Details

sample19.0ms

Algorithm

intervals

Results

8.0ms

256×

body

valid

simplify17.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

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: 38.2b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
35.6b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 72

Calls

3 calls:

3.0ms	(+ (* x x) (* y y))
30.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
17.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series281.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(+ (* x x) (* y y))
57.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
194.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify141.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	310	729
1	1303	650
2	4811	634
3	5001	634

prune261.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 18.5b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.4b	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
35.5b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 83

Calls

3 calls:

3.0ms	(+ (* x x) (* y y))
44.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
15.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series331.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(+ (* x x) (* y y))
183.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
116.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify59.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	333	887
1	1288	848
2	5001	821

prune262.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 13.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (sqrt (+ (* x x) (* y y))) z)
0.0b	(+ (* x x) (* y y))
0.4b	(* (hypot (sqrt (+ (* x x) (* y y))) z) (sqrt (/ 1 3.0)))
31.0b	(sqrt (+ (* x x) (* y y)))

rewrite21.0ms

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))
12.0ms	(* (hypot (sqrt (+ (* x x) (* y y))) z) (sqrt (/ 1 3.0)))
4.0ms	(sqrt (+ (* x x) (* y y)))

series525.0ms

Counts

4 → 12

Calls

4 calls:

193.0ms	(hypot (sqrt (+ (* x x) (* y y))) z)
29.0ms	(+ (* x x) (* y y))
259.0ms	(* (hypot (sqrt (+ (* x x) (* y y))) z) (sqrt (/ 1 3.0)))
43.0ms	(sqrt (+ (* x x) (* y y)))

simplify118.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 3 (109.0ms)

Iter	Nodes	Cost
0	285	679
1	1102	617
2	4026	596
3	5001	595

prune290.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite14.0ms

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 (hypot x y) z)
12.0ms	(* (hypot (hypot x y) z) (sqrt (/ 1 3.0)))

series479.0ms

Counts

2 → 6

Calls

2 calls:

200.0ms	(hypot (hypot x y) z)
279.0ms	(* (hypot (hypot x y) z) (sqrt (/ 1 3.0)))

simplify69.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 3 (33.0ms)

Iter	Nodes	Cost
0	161	331
1	493	304
2	1218	288
3	2234	277
4	5002	277

prune147.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

regimes57.0ms

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

sample438.0ms

Algorithm

intervals

Results

266.0ms

8000×

body

valid