Details

sample19.0ms

Algorithm

intervals

Results

9.0ms

256×

body

valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	15	7
1	22	7
2	24	7
3	24	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))

rewrite54.0ms

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×	`associate-/r` `associate-/l`
2×	`rem-sqrt-square` `flip3-+` `flip-+` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-exp` `clear-num` `sum-log`

Counts

3 → 65

Calls

3 calls:

3.0ms	(+ (* x x) (* y y))
30.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
15.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series247.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ (* x x) (* y y))
52.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
169.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify121.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (111.0ms)

Iter	Nodes	Cost
0	294	707
1	1224	644
2	4405	642
3	5001	640

prune247.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 21.4b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (pow y 2) (pow z 2))
0.3b	(* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2))))
38.8b	(sqrt (* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2)))))

rewrite156.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
8×	`pow1`
7×	`add-sqr-sqrt` `distribute-lft-out`
6×	`associate-r`
5×	`add-exp-log` `add-cube-cbrt` `unpow-prod-down` `add-cbrt-cube` `add-log-exp`
4×	`associate-*r/`
3×	`flip3-+` `associate-l` `flip-+`
2×	`sqrt-pow1` `sqrt-div` `pow-prod-down`
1×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `pow1/2` `prod-exp` `sum-log` `sqrt-prod` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

3 → 51

Calls

3 calls:

10.0ms	(+ (pow y 2) (pow z 2))
115.0ms	(* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2))))
30.0ms	(sqrt (* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2)))))

series240.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(+ (pow y 2) (pow z 2))
47.0ms	(* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2))))
162.0ms	(sqrt (* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2)))))

simplify39.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	260	411
1	1384	379
2	5002	378

prune145.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 21.4b

localize14.0ms

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)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

45×	`sqrt-prod`
36×	`times-frac`
33×	`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×	`flip3-+` `flip-+`
2×	`associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `sqrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 89

Calls

3 calls:

3.0ms	(+ (* x x) (* y y))
23.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
14.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series355.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (* x x) (* y y))
229.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
99.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify99.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	294	1188
1	1083	1124
2	4083	1101
3	5001	1101

prune211.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 21.3b

localize3.0ms

Local error

Found 1 expressions with local error:

0.4b	(/ z (sqrt 3.0))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

18×	`times-frac`
16×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`sqrt-prod`
6×	`associate-/r*`
3×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
1×	`pow1` `cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv` `add-log-exp`

Counts

1 → 39

Calls

1 calls:

3.0ms

(/ z (sqrt 3.0))

series57.0ms

Counts

1 → 3

Calls

1 calls:

57.0ms

(/ z (sqrt 3.0))

simplify50.0ms

Algorithm

egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 4 (46.0ms)

Iter	Nodes	Cost
0	103	217
1	273	207
2	729	197
3	2027	197
4	5001	196

prune61.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 21.3b

regimes576.0ms

Accuracy

55.3% (8.8b remaining)

Error of 27.4b against oracle of 18.6b and baseline of 38.3b

bsearch90.0ms

Steps

Iters	Range		Point
3	1.5765673566733113e+121	1.9108656425680437e+121	1.597460999541732e+121
9	1.6611258736907357e+60	4.620139067381952e+65	4.545831989981156e+65
10	-3.5223794056915216e+55	-5.778619763743718e+44	-3.4794970398246474e+55

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	14
1	40	14
2	40	14

end0.0ms

sample422.0ms

Algorithm

intervals

Results

260.0ms

8000×

body

valid