bug366 (missed optimization)

Percentage Accurate: 44.7% → 100.0%

Time: 2.8s

Alternatives: 3

Speedup: 111.0×

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: 44.7% 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, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	return hypot(hypot(x, y), z)
end

MATLAB

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

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := N[Sqrt[N[Sqrt[x ^ 2 + y ^ 2], $MachinePrecision] ^ 2 + z ^ 2], $MachinePrecision]

Derivation

1. Initial program 35.9%

   \[\sqrt{x \cdot x + \left(y \cdot y + z \cdot z\right)} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. associate-+r+ 35.9%

      \[\leadsto \sqrt{\color{blue}{\left(x \cdot x + y \cdot y\right) + z \cdot z}} \]

   2. add-sqr-sqrt 35.9%

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

   3. hypot-define 51.9%

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

   4. hypot-define 100.0%

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

4. Applied egg-rr 100.0%

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

Alternative 2: 52.5% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	return hypot(y, z)
end

MATLAB

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

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := N[Sqrt[y ^ 2 + z ^ 2], $MachinePrecision]

Derivation

1. Initial program 35.9%

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

3. Taylor expanded in x around 0 29.5%

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

   1. unpow2 29.5%

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

   2. unpow2 29.5%

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

   3. hypot-undefine 74.1%

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

5. Simplified 74.1%

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

Alternative 3: 51.3% accurate, 111.0× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ z \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 z)

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	return z;
}

Fortran

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

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	return z;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	return z

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	return z
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp = code(x, y, z)
	tmp = z;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := z

Derivation

1. Initial program 35.9%

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

3. Taylor expanded in z around inf 18.5%

   \[\leadsto \color{blue}{z} \]
4. Add Preprocessing

Developer Target 1: 100.0% accurate, 0.5× 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 2024146 
(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)))))