bug366 (missed optimization)

Percentage Accurate: 45.2% → 100.0%

Time: 6.8s

Alternatives: 7

Speedup: 1.5×

Specification

Math

\[\begin{array}{l} \\ \sqrt{x \cdot x + \left(y \cdot y + z \cdot z\right)} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (sqrt (+ (* x x) (+ (* y y) (* z z)))))

C

double code(double x, double y, double z) {
	return sqrt(((x * x) + ((y * y) + (z * z))));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = sqrt(((x * x) + ((y * y) + (z * z))))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 45.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \sqrt{x \cdot x + \left(y \cdot y + z \cdot z\right)} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (sqrt (+ (* x x) (+ (* y y) (* z z)))))

C

double code(double x, double y, double z) {
	return sqrt(((x * x) + ((y * y) + (z * z))));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = sqrt(((x * x) + ((y * y) + (z * z))))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ y_m = \left|y\right| \\ x_m = \left|x\right| \\ [x_m, y_m, z_m] = \mathsf{sort}([x_m, y_m, z_m])\\ \\ \mathsf{hypot}\left(z\_m, y\_m\right) \end{array} \]

FPCore

z_m = (fabs.f64 z)
y_m = (fabs.f64 y)
x_m = (fabs.f64 x)
NOTE: x_m, y_m, and z_m should be sorted in increasing order before calling this function.
(FPCore (x_m y_m z_m) :precision binary64 (hypot z_m y_m))

C

z_m = fabs(z);
y_m = fabs(y);
x_m = fabs(x);
assert(x_m < y_m && y_m < z_m);
double code(double x_m, double y_m, double z_m) {
	return hypot(z_m, y_m);
}

Java

z_m = Math.abs(z);
y_m = Math.abs(y);
x_m = Math.abs(x);
assert x_m < y_m && y_m < z_m;
public static double code(double x_m, double y_m, double z_m) {
	return Math.hypot(z_m, y_m);
}

Python

z_m = math.fabs(z)
y_m = math.fabs(y)
x_m = math.fabs(x)
[x_m, y_m, z_m] = sort([x_m, y_m, z_m])
def code(x_m, y_m, z_m):
	return math.hypot(z_m, y_m)

Julia

z_m = abs(z)
y_m = abs(y)
x_m = abs(x)
x_m, y_m, z_m = sort([x_m, y_m, z_m])
function code(x_m, y_m, z_m)
	return hypot(z_m, y_m)
end

MATLAB

z_m = abs(z);
y_m = abs(y);
x_m = abs(x);
x_m, y_m, z_m = num2cell(sort([x_m, y_m, z_m])){:}
function tmp = code(x_m, y_m, z_m)
	tmp = hypot(z_m, y_m);
end

Wolfram

z_m = N[Abs[z], $MachinePrecision]
y_m = N[Abs[y], $MachinePrecision]
x_m = N[Abs[x], $MachinePrecision]
NOTE: x_m, y_m, and z_m should be sorted in increasing order before calling this function.
code[x$95$m_, y$95$m_, z$95$m_] := N[Sqrt[z$95$m ^ 2 + y$95$m ^ 2], $MachinePrecision]

Derivation

1. Initial program 43.4%

   \[\sqrt{x \cdot x + \left(y \cdot y + z \cdot z\right)} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\sqrt{{y}^{2} + {z}^{2}}} \]
4. Step-by-step derivation

   1. +-commutative N/A

      \[\leadsto \sqrt{\color{blue}{{z}^{2} + {y}^{2}}} \]

   2. unpow2 N/A

      \[\leadsto \sqrt{\color{blue}{z \cdot z} + {y}^{2}} \]

   3. unpow2 N/A

      \[\leadsto \sqrt{z \cdot z + \color{blue}{y \cdot y}} \]

   4. lower-hypot.f64 66.4

      \[\leadsto \color{blue}{\mathsf{hypot}\left(z, y\right)} \]

5. Applied rewrites 66.4%

   \[\leadsto \color{blue}{\mathsf{hypot}\left(z, y\right)} \]
6. Add Preprocessing

Alternative 2: 99.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ y_m = \left|y\right| \\ x_m = \left|x\right| \\ [x_m, y_m, z_m] = \mathsf{sort}([x_m, y_m, z_m])\\ \\ \mathsf{fma}\left(\frac{0.5}{z\_m} \cdot y\_m, y\_m, z\_m\right) \end{array} \]

FPCore

z_m = (fabs.f64 z)
y_m = (fabs.f64 y)
x_m = (fabs.f64 x)
NOTE: x_m, y_m, and z_m should be sorted in increasing order before calling this function.
(FPCore (x_m y_m z_m) :precision binary64 (fma (* (/ 0.5 z_m) y_m) y_m z_m))

