Details

sample27.0ms

Algorithm

intervals

Results

18.0ms

256×

body

valid

simplify8.0ms

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: 39.0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
36.3b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 58

Calls

2 calls:

29.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
17.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series213.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
165.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify103.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	223	655
1	877	586
2	3651	577
3	5001	577

prune191.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 18.5b

localize16.0ms

Local error

Found 2 expressions with local error:

0.4b	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
36.2b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 69

Calls

2 calls:

39.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
14.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series273.0ms

Counts

2 → 6

Calls

2 calls:

173.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
99.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify71.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 3 (63.0ms)

Iter	Nodes	Cost
0	243	819
1	804	784
2	2795	760
3	5002	747

prune190.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 12.9b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot (sqrt (+ (* x x) (* y y))) z)
0.4b	(* (hypot (sqrt (+ (* x x) (* y y))) z) (sqrt (/ 1 3.0)))
29.9b	(sqrt (+ (* x x) (* y y)))

rewrite16.0ms

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`
4×	`unswap-sqr`
3×	`expm1-log1p-u` `sqrt-div` `associate-l` `log1p-expm1-u` `add-log-exp`
2×	`hypot-udef`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-unprod` `associate-r/` `pow-prod-down` `prod-exp` `-commutative` `cbrt-unprod` `flip-+` `hypot-def` `div-inv`

Counts

3 → 66

Calls

3 calls:

0.0ms	(hypot (sqrt (+ (* x x) (* y y))) z)
11.0ms	(* (hypot (sqrt (+ (* x x) (* y y))) z) (sqrt (/ 1 3.0)))
4.0ms	(sqrt (+ (* x x) (* y y)))

series440.0ms

Counts

3 → 9

Calls

3 calls:

171.0ms	(hypot (sqrt (+ (* x x) (* y y))) z)
235.0ms	(* (hypot (sqrt (+ (* x x) (* y y))) z) (sqrt (/ 1 3.0)))
34.0ms	(sqrt (+ (* x x) (* y y)))

simplify121.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 3 (49.0ms)

Iter	Nodes	Cost
0	247	605
1	745	553
2	1939	536
3	4658	525
4	5001	525

prune211.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot (hypot x y) z)
0.0b	(hypot x y)
0.4b	(* (hypot (hypot x y) z) (sqrt (/ 1 3.0)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 58

Calls

3 calls:

0.0ms	(hypot (hypot x y) z)
0.0ms	(hypot x y)
11.0ms	(* (hypot (hypot x y) z) (sqrt (/ 1 3.0)))

series497.0ms

Counts

3 → 9

Calls

3 calls:

192.0ms	(hypot (hypot x y) z)
44.0ms	(hypot x y)
261.0ms	(* (hypot (hypot x y) z) (sqrt (/ 1 3.0)))

simplify68.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 3 (34.0ms)

Iter	Nodes	Cost
0	175	358
1	509	328
2	1236	312
3	2257	301
4	5001	301

prune186.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

regimes48.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	5
1	13	5

end0.0ms

sample734.0ms

Algorithm

intervals

Results

561.0ms

8000×

body

valid