3×	`pow1` `add-exp-log` `associate-l` `add-cbrt-cube`
1×	`expm1-log1p-u` `hypot-udef` `sqrt-unprod` `sqrt-div` `associate-r/` `pow-prod-down` `prod-exp` `-commutative` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 38

Calls

1 calls:

12.0ms

(* (hypot (hypot x y) z) (sqrt (/ 1 3.0)))

series296.0ms

Counts

1 → 3

Calls

1 calls:

296.0ms

(* (hypot (hypot x y) z) (sqrt (/ 1 3.0)))

simplify61.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 3 (29.0ms)

Iter	Nodes	Cost
0	156	290
1	490	268
2	1216	252
3	2232	241
4	5003	241

prune110.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

regimes47.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	5
1	13	5

end0.0ms

sample1.1s

Algorithm

intervals

Results

918.0ms

8000×

body

valid