C

z_m = fabs(z);
y_m = fabs(y);
x_m = fabs(x);
assert(x_m < y_m && y_m < z_m);
double code(double x_m, double y_m, double z_m) {
	return fma(((0.5 / z_m) * y_m), y_m, z_m);
}

Julia

z_m = abs(z)
y_m = abs(y)
x_m = abs(x)
x_m, y_m, z_m = sort([x_m, y_m, z_m])
function code(x_m, y_m, z_m)
	return fma(Float64(Float64(0.5 / z_m) * y_m), y_m, z_m)
end

Wolfram

z_m = N[Abs[z], $MachinePrecision]
y_m = N[Abs[y], $MachinePrecision]
x_m = N[Abs[x], $MachinePrecision]
NOTE: x_m, y_m, and z_m should be sorted in increasing order before calling this function.
code[x$95$m_, y$95$m_, z$95$m_] := N[(N[(N[(0.5 / z$95$m), $MachinePrecision] * y$95$m), $MachinePrecision] * y$95$m + z$95$m), $MachinePrecision]

Derivation

1. Initial program 43.4%

   \[\sqrt{x \cdot x + \left(y \cdot y + z \cdot z\right)} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\sqrt{{y}^{2} + {z}^{2}}} \]
4. Step-by-step derivation

   1. +-commutative N/A

      \[\leadsto \sqrt{\color{blue}{{z}^{2} + {y}^{2}}} \]

   2. unpow2 N/A

      \[\leadsto \sqrt{\color{blue}{z \cdot z} + {y}^{2}} \]

   3. unpow2 N/A

      \[\leadsto \sqrt{z \cdot z + \color{blue}{y \cdot y}} \]

   4. lower-hypot.f64 66.4

      \[\leadsto \color{blue}{\mathsf{hypot}\left(z, y\right)} \]

5. Applied rewrites 66.4%

   \[\leadsto \color{blue}{\mathsf{hypot}\left(z, y\right)} \]

6. Taylor expanded in y around 0

   \[\leadsto z + \color{blue}{\frac{1}{2} \cdot \frac{{y}^{2}}{z}} \]
7. Step-by-step derivation

8. Applied rewrites 17.7%

   \[\leadsto \mathsf{fma}\left(\frac{0.5}{z}, \color{blue}{y \cdot y}, z\right) \]
9. Step-by-step derivation

10. Applied rewrites 20.0%

    \[\leadsto \mathsf{fma}\left(\frac{0.5}{z} \cdot y, y, z\right) \]
11. Add Preprocessing

Alternative 3: 45.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ y_m = \left|y\right| \\ x_m = \left|x\right| \\ [x_m, y_m, z_m] = \mathsf{sort}([x_m, y_m, z_m])\\ \\ \sqrt{\mathsf{fma}\left(z\_m, z\_m, y\_m \cdot y\_m\right)} \end{array} \]

FPCore

z_m = (fabs.f64 z)
y_m = (fabs.f64 y)
x_m = (fabs.f64 x)
NOTE: x_m, y_m, and z_m should be sorted in increasing order before calling this function.
(FPCore (x_m y_m z_m) :precision binary64 (sqrt (fma z_m z_m (* y_m y_m))))

C

z_m = fabs(z);
y_m = fabs(y);
x_m = fabs(x);
assert(x_m < y_m && y_m < z_m);
double code(double x_m, double y_m, double z_m) {
	return sqrt(fma(z_m, z_m, (y_m * y_m)));
}

Julia

z_m = abs(z)
y_m = abs(y)
x_m = abs(x)
x_m, y_m, z_m = sort([x_m, y_m, z_m])
function code(x_m, y_m, z_m)
	return sqrt(fma(z_m, z_m, Float64(y_m * y_m)))
end

Wolfram

z_m = N[Abs[z], $MachinePrecision]
y_m = N[Abs[y], $MachinePrecision]
x_m = N[Abs[x], $MachinePrecision]
NOTE: x_m, y_m, and z_m should be sorted in increasing order before calling this function.
code[x$95$m_, y$95$m_, z$95$m_] := N[Sqrt[N[(z$95$m * z$95$m + N[(y$95$m * y$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 43.4%

   \[\sqrt{x \cdot x + \left(y \cdot y + z \cdot z\right)} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \sqrt{\color{blue}{{y}^{2} + {z}^{2}}} \]
4. Step-by-step derivation

   1. +-commutative N/A

      \[\leadsto \sqrt{\color{blue}{{z}^{2} + {y}^{2}}} \]

