Details

Time bar (total: 3.5s)

sample19.0ms

Algorithm
intervals
Results
9.0ms256×body80valid

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0167
1277
2337
3347
4347

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.4b

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
34.8b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite52.0ms

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:
35.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
15.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series251.0ms

Counts
2 → 6
Calls
2 calls:
58.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
192.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify126.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0223655
1877586
23651577
35001577

prune228.0ms

Filtered
64 candidates to 55 candidates (85.9%)
Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 19.5b

localize9.0ms

Local error

Found 2 expressions with local error:

0.1b
(* 0.3333333333333333 (fma z z (fma x x (* y y))))
34.8b
(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:
3.0ms
(* 0.3333333333333333 (fma z z (fma x x (* y y))))
3.0ms
(sqrt (* 0.3333333333333333 (fma z z (fma x x (* y y)))))

series270.0ms

Counts
2 → 6
Calls
2 calls:
71.0ms
(* 0.3333333333333333 (fma z z (fma x x (* y y))))
199.0ms
(sqrt (* 0.3333333333333333 (fma z z (fma x x (* y y)))))

simplify93.0ms

Algorithm
egg-herbie
Counts
41 → 41
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
0126229
1501201
22724201
35002201

prune113.0ms

Filtered
41 candidates to 29 candidates (70.7%)
Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.7b

localize12.0ms

Local error

Found 2 expressions with local error:

0.4b
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
34.7b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite42.0ms

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:
24.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
15.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series369.0ms

Counts
2 → 6
Calls
2 calls:
249.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
119.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify76.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
02191151
16571087
224431063
350021063

prune249.0ms

Filtered
89 candidates to 56 candidates (62.9%)
Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.5b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(hypot (sqrt (+ (* x x) (* y y))) z)
0.4b
(/ (hypot (sqrt (+ (* x x) (* y y))) z) (sqrt 3.0))
32.4b
(sqrt (+ (* x x) (* y y)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×add-cube-cbrt *-un-lft-identity
18×times-frac
15×sqrt-prod
6×associate-/r*
5×add-exp-log add-cbrt-cube
4×pow1
3×expm1-log1p-u log1p-expm1-u associate-/l* add-log-exp
2×hypot-udef sqrt-div
1×cbrt-undiv rem-sqrt-square sqrt-undiv frac-2neg sqrt-pow1 flip3-+ pow1/2 div-exp clear-num flip-+ hypot-def div-inv
Counts
3 → 70
Calls
3 calls:
0.0ms
(hypot (sqrt (+ (* x x) (* y y))) z)
3.0ms
(/ (hypot (sqrt (+ (* x x) (* y y))) z) (sqrt 3.0))
4.0ms
(sqrt (+ (* x x) (* y y)))

series551.0ms

Counts
3 → 9
Calls
3 calls:
189.0ms
(hypot (sqrt (+ (* x x) (* y y))) z)
317.0ms
(/ (hypot (sqrt (+ (* x x) (* y y))) z) (sqrt 3.0))
45.0ms
(sqrt (+ (* x x) (* y y)))

simplify128.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
0214731
1558679
21420665
34000665
45001665

prune251.0ms

Filtered
79 candidates to 60 candidates (75.9%)
Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

regimes130.0ms

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 (1.0ms)

IterNodesCost
0146
1166
2166

end0.0ms

sample457.0ms

Algorithm
intervals
Results
278.0ms8000×body80valid