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	15	7
1	22	7
2	24	7
3	24	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.4b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.3b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
34.6b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
13×	`sqrt-prod`
11×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`sum-log`
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 → 78

Calls

4 calls:

4.0ms	(+ (* x x) (* y y))
6.0ms	(+ (+ (* x x) (* y y)) (* z z))
8.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
5.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series272.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(+ (* x x) (* y y))
35.0ms	(+ (+ (* x x) (* y y)) (* z z))
50.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
159.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify38.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	325	828
1	1345	761
2	5001	755

prune242.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 16.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.4b	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
34.8b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
29×	`sqrt-prod`
17×	`*-un-lft-identity`
16×	`associate-r`
15×	`add-cube-cbrt`
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×	`sum-log`
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` `div-inv`

Counts

4 → 88

Calls

4 calls:

4.0ms	(+ (* x x) (* y y))
6.0ms	(+ (+ (* x x) (* y y)) (* z z))
15.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series340.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ (* x x) (* y y))
39.0ms	(+ (+ (* x x) (* y y)) (* z z))
172.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
102.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify48.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	354	986
1	1482	945
2	5001	924

prune245.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 16.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.4b	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
34.8b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 102

Calls

4 calls:

4.0ms	(+ (* x x) (* y y))
9.0ms	(+ (+ (* x x) (* y y)) (* z z))
9.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series378.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* x x) (* y y))
39.0ms	(+ (+ (* x x) (* y y)) (* z z))
215.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
97.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify44.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	330	1316
1	1338	1241
2	5002	1218

prune260.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 11.2b

localize5.0ms

Local error

Found 1 expressions with local error:

0.4b	(/ x (sqrt 3.0))

rewrite5.0ms

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:

4.0ms

(/ x (sqrt 3.0))

series54.0ms

Counts

1 → 3

Calls

1 calls:

54.0ms

(/ x (sqrt 3.0))

simplify49.0ms

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

prune70.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 11.2b

regimes662.0ms

Accuracy

41.2% (15.1b remaining)

Error of 27.5b against oracle of 12.3b and baseline of 38.1b

bsearch146.0ms

Steps

Iters	Range		Point
1	2.9327781880365277e+74	3.19599804787263e+74	3.1301930829136045e+74
8	2.3072659915934912e-49	9.553185046318115e-46	3.091893896959137e-47
7	1.9648999546114105e-170	4.36395176946701e-168	4.3156769894868627e-169
9	-3.0449375107827034e-277	-3.672009949019216e-282	-3.3197380773614497e-280
6	-2.038249239639625e+41	-4.492569743774758e+40	-2.009142108550562e+41

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	57	44
1	65	44
2	70	44
3	70	44

end0.0ms

sample442.0ms

Algorithm

intervals

Results

276.0ms

8000×

body

valid