Details

Time bar (total: 3.0s)

sample17.0ms

Algorithm
intervals
Results
8.0ms256×body80valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0167
1277
2337
3347
4347

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.7b

localize12.0ms

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))

rewrite17.0ms

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×expm1-log1p-u rem-sqrt-square log1p-expm1-u 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 → 58
Calls
2 calls:
9.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
6.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series237.0ms

Counts
2 → 6
Calls
2 calls:
55.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
182.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify110.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
0223655
1877586
23651577
35001577

prune216.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 19.4b

localize9.0ms

Local error

Found 2 expressions with local error:

0.1b
(* 0.3333333333333333 (fma z z (fma x x (* y y))))
36.0b
(sqrt (* 0.3333333333333333 (fma z z (fma x x (* y y)))))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
7×pow1
6×add-sqr-sqrt
4×add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
3×associate-*r* associate-*l*
2×expm1-log1p-u sqrt-pow1 pow-prod-down fma-udef log1p-expm1-u add-log-exp
1×distribute-rgt-in distribute-lft-in pow1/2 prod-exp sqrt-prod *-commutative cbrt-unprod unswap-sqr
Counts
2 → 35
Calls
2 calls:
4.0ms
(* 0.3333333333333333 (fma z z (fma x x (* y y))))
3.0ms
(sqrt (* 0.3333333333333333 (fma z z (fma x x (* y y)))))

series262.0ms

Counts
2 → 6
Calls
2 calls:
68.0ms
(* 0.3333333333333333 (fma z z (fma x x (* y y))))
194.0ms
(sqrt (* 0.3333333333333333 (fma z z (fma x x (* y y)))))

simplify79.0ms

Algorithm
egg-herbie
Counts
41 → 41
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0126229
1501201
22724201
35002201

prune111.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.2b

localize12.0ms

Local error

Found 2 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)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
45×sqrt-prod
36×times-frac
33×add-sqr-sqrt
31×add-cube-cbrt *-un-lft-identity
6×associate-/r* associate-/l*
4×add-exp-log sqrt-div add-cbrt-cube
3×pow1
2×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u associate-/l/ add-log-exp
1×cbrt-undiv rem-sqrt-square sqrt-undiv frac-2neg sqrt-pow1 pow1/2 div-exp clear-num hypot-def div-inv
Counts
2 → 83
Calls
2 calls:
10.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
6.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series354.0ms

Counts
2 → 6
Calls
2 calls:
244.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
110.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify66.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (22.0ms)

IterNodesCost
02191151
16571087
224431063
350021063

prune233.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.1b

localize10.0ms

Local error

Found 2 expressions with local error:

0.4b
(/ (hypot (sqrt (+ (* x x) (* y y))) z) (sqrt 3.0))
30.8b
(sqrt (+ (* x x) (* y y)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
18×add-cube-cbrt *-un-lft-identity times-frac
15×sqrt-prod
6×associate-/r*
4×add-exp-log add-cbrt-cube
3×pow1 associate-/l*
2×expm1-log1p-u sqrt-div log1p-expm1-u add-log-exp
1×cbrt-undiv rem-sqrt-square sqrt-undiv hypot-udef frac-2neg sqrt-pow1 flip3-+ pow1/2 div-exp clear-num flip-+ hypot-def div-inv
Counts
2 → 60
Calls
2 calls:
4.0ms
(/ (hypot (sqrt (+ (* x x) (* y y))) z) (sqrt 3.0))
4.0ms
(sqrt (+ (* x x) (* y y)))

series334.0ms

Counts
2 → 6
Calls
2 calls:
297.0ms
(/ (hypot (sqrt (+ (* x x) (* y y))) z) (sqrt 3.0))
37.0ms
(sqrt (+ (* x x) (* y y)))

simplify113.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 2 (17.0ms)

IterNodesCost
0211654
1555614
21415600
33989600
45002600

prune210.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes125.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0146
1166
2166

end0.0ms

sample426.0ms

Algorithm
intervals
Results
265.0ms8000×body80valid