Main:bigenough2 from A

Percentage Accurate: 100.0% → 100.0%

Time: 6.5s

Alternatives: 8

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.1× speedup

Math

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

FPCore

(FPCore (x y z) :precision binary64 (fma y (+ x z) x))

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x + y \cdot \left(z + x\right) \]
2. Step-by-step derivation

   1. +-commutative 100.0%

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

   2. fma-define 100.0%

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

   3. +-commutative 100.0%

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

3. Simplified 100.0%

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

Alternative 2: 98.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 1.0))) (* y (+ x z)) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.0) || !(y <= 1.0)) {
		tmp = y * (x + z);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1.0d0)) .or. (.not. (y <= 1.0d0))) then
        tmp = y * (x + z)
    else
        tmp = x + (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.0) || !(y <= 1.0)) {
		tmp = y * (x + z);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.0) or not (y <= 1.0):
		tmp = y * (x + z)
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 1.0))
		tmp = Float64(y * Float64(x + z));
	else
		tmp = Float64(x + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.0) || ~((y <= 1.0)))
		tmp = y * (x + z);
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(y * N[(x + z), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 99.9%

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

   4. Taylor expanded in z around inf 99.2%

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

   if -1 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 98.3%

      \[\leadsto x + \color{blue}{y \cdot z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 80.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -175 \lor \neg \left(x \leq 2.1 \cdot 10^{-7}\right):\\ \;\;\;\;x + y \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -175.0) (not (<= x 2.1e-7))) (+ x (* y x)) (* y (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -175.0) || !(x <= 2.1e-7)) {
		tmp = x + (y * x);
	} else {
		tmp = y * (x + z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-175.0d0)) .or. (.not. (x <= 2.1d-7))) then
        tmp = x + (y * x)
    else
        tmp = y * (x + z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -175.0) || !(x <= 2.1e-7)) {
		tmp = x + (y * x);
	} else {
		tmp = y * (x + z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -175.0) or not (x <= 2.1e-7):
		tmp = x + (y * x)
	else:
		tmp = y * (x + z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -175.0) || !(x <= 2.1e-7))
		tmp = Float64(x + Float64(y * x));
	else
		tmp = Float64(y * Float64(x + z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -175.0) || ~((x <= 2.1e-7)))
		tmp = x + (y * x);
	else
		tmp = y * (x + z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -175.0], N[Not[LessEqual[x, 2.1e-7]], $MachinePrecision]], N[(x + N[(y * x), $MachinePrecision]), $MachinePrecision], N[(y * N[(x + z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -175 or 2.1e-7 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 88.6%

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

      1. *-commutative 88.6%

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

   5. Simplified 88.6%

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

   if -175 < x < 2.1e-7

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 100.0%

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

   4. Taylor expanded in z around inf 82.4%

      \[\leadsto y \cdot \left(x + \color{blue}{z}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -175 \lor \neg \left(x \leq 2.1 \cdot 10^{-7}\right):\\ \;\;\;\;x + y \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-32} \lor \neg \left(y \leq 4.8 \cdot 10^{-9}\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.5e-32) (not (<= y 4.8e-9))) (* y (+ x z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.5e-32) || !(y <= 4.8e-9)) {
		tmp = y * (x + z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1.5d-32)) .or. (.not. (y <= 4.8d-9))) then
        tmp = y * (x + z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.5e-32) || !(y <= 4.8e-9)) {
		tmp = y * (x + z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.5e-32) or not (y <= 4.8e-9):
		tmp = y * (x + z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.5e-32) || !(y <= 4.8e-9))
		tmp = Float64(y * Float64(x + z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.5e-32) || ~((y <= 4.8e-9)))
		tmp = y * (x + z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.5e-32], N[Not[LessEqual[y, 4.8e-9]], $MachinePrecision]], N[(y * N[(x + z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.5e-32 or 4.8e-9 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 99.9%

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

   4. Taylor expanded in z around inf 95.5%

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

   if -1.5e-32 < y < 4.8e-9

   1. Initial program 100.0%

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

      1. distribute-rgt-in 100.0%

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

      2. fma-define 100.0%

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

      3. *-commutative 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around 0 70.5%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-32} \lor \neg \left(y \leq 4.8 \cdot 10^{-9}\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 59.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 8400000000000\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 8400000000000.0))) (* y x) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.0) || !(y <= 8400000000000.0)) {
		tmp = y * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1.0d0)) .or. (.not. (y <= 8400000000000.0d0))) then
        tmp = y * x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.0) || !(y <= 8400000000000.0)) {
		tmp = y * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.0) or not (y <= 8400000000000.0):
		tmp = y * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 8400000000000.0))
		tmp = Float64(y * x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.0) || ~((y <= 8400000000000.0)))
		tmp = y * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 8400000000000.0]], $MachinePrecision]], N[(y * x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 8.4e12 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 99.9%

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

   4. Taylor expanded in z around inf 99.2%

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

   5. Taylor expanded in x around inf 51.1%

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

      1. *-commutative 51.1%

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

   7. Simplified 51.1%

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

   if -1 < y < 8.4e12

   1. Initial program 100.0%

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

      1. distribute-rgt-in 100.0%

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

      2. fma-define 100.0%

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

      3. *-commutative 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around 0 65.5%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 8400000000000\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.6 \cdot 10^{-34}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 8400000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -9.6e-34) (* y z) (if (<= y 8400000000000.0) x (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -9.6e-34) {
		tmp = y * z;
	} else if (y <= 8400000000000.0) {
		tmp = x;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-9.6d-34)) then
        tmp = y * z
    else if (y <= 8400000000000.0d0) then
        tmp = x
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -9.6e-34) {
		tmp = y * z;
	} else if (y <= 8400000000000.0) {
		tmp = x;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -9.6e-34:
		tmp = y * z
	elif y <= 8400000000000.0:
		tmp = x
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -9.6e-34)
		tmp = Float64(y * z);
	elseif (y <= 8400000000000.0)
		tmp = x;
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -9.6e-34)
		tmp = y * z;
	elseif (y <= 8400000000000.0)
		tmp = x;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -9.6e-34], N[(y * z), $MachinePrecision], If[LessEqual[y, 8400000000000.0], x, N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.59999999999999965e-34

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 60.9%

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

   4. Taylor expanded in z around inf 60.5%

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

   5. Taylor expanded in y around inf 57.1%

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

   if -9.59999999999999965e-34 < y < 8.4e12

   1. Initial program 100.0%

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

      1. distribute-rgt-in 100.0%

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

      2. fma-define 100.0%

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

      3. *-commutative 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around 0 68.8%

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

   if 8.4e12 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 99.9%

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

   4. Taylor expanded in z around inf 99.9%

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

   5. Taylor expanded in x around inf 57.3%

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

      1. *-commutative 57.3%

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

   7. Simplified 57.3%

      \[\leadsto \color{blue}{y \cdot x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.6 \cdot 10^{-34}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 8400000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return x + (y * (x + 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 = x + (y * (x + z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

   \[\leadsto x + y \cdot \left(x + z\right) \]
4. Add Preprocessing

Alternative 8: 36.7% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y, z):
	return x

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 100.0%

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

   1. distribute-rgt-in 99.2%

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

   2. fma-define 99.6%

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

   3. *-commutative 99.6%

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

4. Applied egg-rr 99.6%

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

5. Taylor expanded in y around 0 36.8%

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

Reproduce

herbie shell --seed 2024185 
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))