Details

sample17.0ms

Algorithm

intervals

Results

8.0ms

256×

body

valid

simplify7.0ms

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: 43.4b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
40.4b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite48.0ms

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:

2.0ms	(+ (* x x) (* y y))
31.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
13.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series242.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(+ (* x x) (* y y))
48.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
164.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify122.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (114.0ms)

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

prune201.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 21.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
40.4b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
40.4b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
40.4b	(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0)) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

49×	`sqrt-prod`
36×	`add-sqr-sqrt` `times-frac`
34×	`add-cube-cbrt` `*-un-lft-identity`
14×	`pow1`
9×	`sqrt-div`
8×	`sqrt-pow1`
6×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
4×	`add-log-exp`
3×	`rem-sqrt-square` `flip3-+` `pow1/2` `flip-+`
2×	`associate-/l/`
1×	`cbrt-undiv` `pow2` `frac-times` `sqrt-undiv` `frac-2neg` `pow-plus` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `clear-num` `pow-sqr` `pow-prod-up` `div-inv`

Counts

4 → 112

Calls

4 calls:

21.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
12.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
14.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
21.0ms	(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0)) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))))

series643.0ms

Counts

4 → 12

Calls

4 calls:

232.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
97.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
96.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
218.0ms	(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0)) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))))

simplify88.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	238	1481
1	728	1407
2	3613	1383
3	5002	1383

prune347.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 21.2b

localize11.0ms

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)))
40.4b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

33×	`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×	`sqrt-pow1` `pow1/2` `pow-prod-down`
2×	`frac-times` `associate-*l/`
1×	`+-commutative` `rem-sqrt-square` `sqrt-unprod` `associate-r/` `prod-exp` `sum-log` `-commutative` `cbrt-unprod` `div-inv`

Counts

3 → 75

Calls

3 calls:

2.0ms	(+ (* x x) (* y y))
36.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
15.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series315.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(+ (* x x) (* y y))
193.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
94.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify121.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (107.0ms)

Iter	Nodes	Cost
0	318	858
1	1226	828
2	4730	804
3	5002	796

prune228.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 21.2b

localize3.0ms

Local error

Found 1 expressions with local error:

0.4b	(/ x (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

(/ x (sqrt 3.0))

series83.0ms

Counts

1 → 3

Calls

1 calls:

83.0ms

(/ x (sqrt 3.0))

simplify56.0ms

Algorithm

egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 4 (53.0ms)

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

prune66.0ms

Pruning

15 alts after pruning (12 fresh and 3 done)

Merged error: 21.2b

regimes623.0ms

Accuracy

61.5% (7.6b remaining)

Error of 25.9b against oracle of 18.3b and baseline of 38.1b

bsearch50.0ms

Steps

Iters	Range		Point
7	5.617467149036996e+119	4.0732344434354675e+121	2.816119708780296e+121
5	-1.597925375452575e+48	-5.274225135082189e+47	-1.5602497723888015e+48

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	24
1	38	24
2	41	24
3	41	24

end0.0ms

sample442.0ms

Algorithm

intervals

Results

271.0ms

8000×

body

valid