Details

sample28.0ms

Algorithm

intervals

Results

18.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.6b

localize9.0ms

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)
38.7b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite65.0ms

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:

15.0ms	(+ (+ (* x x) (* y y)) (* z z))
3.0ms	(+ (* x x) (* y y))
29.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
15.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series291.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(+ (+ (* x x) (* y y)) (* z z))
27.0ms	(+ (* x x) (* y y))
55.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
168.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify44.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (34.0ms)

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

prune307.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 18.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.0b	(+ (* x x) (* y y))
0.3b	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
38.7b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite76.0ms

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:

13.0ms	(+ (+ (* x x) (* y y)) (* z z))
3.0ms	(+ (* x x) (* y y))
42.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
15.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series337.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(+ (+ (* x x) (* y y)) (* z z))
27.0ms	(+ (* x x) (* y y))
168.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
102.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify49.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (39.0ms)

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

prune310.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 13.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (sqrt (+ (* x x) (* y y))) z)
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)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`sqrt-prod`
16×	`associate-r`
15×	`*-un-lft-identity`
14×	`add-cube-cbrt`
11×	`times-frac`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `unswap-sqr`
3×	`sqrt-div` `associate-l`
2×	`hypot-udef` `flip3-+` `flip-+`
1×	`+-commutative` `rem-sqrt-square` `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

4 → 80

Calls

4 calls:

0.0ms	(hypot (sqrt (+ (* x x) (* y y))) z)
3.0ms	(+ (* x x) (* y y))
10.0ms	(* (hypot (sqrt (+ (* x x) (* y y))) z) (sqrt (/ 1 3.0)))
4.0ms	(sqrt (+ (* x x) (* y y)))

series464.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(hypot (sqrt (+ (* x x) (* y y))) z)
27.0ms	(+ (* x x) (* y y))
232.0ms	(* (hypot (sqrt (+ (* x x) (* y y))) z) (sqrt (/ 1 3.0)))
40.0ms	(sqrt (+ (* x x) (* y y)))

simplify103.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 3 (95.0ms)

Iter	Nodes	Cost
0	285	680
1	1102	617
2	4026	596
3	5001	595

prune261.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 48

Calls

2 calls:

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

series451.0ms

Counts

2 → 6

Calls

2 calls:

188.0ms	(hypot (* 1 (hypot x y)) z)
263.0ms	(* (hypot (* 1 (hypot x y)) z) (sqrt (/ 1 3.0)))

simplify70.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	170	392
1	516	339
2	1450	328
3	2820	328
4	5001	328

prune143.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

regimes55.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	11
1	20	11
2	20	11

end0.0ms

sample674.0ms

Algorithm

intervals

Results

499.0ms

8000×

body

valid