   2. unpow2 N/A

      \[\leadsto \sqrt{\color{blue}{z \cdot z} + {y}^{2}} \]

   3. lower-fma.f64 N/A

      \[\leadsto \sqrt{\color{blue}{\mathsf{fma}\left(z, z, {y}^{2}\right)}} \]

   4. unpow2 N/A

      \[\leadsto \sqrt{\mathsf{fma}\left(z, z, \color{blue}{y \cdot y}\right)} \]

   5. lower-*.f64 28.0

      \[\leadsto \sqrt{\mathsf{fma}\left(z, z, \color{blue}{y \cdot y}\right)} \]

5. Applied rewrites 28.0%

   \[\leadsto \sqrt{\color{blue}{\mathsf{fma}\left(z, z, y \cdot y\right)}} \]
6. Add Preprocessing

Alternative 4: 44.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ y_m = \left|y\right| \\ x_m = \left|x\right| \\ [x_m, y_m, z_m] = \mathsf{sort}([x_m, y_m, z_m])\\ \\ \sqrt{z\_m \cdot z\_m} \end{array} \]

FPCore

z_m = (fabs.f64 z)
y_m = (fabs.f64 y)
x_m = (fabs.f64 x)
NOTE: x_m, y_m, and z_m should be sorted in increasing order before calling this function.
(FPCore (x_m y_m z_m) :precision binary64 (sqrt (* z_m z_m)))

C

z_m = fabs(z);
y_m = fabs(y);
x_m = fabs(x);
assert(x_m < y_m && y_m < z_m);
double code(double x_m, double y_m, double z_m) {
	return sqrt((z_m * z_m));
}

Fortran

z_m = abs(z)
y_m = abs(y)
x_m = abs(x)
NOTE: x_m, y_m, and z_m should be sorted in increasing order before calling this function.
real(8) function code(x_m, y_m, z_m)
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z_m
    code = sqrt((z_m * z_m))
end function

Java

z_m = Math.abs(z);
y_m = Math.abs(y);
x_m = Math.abs(x);
assert x_m < y_m && y_m < z_m;
public static double code(double x_m, double y_m, double z_m) {
	return Math.sqrt((z_m * z_m));
}

Python

z_m = math.fabs(z)
y_m = math.fabs(y)
x_m = math.fabs(x)
[x_m, y_m, z_m] = sort([x_m, y_m, z_m])
def code(x_m, y_m, z_m):
	return math.sqrt((z_m * z_m))

Julia

z_m = abs(z)
y_m = abs(y)
x_m = abs(x)
x_m, y_m, z_m = sort([x_m, y_m, z_m])
function code(x_m, y_m, z_m)
	return sqrt(Float64(z_m * z_m))
end

MATLAB

z_m = abs(z);
y_m = abs(y);
x_m = abs(x);
x_m, y_m, z_m = num2cell(sort([x_m, y_m, z_m])){:}
function tmp = code(x_m, y_m, z_m)
	tmp = sqrt((z_m * z_m));
end

Wolfram

z_m = N[Abs[z], $MachinePrecision]
y_m = N[Abs[y], $MachinePrecision]
x_m = N[Abs[x], $MachinePrecision]
NOTE: x_m, y_m, and z_m should be sorted in increasing order before calling this function.
code[x$95$m_, y$95$m_, z$95$m_] := N[Sqrt[N[(z$95$m * z$95$m), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 43.4%

   \[\sqrt{x \cdot x + \left(y \cdot y + z \cdot z\right)} \]
2. Add Preprocessing

3. Taylor expanded in z around inf

   \[\leadsto \sqrt{\color{blue}{{z}^{2}}} \]
4. Step-by-step derivation

   1. unpow2 N/A

      \[\leadsto \sqrt{\color{blue}{z \cdot z}} \]

   2. lower-*.f64 16.2

      \[\leadsto \sqrt{\color{blue}{z \cdot z}} \]

5. Applied rewrites 16.2%

   \[\leadsto \sqrt{\color{blue}{z \cdot z}} \]
6. Add Preprocessing

Alternative 5: 5.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ y_m = \left|y\right| \\ x_m = \left|x\right| \\ [x_m, y_m, z_m] = \mathsf{sort}([x_m, y_m, z_m])\\ \\ \sqrt{y\_m \cdot y\_m} \end{array} \]

FPCore

z_m = (fabs.f64 z)
y_m = (fabs.f64 y)
x_m = (fabs.f64 x)
NOTE: x_m, y_m, and z_m should be sorted in increasing order before calling this function.
(FPCore (x_m y_m z_m) :precision binary64 (sqrt (* y_m y_m)))

