Details

sample35.0ms

Algorithm

intervals

Results

25.0ms

256×

body

valid

simplify9.0ms

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: 42.0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.3b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
38.8b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite50.0ms

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

series281.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(+ (* x x) (* y y))
64.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
187.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify132.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (33.0ms)

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

prune272.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 21.4b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma x x (* y y))
0.3b	(* 0.3333333333333333 (fma z z (fma x x (* y y))))
38.8b	(sqrt (* 0.3333333333333333 (fma z z (fma x x (* y y)))))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

8×	`pow1`
7×	`add-sqr-sqrt`
5×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
3×	`expm1-log1p-u` `associate-r` `associate-l` `fma-udef` `log1p-expm1-u` `add-log-exp`
2×	`sqrt-pow1` `pow-prod-down`
1×	`distribute-rgt-in` `distribute-lft-in` `pow1/2` `prod-exp` `sqrt-prod` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

3 → 45

Calls

3 calls:

0.0ms	(fma x x (* y y))
3.0ms	(* 0.3333333333333333 (fma z z (fma x x (* y y))))
2.0ms	(sqrt (* 0.3333333333333333 (fma z z (fma x x (* y y)))))

series318.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(fma x x (* y y))
73.0ms	(* 0.3333333333333333 (fma z z (fma x x (* y y))))
206.0ms	(sqrt (* 0.3333333333333333 (fma z z (fma x x (* y y)))))

simplify81.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	138	272
1	551	235
2	2915	235
3	5002	235

prune152.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.2b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.3b	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
39.0b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 97

Calls

3 calls:

3.0ms	(+ (* x x) (* y y))
24.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
15.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series395.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(+ (* x x) (* y y))
251.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
114.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify118.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 3 (99.0ms)

Iter	Nodes	Cost
0	309	1218
1	1145	1151
2	4412	1124
3	5001	1123

prune277.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(hypot (sqrt (+ (* x x) (* y y))) z)
0.3b	(/ (hypot (sqrt (+ (* x x) (* y y))) z) (sqrt 3.0))
29.2b	(sqrt (+ (* x x) (* y y)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

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

series580.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(+ (* x x) (* y y))
178.0ms	(hypot (sqrt (+ (* x x) (* y y))) z)
324.0ms	(/ (hypot (sqrt (+ (* x x) (* y y))) z) (sqrt 3.0))
41.0ms	(sqrt (+ (* x x) (* y y)))

simplify87.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 3 (79.0ms)

Iter	Nodes	Cost
0	252	805
1	915	743
2	3048	725
3	5002	724

prune279.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes159.0ms

Accuracy

0% (0.3b 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	15	5
2	15	5

end0.0ms

sample899.0ms

Algorithm

intervals

Results

718.0ms

8000×

body

valid