Details

Time bar (total: 5.7s)

sample23.0ms

Algorithm
intervals
Results
9.0ms256×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: 36.2b

localize10.0ms

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))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
20×add-cube-cbrt *-un-lft-identity
19×times-frac
13×sqrt-prod
11×add-log-exp
6×add-exp-log add-cbrt-cube
5×pow1
4×expm1-log1p-u fma-def sum-log log1p-expm1-u
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 → 90
Calls
4 calls:
17.0ms
(+ (+ (* x x) (* y y)) (* z z))
4.0ms
(+ (* x x) (* y y))
30.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
16.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series329.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(+ (+ (* x x) (* y y)) (* z z))
32.0ms
(+ (* x x) (* y y))
67.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
179.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify55.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0345852
11445759
25001739

prune343.0ms

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)))

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
41×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×expm1-log1p-u frac-times sqrt-pow1 associate-*l/ log1p-expm1-u add-log-exp
3×pow1/2
2×rem-sqrt-square associate-*r/ pow-prod-down prod-exp cbrt-unprod hypot-def
1×cbrt-undiv div-exp *-commutative div-inv
Counts
4 → 108
Calls
4 calls:
70.0ms
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
14.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
15.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
19.0ms
(sqrt (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))

series477.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
110.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
112.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
194.0ms
(sqrt (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))

simplify62.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
03441625
115051406
250011336

prune363.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 16.4b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma x x (fma y y (* z z)))
0.0b
(fma y y (* z z))
0.1b
(* 0.3333333333333333 (fma x x (fma y y (* z z))))
33.7b
(sqrt (* 0.3333333333333333 (fma x x (fma y y (* z z)))))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1
8×add-sqr-sqrt
6×add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
4×expm1-log1p-u fma-udef log1p-expm1-u add-log-exp
3×associate-*r* associate-*l*
2×sqrt-pow1 pow-prod-down
1×distribute-rgt-in distribute-lft-in pow1/2 prod-exp sqrt-prod *-commutative cbrt-unprod unswap-sqr
Counts
4 → 55
Calls
4 calls:
0.0ms
(fma x x (fma y y (* z z)))
0.0ms
(fma y y (* z z))
3.0ms
(* 0.3333333333333333 (fma x x (fma y y (* z z))))
2.0ms
(sqrt (* 0.3333333333333333 (fma x x (fma y y (* z z)))))

series362.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(fma x x (fma y y (* z z)))
37.0ms
(fma y y (* z z))
70.0ms
(* 0.3333333333333333 (fma x x (fma y y (* z z))))
199.0ms
(sqrt (* 0.3333333333333333 (fma x x (fma y y (* z z)))))

simplify105.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
0144330
1630286
23536286
35001286

prune175.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 16.4b

localize18.0ms

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)))

rewrite442.0ms

Algorithm
rewrite-expression-head
Rules
574×sqrt-prod
346×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×expm1-log1p-u log1p-expm1-u add-log-exp
3×flip3-+ pow-prod-down pow-sqr flip-+
2×rem-sqrt-square hypot-def 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 → 326
Calls
4 calls:
24.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
361.0ms
(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))))
15.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
15.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series710.0ms

Counts
4 → 12
Calls
4 calls:
242.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
240.0ms
(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))))
110.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
117.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify115.0ms

Algorithm
egg-herbie
Counts
338 → 338
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
04595794
120915463
250015428

prune699.0ms

Pruning

11 alts after pruning (7 fresh and 4 done)

Merged error: 16.3b

regimes589.0ms

Accuracy

54.8% (8.8b remaining)

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

bsearch159.0ms

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 (1.0ms)

IterNodesCost
04037
14237
24237

end0.0ms

sample445.0ms

Algorithm
intervals
Results
273.0ms8000×body80valid