C

z_m = fabs(z);
y_m = fabs(y);
x_m = fabs(x);
assert(x_m < y_m && y_m < z_m);
double code(double x_m, double y_m, double z_m) {
	return sqrt((y_m * y_m));
}

Fortran

z_m = abs(z)
y_m = abs(y)
x_m = abs(x)
NOTE: x_m, y_m, and z_m should be sorted in increasing order before calling this function.
real(8) function code(x_m, y_m, z_m)
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z_m
    code = sqrt((y_m * y_m))
end function

Java

z_m = Math.abs(z);
y_m = Math.abs(y);
x_m = Math.abs(x);
assert x_m < y_m && y_m < z_m;
public static double code(double x_m, double y_m, double z_m) {
	return Math.sqrt((y_m * y_m));
}

Python

z_m = math.fabs(z)
y_m = math.fabs(y)
x_m = math.fabs(x)
[x_m, y_m, z_m] = sort([x_m, y_m, z_m])
def code(x_m, y_m, z_m):
	return math.sqrt((y_m * y_m))

Julia

z_m = abs(z)
y_m = abs(y)
x_m = abs(x)
x_m, y_m, z_m = sort([x_m, y_m, z_m])
function code(x_m, y_m, z_m)
	return sqrt(Float64(y_m * y_m))
end

MATLAB

z_m = abs(z);
y_m = abs(y);
x_m = abs(x);
x_m, y_m, z_m = num2cell(sort([x_m, y_m, z_m])){:}
function tmp = code(x_m, y_m, z_m)
	tmp = sqrt((y_m * y_m));
end

Wolfram

z_m = N[Abs[z], $MachinePrecision]
y_m = N[Abs[y], $MachinePrecision]
x_m = N[Abs[x], $MachinePrecision]
NOTE: x_m, y_m, and z_m should be sorted in increasing order before calling this function.
code[x$95$m_, y$95$m_, z$95$m_] := N[Sqrt[N[(y$95$m * y$95$m), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 43.4%

   \[\sqrt{x \cdot x + \left(y \cdot y + z \cdot z\right)} \]
2. Add Preprocessing

3. Taylor expanded in y around inf

   \[\leadsto \sqrt{\color{blue}{{y}^{2}}} \]
4. Step-by-step derivation

   1. unpow2 N/A

      \[\leadsto \sqrt{\color{blue}{y \cdot y}} \]

   2. lower-*.f64 15.8

      \[\leadsto \sqrt{\color{blue}{y \cdot y}} \]

5. Applied rewrites 15.8%

   \[\leadsto \sqrt{\color{blue}{y \cdot y}} \]
6. Add Preprocessing

Alternative 6: 3.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ y_m = \left|y\right| \\ x_m = \left|x\right| \\ [x_m, y_m, z_m] = \mathsf{sort}([x_m, y_m, z_m])\\ \\ \sqrt{x\_m \cdot x\_m} \end{array} \]

FPCore

z_m = (fabs.f64 z)
y_m = (fabs.f64 y)
x_m = (fabs.f64 x)
NOTE: x_m, y_m, and z_m should be sorted in increasing order before calling this function.
(FPCore (x_m y_m z_m) :precision binary64 (sqrt (* x_m x_m)))

C

z_m = fabs(z);
y_m = fabs(y);
x_m = fabs(x);
assert(x_m < y_m && y_m < z_m);
double code(double x_m, double y_m, double z_m) {
	return sqrt((x_m * x_m));
}

Fortran

z_m = abs(z)
y_m = abs(y)
x_m = abs(x)
NOTE: x_m, y_m, and z_m should be sorted in increasing order before calling this function.
real(8) function code(x_m, y_m, z_m)
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z_m
    code = sqrt((x_m * x_m))
end function

Java

z_m = Math.abs(z);
y_m = Math.abs(y);
x_m = Math.abs(x);
assert x_m < y_m && y_m < z_m;
public static double code(double x_m, double y_m, double z_m) {
	return Math.sqrt((x_m * x_m));
}

Python

z_m = math.fabs(z)
y_m = math.fabs(y)
x_m = math.fabs(x)
[x_m, y_m, z_m] = sort([x_m, y_m, z_m])
def code(x_m, y_m, z_m):
	return math.sqrt((x_m * x_m))

Julia

z_m = abs(z)
y_m = abs(y)
x_m = abs(x)
x_m, y_m, z_m = sort([x_m, y_m, z_m])
function code(x_m, y_m, z_m)
	return sqrt(Float64(x_m * x_m))
end

MATLAB

z_m = abs(z);
y_m = abs(y);
x_m = abs(x);
x_m, y_m, z_m = num2cell(sort([x_m, y_m, z_m])){:}
function tmp = code(x_m, y_m, z_m)
	tmp = sqrt((x_m * x_m));
end

Wolfram

z_m = N[Abs[z], $MachinePrecision]
y_m = N[Abs[y], $MachinePrecision]
x_m = N[Abs[x], $MachinePrecision]
NOTE: x_m, y_m, and z_m should be sorted in increasing order before calling this function.
code[x$95$m_, y$95$m_, z$95$m_] := N[Sqrt[N[(x$95$m * x$95$m), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 43.4%

   \[\sqrt{x \cdot x + \left(y \cdot y + z \cdot z\right)} \]
2. Add Preprocessing

3. Taylor expanded in x around inf

   \[\leadsto \sqrt{\color{blue}{{x}^{2}}} \]
4. Step-by-step derivation

   1. unpow2 N/A

      \[\leadsto \sqrt{\color{blue}{x \cdot x}} \]

   2. lower-*.f64 19.4

      \[\leadsto \sqrt{\color{blue}{x \cdot x}} \]

5. Applied rewrites 19.4%

   \[\leadsto \sqrt{\color{blue}{x \cdot x}} \]
6. Add Preprocessing

Alternative 7: 1.7% accurate, 10.7× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ y_m = \left|y\right| \\ x_m = \left|x\right| \\ [x_m, y_m, z_m] = \mathsf{sort}([x_m, y_m, z_m])\\ \\ -x\_m \end{array} \]

FPCore

z_m = (fabs.f64 z)
y_m = (fabs.f64 y)
x_m = (fabs.f64 x)
NOTE: x_m, y_m, and z_m should be sorted in increasing order before calling this function.
(FPCore (x_m y_m z_m) :precision binary64 (- x_m))

C

z_m = fabs(z);
y_m = fabs(y);
x_m = fabs(x);
assert(x_m < y_m && y_m < z_m);
double code(double x_m, double y_m, double z_m) {
	return -x_m;
}

Fortran

z_m = abs(z)
y_m = abs(y)
x_m = abs(x)
NOTE: x_m, y_m, and z_m should be sorted in increasing order before calling this function.
real(8) function code(x_m, y_m, z_m)
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z_m
    code = -x_m
end function

Java

z_m = Math.abs(z);
y_m = Math.abs(y);
x_m = Math.abs(x);
assert x_m < y_m && y_m < z_m;
public static double code(double x_m, double y_m, double z_m) {
	return -x_m;
}

Python

z_m = math.fabs(z)
y_m = math.fabs(y)
x_m = math.fabs(x)
[x_m, y_m, z_m] = sort([x_m, y_m, z_m])
def code(x_m, y_m, z_m):
	return -x_m

Julia

z_m = abs(z)
y_m = abs(y)
x_m = abs(x)
x_m, y_m, z_m = sort([x_m, y_m, z_m])
function code(x_m, y_m, z_m)
	return Float64(-x_m)
end

MATLAB

z_m = abs(z);
y_m = abs(y);
x_m = abs(x);
x_m, y_m, z_m = num2cell(sort([x_m, y_m, z_m])){:}
function tmp = code(x_m, y_m, z_m)
	tmp = -x_m;
end

Wolfram

z_m = N[Abs[z], $MachinePrecision]
y_m = N[Abs[y], $MachinePrecision]
x_m = N[Abs[x], $MachinePrecision]
NOTE: x_m, y_m, and z_m should be sorted in increasing order before calling this function.
code[x$95$m_, y$95$m_, z$95$m_] := (-x$95$m)

Derivation

1. Initial program 43.4%

   \[\sqrt{x \cdot x + \left(y \cdot y + z \cdot z\right)} \]
2. Add Preprocessing

3. Taylor expanded in x around -inf

   \[\leadsto \color{blue}{-1 \cdot x} \]
4. Step-by-step derivation

   1. mul-1-neg N/A

      \[\leadsto \color{blue}{\mathsf{neg}\left(x\right)} \]

   2. lower-neg.f64 17.9

      \[\leadsto \color{blue}{-x} \]

5. Applied rewrites 17.9%

   \[\leadsto \color{blue}{-x} \]
6. Add Preprocessing

Developer Target 1: 100.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \mathsf{hypot}\left(x, \mathsf{hypot}\left(y, z\right)\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (hypot x (hypot y z)))

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024242 
(FPCore (x y z)
  :name "bug366 (missed optimization)"
  :precision binary64

  :alt
  (! :herbie-platform default (hypot x (hypot y z)))

  (sqrt (+ (* x x) (+ (* y y) (* z z)))))