Details

Time bar (total: 3.2s)

sample19.0ms

Algorithm
intervals
Results
9.0ms256×body80valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0157
1227
2247
3247

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.7b

localize13.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
36.0b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×times-frac
17×add-cube-cbrt *-un-lft-identity
13×sqrt-prod
4×add-exp-log add-cbrt-cube
3×pow1 associate-/r* associate-/l*
2×rem-sqrt-square div-inv associate-/l/ add-log-exp
1×cbrt-undiv frac-2neg sqrt-pow1 flip3-+ pow1/2 sqrt-div div-exp clear-num flip-+
Counts
2 → 54
Calls
2 calls:
8.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
5.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series225.0ms

Counts
2 → 6
Calls
2 calls:
50.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
175.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify93.0ms

Algorithm
egg-herbie
Counts
60 → 60
Iterations

Useful iterations: 3 (86.0ms)

IterNodesCost
0214630
1835578
23408576
35001574

prune173.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 19.4b

localize12.0ms

Local error

Found 2 expressions with local error:

0.1b
(* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2))))
36.0b
(sqrt (* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2)))))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity
7×pow1
6×add-sqr-sqrt associate-*r*
5×distribute-lft-out
4×add-exp-log add-cube-cbrt associate-*r/ add-cbrt-cube
3×unpow-prod-down associate-*l*
2×sqrt-pow1 flip3-+ sqrt-div pow-prod-down flip-+ add-log-exp
1×distribute-rgt-in distribute-lft-in pow1/2 prod-exp sqrt-prod *-commutative cbrt-unprod unswap-sqr
Counts
2 → 38
Calls
2 calls:
13.0ms
(* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2))))
11.0ms
(sqrt (* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2)))))

series219.0ms

Counts
2 → 6
Calls
2 calls:
53.0ms
(* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2))))
165.0ms
(sqrt (* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2)))))

simplify34.0ms

Algorithm
egg-herbie
Counts
44 → 44
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0211340
11120308
25002307

prune106.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 19.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
36.0b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
36.0b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
36.0b
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0)) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))))

rewrite38.0ms

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:
9.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
5.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
5.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
15.0ms
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0)) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))))

series669.0ms

Counts
4 → 12
Calls
4 calls:
236.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
102.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
102.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
228.0ms
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0)) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))))

simplify91.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
02381481
17281407
236131383
350021383

prune321.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 19.4b

localize3.0ms

Local error

Found 1 expressions with local error:

0.2b
(* x (sqrt 0.3333333333333333))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×associate-*r*
4×add-cube-cbrt *-un-lft-identity sqrt-prod
3×pow1 add-exp-log associate-*l* add-cbrt-cube
2×unswap-sqr
1×pow-prod-down prod-exp *-commutative cbrt-unprod add-log-exp
Counts
1 → 22
Calls
1 calls:
5.0ms
(* x (sqrt 0.3333333333333333))

series44.0ms

Counts
1 → 3
Calls
1 calls:
44.0ms
(* x (sqrt 0.3333333333333333))

simplify56.0ms

Algorithm
egg-herbie
Counts
25 → 25
Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
06984
124580
256978
389378
4200178
5500178

prune30.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 19.4b

regimes486.0ms

Accuracy

61% (7.5b remaining)

Error of 26.4b against oracle of 18.9b and baseline of 38.2b

bsearch83.0ms

Steps
ItersRangePoint
10
1.293024730927888e+62
7.859475946845184e+79
6.320553119104956e+79
9
-1.7197323818274665e+112
-6.983454415202426e+105
-4.3608302761035286e+110

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02812
13412
23412

end0.0ms

sample447.0ms

Algorithm
intervals
Results
287.0ms8000×body80valid