Details

sample29.0ms

Algorithm

intervals

Results

14.0ms

256×

body

valid

simplify10.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.0b	(+ (* x x) (* y y))
0.3b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
35.0b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite61.0ms

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:

11.0ms	(+ (+ (* x x) (* y y)) (* z z))
3.0ms	(+ (* x x) (* y y))
31.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
15.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series315.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(+ (+ (* x x) (* y y)) (* z z))
42.0ms	(+ (* x x) (* y y))
69.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
169.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify40.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (31.0ms)

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

prune259.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 15.5b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.0b	(+ (* x x) (* y y))
0.3b	(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
34.9b	(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

12.0ms	(+ (+ (* x x) (* y y)) (* z z))
2.0ms	(+ (* x x) (* y y))
34.0ms	(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
9.0ms	(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

series287.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(+ (+ (* x x) (* y y)) (* z z))
32.0ms	(+ (* x x) (* y y))
50.0ms	(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
169.0ms	(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

simplify43.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	310	539
1	1615	492
2	5001	492

prune167.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 15.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.2b	(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
0.4b	(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
35.2b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

90×	`add-sqr-sqrt`
75×	`times-frac` `sqrt-prod`
53×	`*-un-lft-identity`
49×	`add-cube-cbrt`
35×	`cbrt-prod`
25×	`associate-r`
16×	`unswap-sqr`
10×	`associate-l`
9×	`pow1`
8×	`add-exp-log`
7×	`add-cbrt-cube`
6×	`associate-/r*` `add-log-exp`
5×	`sqrt-div`
4×	`div-inv`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-/l*`
2×	`flip3-+` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-times` `frac-2neg` `sqrt-unprod` `associate-r/` `div-exp` `associate-l/` `prod-exp` `clear-num` `sum-log` `*-commutative` `cbrt-unprod`

Counts

4 → 155

Calls

4 calls:

2.0ms	(+ (* x x) (* y y))
30.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
68.0ms	(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
16.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

series865.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ (* x x) (* y y))
132.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
345.0ms	(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
361.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

simplify67.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	467	2452
1	1797	2356
2	5002	2337

prune588.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 15.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.0b	(+ (* x x) (* y y))
0.4b	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (sqrt (cbrt 3.0)) (fabs (cbrt 3.0))))
35.1b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

12.0ms	(+ (+ (* x x) (* y y)) (* z z))
2.0ms	(+ (* x x) (* y y))
27.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (sqrt (cbrt 3.0)) (fabs (cbrt 3.0))))
13.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series721.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(+ (+ (* x x) (* y y)) (* z z))
34.0ms	(+ (* x x) (* y y))
552.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (sqrt (cbrt 3.0)) (fabs (cbrt 3.0))))
99.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify112.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	334	842
1	1391	771
2	4983	767
3	5001	767

prune262.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 15.3b

regimes596.0ms

Accuracy

63.2% (7.3b remaining)

Error of 25.7b against oracle of 18.4b and baseline of 38.1b

bsearch76.0ms

Steps

Iters	Range		Point
8	1.1829225377078756e+70	5.1210306950163065e+73	5.054235297312576e+73
8	-8.637657805868028e+137	-2.1049707540843454e+135	-1.9353333948222178e+136

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	20
1	51	20
2	54	20
3	54	20

end0.0ms

sample442.0ms

Algorithm

intervals

Results

271.0ms

8000×

body

valid