Details

sample17.0ms

Algorithm

intervals

Results

8.0ms

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

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: 36.7b

Counts

2 → 1

localize9.0ms

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)
33.9b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite28.0ms

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:

4.0ms	(+ (* x x) (* y y))
6.0ms	(+ (+ (* x x) (* y y)) (* z z))
11.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
5.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series273.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* x x) (* y y))
39.0ms	(+ (+ (* x x) (* y y)) (* z z))
47.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
160.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify40.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (31.0ms)

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

prune285.0ms

Filtered

102 candidates to 84 candidates (82.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	97	5	102
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	97	6	103

Merged error: 18.5b

Counts

103 → 6

localize11.0ms

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)))
33.9b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite33.0ms

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:

4.0ms	(+ (* x x) (* y y))
6.0ms	(+ (+ (* x x) (* y y)) (* z z))
14.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series333.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* x x) (* y y))
41.0ms	(+ (+ (* x x) (* y y)) (* z z))
166.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
100.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify48.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (37.0ms)

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

prune287.0ms

Filtered

113 candidates to 83 candidates (73.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	113	6	119

Merged error: 12.7b

Counts

119 → 6

localize10.0ms

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)))
27.8b	(sqrt (+ (* x x) (* y y)))

rewrite21.0ms

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:

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

series294.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ (* x x) (* y y))
233.0ms	(* (hypot (sqrt (+ (* x x) (* y y))) z) (sqrt (/ 1 3.0)))
34.0ms	(sqrt (+ (* x x) (* y y)))

simplify98.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 3 (91.0ms)

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

prune217.0ms

Filtered

79 candidates to 59 candidates (74.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	77	2	79
Fresh	4	0	4
Picked	1	0	1
Done	1	0	1
Total	83	2	85

Merged error: 0.1b

Counts

85 → 2

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite10.0ms

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:

1.0ms	(hypot x y)
8.0ms	(* (hypot (* 1 (hypot x y)) z) (sqrt (/ 1 3.0)))

series305.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(hypot x y)
254.0ms	(* (hypot (* 1 (hypot x y)) z) (sqrt (/ 1 3.0)))

simplify66.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	181	364
1	539	317
2	1485	306
3	2912	306
4	5002	306

prune138.0ms

Filtered

54 candidates to 43 candidates (79.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	53	1	54
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	54	2	56

Merged error: 0b

Counts

56 → 2

regimes43.0ms

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	15	6
1	17	6
2	17	6

end0.0ms

sample424.0ms

Algorithm

intervals

Results

261.0ms

8000×

body

valid