Details

Time bar (total: 5.1s)

sample21.0ms

Algorithm
intervals
Results
10.0ms256×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: 36.2b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (* x x) (* y y)) (* z z))
0.0b
(+ (* x x) (* y y))
0.1b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
33.7b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite63.0ms

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:
12.0ms
(+ (+ (* x x) (* y y)) (* z z))
3.0ms
(+ (* x x) (* y y))
30.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
17.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series277.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(+ (+ (* x x) (* y y)) (* z z))
29.0ms
(+ (* x x) (* y y))
48.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
163.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify41.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0325828
11345761
25001755

prune258.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 16.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
33.6b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
33.6b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
33.7b
(sqrt (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))

rewrite118.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
24×sqrt-prod
22×times-frac associate-*r*
21×add-cube-cbrt *-un-lft-identity
17×sqrt-div
11×pow1
9×add-exp-log add-cbrt-cube
6×flip3-+ associate-*l* flip-+ unswap-sqr
4×frac-times sqrt-pow1 associate-*l/ add-log-exp
3×pow1/2
2×rem-sqrt-square associate-*r/ pow-prod-down prod-exp cbrt-unprod
1×cbrt-undiv div-exp *-commutative div-inv
Counts
4 → 98
Calls
4 calls:
67.0ms
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
13.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
13.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
21.0ms
(sqrt (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))

series434.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
103.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
105.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
172.0ms
(sqrt (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))

simplify53.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
03321540
114551341
250011274

prune286.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 16.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
0.0b
(+ (pow y 2) (pow z 2))
0.1b
(* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2))))
33.7b
(sqrt (* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2)))))

rewrite190.0ms

Algorithm
rewrite-expression-head
Rules
26×*-un-lft-identity
12×distribute-lft-out
11×add-log-exp
9×pow1
8×add-sqr-sqrt unpow-prod-down
6×add-exp-log add-cube-cbrt associate-*r* add-cbrt-cube
4×flip3-+ associate-*r/ sum-log flip-+
3×associate-*l*
2×+-commutative sqrt-pow1 sqrt-div pow-prod-down
1×distribute-rgt-in associate-+r+ distribute-lft-in pow1/2 prod-exp sqrt-prod *-commutative cbrt-unprod unswap-sqr
Counts
4 → 67
Calls
4 calls:
33.0ms
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
10.0ms
(+ (pow y 2) (pow z 2))
116.0ms
(* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2))))
29.0ms
(sqrt (* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2)))))

series291.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
27.0ms
(+ (pow y 2) (pow z 2))
54.0ms
(* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2))))
169.0ms
(sqrt (* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2)))))

simplify41.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0269551
11403506
25002504

prune192.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 16.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
0.5b
(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))))
33.6b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
33.6b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite191.0ms

Algorithm
rewrite-expression-head
Rules
574×sqrt-prod
344×add-sqr-sqrt
284×times-frac
154×add-cube-cbrt *-un-lft-identity
73×swap-sqr
43×associate-*r* associate-*l*
36×unswap-sqr
21×pow1
10×sqrt-pow1 pow1/2 sqrt-div
8×add-exp-log add-cbrt-cube
6×associate-/r* associate-/l*
5×pow-prod-up div-inv
4×add-log-exp
3×flip3-+ pow-prod-down pow-sqr flip-+
2×rem-sqrt-square associate-/l/
1×cbrt-undiv pow2 frac-times sqrt-undiv frac-2neg pow-plus sqrt-unprod associate-*r/ div-exp associate-*l/ prod-exp clear-num rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 316
Calls
4 calls:
26.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
114.0ms
(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))))
16.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
13.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series675.0ms

Counts
4 → 12
Calls
4 calls:
224.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
235.0ms
(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))))
105.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
110.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify115.0ms

Algorithm
egg-herbie
Counts
328 → 328
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
04495730
120535405
250015370

prune648.0ms

Pruning

11 alts after pruning (7 fresh and 4 done)

Merged error: 16.3b

regimes574.0ms

Accuracy

54.8% (8.8b remaining)

Error of 27.2b against oracle of 18.4b and baseline of 37.8b

bsearch147.0ms

Steps
ItersRangePoint
9
4.425494315758786e+67
1.2216548257337095e+75
1.199826361110612e+75
9
5.3983651447771314e+42
4.003892320803535e+50
5.4695075101521495e+42
9
2.116861950278137e-44
1.6968575466374542e-37
1.4232710093281964e-37
5
-3.768557111860464e+133
-1.2841116935308668e+133
-2.016424411749676e+133

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04037
14237
24237

end0.0ms

sample460.0ms

Algorithm
intervals
Results
285.0ms8000×body80valid