Average Error: 0.2 → 0.1
Time: 7.8s
Precision: binary64
Cost: 12992
$\left(\left(1 \leq x \land x \leq 1000\right) \land \left(1 \leq y \land y \leq 1000\right)\right) \land \left(1 \leq z \land z \leq 1000\right)$
$\begin{array}{c}[x, y, z] = \mathsf{sort}([x, y, z])\\ \end{array}$
$\sqrt{\left({x}^{2} + {y}^{2}\right) + {z}^{2}}$
$\mathsf{hypot}\left(\mathsf{hypot}\left(x, y\right), z\right)$
(FPCore (x y z)
:precision binary64
(sqrt (+ (+ (pow x 2.0) (pow y 2.0)) (pow z 2.0))))
(FPCore (x y z) :precision binary64 (hypot (hypot x y) z))
double code(double x, double y, double z) {
return sqrt(((pow(x, 2.0) + pow(y, 2.0)) + pow(z, 2.0)));
}

double code(double x, double y, double z) {
return hypot(hypot(x, y), z);
}

public static double code(double x, double y, double z) {
return Math.sqrt(((Math.pow(x, 2.0) + Math.pow(y, 2.0)) + Math.pow(z, 2.0)));
}

public static double code(double x, double y, double z) {
return Math.hypot(Math.hypot(x, y), z);
}

def code(x, y, z):
return math.sqrt(((math.pow(x, 2.0) + math.pow(y, 2.0)) + math.pow(z, 2.0)))

def code(x, y, z):
return math.hypot(math.hypot(x, y), z)

function code(x, y, z)
return sqrt(Float64(Float64((x ^ 2.0) + (y ^ 2.0)) + (z ^ 2.0)))
end

function code(x, y, z)
return hypot(hypot(x, y), z)
end

function tmp = code(x, y, z)
tmp = sqrt((((x ^ 2.0) + (y ^ 2.0)) + (z ^ 2.0)));
end

function tmp = code(x, y, z)
tmp = hypot(hypot(x, y), z);
end

code[x_, y_, z_] := N[Sqrt[N[(N[(N[Power[x, 2.0], $MachinePrecision] + N[Power[y, 2.0],$MachinePrecision]), $MachinePrecision] + N[Power[z, 2.0],$MachinePrecision]), $MachinePrecision]],$MachinePrecision]

code[x_, y_, z_] := N[Sqrt[N[Sqrt[x ^ 2 + y ^ 2], $MachinePrecision] ^ 2 + z ^ 2],$MachinePrecision]

\sqrt{\left({x}^{2} + {y}^{2}\right) + {z}^{2}}

\mathsf{hypot}\left(\mathsf{hypot}\left(x, y\right), z\right)


# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 0.2

$\sqrt{\left({x}^{2} + {y}^{2}\right) + {z}^{2}}$
2. Applied egg-rr0.1

$\leadsto \color{blue}{\mathsf{hypot}\left(\mathsf{hypot}\left(x, y\right), z\right)}$
3. Final simplification0.1

$\leadsto \mathsf{hypot}\left(\mathsf{hypot}\left(x, y\right), z\right)$

# Alternatives

Alternative 1
Error38.5
Cost13636
$\begin{array}{l} \mathbf{if}\;{y}^{2} \leq 7500:\\ \;\;\;\;\mathsf{hypot}\left(x, \left(y \cdot y\right) \cdot \frac{-0.5}{z} - z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{hypot}\left(z, y\right)\\ \end{array}$
Alternative 2
Error0.2
Cost7104
$\sqrt{y \cdot y + \left(x \cdot x + z \cdot z\right)}$
Alternative 3
Error0.2
Cost7104
$\sqrt{\left(x \cdot x + y \cdot y\right) + z \cdot z}$
Alternative 4
Error34.5
Cost7040
$\mathsf{hypot}\left(\left(x \cdot x\right) \cdot \frac{-0.5}{y} - y, z\right)$
Alternative 5
Error41.5
Cost6528
$\mathsf{hypot}\left(z, y\right)$
Alternative 6
Error46.7
Cost64
$z$

# Reproduce

herbie shell --seed 1
(FPCore (x y z)
:name "sqrt(x^2+y^2+z^2)"
:precision binary64
:pre (and (and (and (<= 1.0 x) (<= x 1000.0)) (and (<= 1.0 y) (<= y 1000.0))) (and (<= 1.0 z) (<= z 1000.0)))
(sqrt (+ (+ (pow x 2.0) (pow y 2.0)) (pow z 2.0))))