Main:bigenough2 from A

Percentage Accurate: 100.0% → 100.0%

Time: 3.3s

Alternatives: 8

Speedup: 1.0×

• 20.2% of points produce a very large (infinite) output. You may want to add a precondition.

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: 61.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+205}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{+48}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{+21}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-70}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-39}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 50000000000:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3e+205)
   (* y x)
   (if (<= y -3.2e+48)
     (* y z)
     (if (<= y -1.7e+21)
       (* y x)
       (if (<= y -5.4e-70)
         (* y z)
         (if (<= y 2.9e-39) x (if (<= y 50000000000.0) (* y z) (* y x))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3e+205) {
		tmp = y * x;
	} else if (y <= -3.2e+48) {
		tmp = y * z;
	} else if (y <= -1.7e+21) {
		tmp = y * x;
	} else if (y <= -5.4e-70) {
		tmp = y * z;
	} else if (y <= 2.9e-39) {
		tmp = x;
	} else if (y <= 50000000000.0) {
		tmp = y * z;
	} 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 <= (-3d+205)) then
        tmp = y * x
    else if (y <= (-3.2d+48)) then
        tmp = y * z
    else if (y <= (-1.7d+21)) then
        tmp = y * x
    else if (y <= (-5.4d-70)) then
        tmp = y * z
    else if (y <= 2.9d-39) then
        tmp = x
    else if (y <= 50000000000.0d0) then
        tmp = y * z
    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 <= -3e+205) {
		tmp = y * x;
	} else if (y <= -3.2e+48) {
		tmp = y * z;
	} else if (y <= -1.7e+21) {
		tmp = y * x;
	} else if (y <= -5.4e-70) {
		tmp = y * z;
	} else if (y <= 2.9e-39) {
		tmp = x;
	} else if (y <= 50000000000.0) {
		tmp = y * z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3e+205:
		tmp = y * x
	elif y <= -3.2e+48:
		tmp = y * z
	elif y <= -1.7e+21:
		tmp = y * x
	elif y <= -5.4e-70:
		tmp = y * z
	elif y <= 2.9e-39:
		tmp = x
	elif y <= 50000000000.0:
		tmp = y * z
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3e+205)
		tmp = Float64(y * x);
	elseif (y <= -3.2e+48)
		tmp = Float64(y * z);
	elseif (y <= -1.7e+21)
		tmp = Float64(y * x);
	elseif (y <= -5.4e-70)
		tmp = Float64(y * z);
	elseif (y <= 2.9e-39)
		tmp = x;
	elseif (y <= 50000000000.0)
		tmp = Float64(y * z);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3e+205)
		tmp = y * x;
	elseif (y <= -3.2e+48)
		tmp = y * z;
	elseif (y <= -1.7e+21)
		tmp = y * x;
	elseif (y <= -5.4e-70)
		tmp = y * z;
	elseif (y <= 2.9e-39)
		tmp = x;
	elseif (y <= 50000000000.0)
		tmp = y * z;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3e+205], N[(y * x), $MachinePrecision], If[LessEqual[y, -3.2e+48], N[(y * z), $MachinePrecision], If[LessEqual[y, -1.7e+21], N[(y * x), $MachinePrecision], If[LessEqual[y, -5.4e-70], N[(y * z), $MachinePrecision], If[LessEqual[y, 2.9e-39], x, If[LessEqual[y, 50000000000.0], N[(y * z), $MachinePrecision], N[(y * x), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.9999999999999999e205 or -3.2000000000000001e48 < y < -1.7e21 or 5e10 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 97.9%

      \[\leadsto \color{blue}{x \cdot \left(1 + y\right) + y \cdot z} \]

   4. Taylor expanded in y around inf 99.7%

      \[\leadsto \color{blue}{y \cdot \left(x + z\right)} \]
   5. Step-by-step derivation

      1. +-commutative 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in z around 0 65.8%

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

      1. *-commutative 65.8%

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

   9. Simplified 65.8%

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

   if -2.9999999999999999e205 < y < -3.2000000000000001e48 or -1.7e21 < y < -5.4000000000000003e-70 or 2.89999999999999988e-39 < y < 5e10

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 98.4%

      \[\leadsto \color{blue}{x \cdot \left(1 + y\right) + y \cdot z} \]

   4. Taylor expanded in x around 0 63.1%

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

   if -5.4000000000000003e-70 < y < 2.89999999999999988e-39

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 75.7%

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

Alternative 3: 98.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+20} \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.6e+20) (not (<= y 1.0))) (* y (+ x z)) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.6e+20) || !(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 <= (-2.6d+20)) .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 <= -2.6e+20) || !(y <= 1.0)) {
		tmp = y * (x + z);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.6e+20) 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 <= -2.6e+20) || !(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 <= -2.6e+20) || ~((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, -2.6e+20], 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 < -2.6e20 or 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 97.7%

      \[\leadsto \color{blue}{x \cdot \left(1 + y\right) + y \cdot z} \]

   4. Taylor expanded in y around inf 99.8%

      \[\leadsto \color{blue}{y \cdot \left(x + z\right)} \]
   5. Step-by-step derivation

      1. +-commutative 99.8%

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

   6. Simplified 99.8%

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

   if -2.6e20 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 97.7%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+20} \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+15} \lor \neg \left(x \leq 2.1 \cdot 10^{+69}\right):\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3e+15) (not (<= x 2.1e+69))) (* x (+ y 1.0)) (* y (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3e+15) || !(x <= 2.1e+69)) {
		tmp = x * (y + 1.0);
	} 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 <= (-3d+15)) .or. (.not. (x <= 2.1d+69))) then
        tmp = x * (y + 1.0d0)
    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 <= -3e+15) || !(x <= 2.1e+69)) {
		tmp = x * (y + 1.0);
	} else {
		tmp = y * (x + z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3e+15) or not (x <= 2.1e+69):
		tmp = x * (y + 1.0)
	else:
		tmp = y * (x + z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3e+15) || !(x <= 2.1e+69))
		tmp = Float64(x * Float64(y + 1.0));
	else
		tmp = Float64(y * Float64(x + z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -3e+15) || ~((x <= 2.1e+69)))
		tmp = x * (y + 1.0);
	else
		tmp = y * (x + z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3e+15], N[Not[LessEqual[x, 2.1e+69]], $MachinePrecision]], N[(x * N[(y + 1.0), $MachinePrecision]), $MachinePrecision], N[(y * N[(x + z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3e15 or 2.10000000000000015e69 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 94.8%

      \[\leadsto \color{blue}{x \cdot \left(1 + y\right)} \]
   4. Step-by-step derivation

      1. +-commutative 94.8%

         \[\leadsto x \cdot \color{blue}{\left(y + 1\right)} \]

   5. