Details

Time bar (total: 4.2s)

sample32.0ms

Algorithm
intervals
Results
23.0ms256×body80valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0157
1227
2247
3247

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (+ (* x x) (* y y)) (* z z))
0.1b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
34.4b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
19×times-frac
18×add-cube-cbrt *-un-lft-identity
13×sqrt-prod
8×add-log-exp
5×add-exp-log add-cbrt-cube
4×pow1
3×associate-/r* sum-log associate-/l*
2×rem-sqrt-square flip3-+ flip-+ div-inv associate-/l/
1×cbrt-undiv +-commutative associate-+l+ frac-2neg sqrt-pow1 pow1/2 sqrt-div div-exp clear-num
Counts
3 → 67
Calls
3 calls:
14.0ms
(+ (+ (* x x) (* y y)) (* z z))
32.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
14.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series249.0ms

Counts
3 → 9
Calls
3 calls:
39.0ms
(+ (+ (* x x) (* y y)) (* z z))
47.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
162.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify112.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 3 (104.0ms)

IterNodesCost
0259758
11001695
24269689
35002687

prune210.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 15.6b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (+ (* x x) (* y y)) (* z z))
0.1b
(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
34.4b
(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
8×pow1 add-log-exp
7×add-sqr-sqrt
5×add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
4×associate-*r/
3×flip3-+ associate-*r* associate-*l* sum-log flip-+
2×sqrt-pow1 sqrt-div pow-prod-down
1×+-commutative distribute-rgt-in associate-+l+ distribute-lft-in pow1/2 prod-exp sqrt-prod *-commutative cbrt-unprod unswap-sqr
Counts
3 → 48
Calls
3 calls:
14.0ms
(+ (+ (* x x) (* y y)) (* z z))
31.0ms
(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
9.0ms
(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

series246.0ms

Counts
3 → 9
Calls
3 calls:
35.0ms
(+ (+ (* x x) (* y y)) (* z z))
53.0ms
(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
158.0ms
(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

simplify40.0ms

Algorithm
egg-herbie
Counts
57 → 57
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0244469
11256426
25002424

prune134.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 15.6b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (+ (* x x) (* y y)) (* z z))
0.2b
(* (sqrt 0.3333333333333333) (sqrt (+ (+ (* x x) (* y y)) (* z z))))
34.3b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
13×sqrt-prod
8×pow1 add-cube-cbrt *-un-lft-identity add-log-exp
6×associate-*r* associate-*l*
5×add-exp-log add-cbrt-cube
4×sqrt-div unswap-sqr
3×sqrt-pow1 flip3-+ pow1/2 pow-prod-down sum-log flip-+
2×associate-*r/
1×+-commutative rem-sqrt-square associate-+l+ sqrt-unprod prod-exp *-commutative cbrt-unprod
Counts
3 → 60
Calls
3 calls:
14.0ms
(+ (+ (* x x) (* y y)) (* z z))
33.0ms
(* (sqrt 0.3333333333333333) (sqrt (+ (+ (* x x) (* y y)) (* z z))))
13.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series306.0ms

Counts
3 → 9
Calls
3 calls:
35.0ms
(+ (+ (* x x) (* y y)) (* z z))
170.0ms
(* (sqrt 0.3333333333333333) (sqrt (+ (+ (* x x) (* y y)) (* z z))))
101.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify105.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
0220610
1992582
24454575
35001575

prune153.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 15.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (* x x) (* y y)) (* z z))
0.0b
(* (sqrt (sqrt 0.3333333333333333)) (sqrt (+ (+ (* x x) (* y y)) (* z z))))
0.2b
(* (sqrt (sqrt 0.3333333333333333)) (* (sqrt (sqrt 0.3333333333333333)) (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
34.3b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
33×sqrt-prod
26×add-sqr-sqrt
18×associate-*l*
17×pow1
13×add-cube-cbrt *-un-lft-identity
11×add-exp-log add-cbrt-cube
10×pow-prod-down
9×add-log-exp
7×associate-*r*
6×sqrt-pow1 pow1/2 sqrt-div associate-*r/ unswap-sqr
4×flip3-+ prod-exp cbrt-unprod flip-+
3×sqrt-unprod sum-log
2×*-commutative
1×+-commutative rem-sqrt-square associate-+l+
Counts
4 → 94
Calls
4 calls:
11.0ms
(+ (+ (* x x) (* y y)) (* z z))
34.0ms
(* (sqrt (sqrt 0.3333333333333333)) (sqrt (+ (+ (* x x) (* y y)) (* z z))))
45.0ms
(* (sqrt (sqrt 0.3333333333333333)) (* (sqrt (sqrt 0.3333333333333333)) (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
13.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series603.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(+ (+ (* x x) (* y y)) (* z z))
307.0ms
(* (sqrt (sqrt 0.3333333333333333)) (sqrt (+ (+ (* x x) (* y y)) (* z z))))
165.0ms
(* (sqrt (sqrt 0.3333333333333333)) (* (sqrt (sqrt 0.3333333333333333)) (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
95.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify48.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
02961081
11398994
25002991

prune272.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 15.5b

regimes388.0ms

Accuracy

63.2% (7.0b remaining)

Error of 25.5b against oracle of 18.5b and baseline of 37.6b

bsearch68.0ms

Steps
ItersRangePoint
6
1.646495042169786e+116
1.0643100901350527e+117
8.429679290695843e+116
7
-5.131336026657072e+149
-1.466971091299658e+148
-3.6728622288524372e+149

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03420
13520
23920
34120
44120

end0.0ms

sample904.0ms

Algorithm
intervals
Results
728.0ms8000×body80valid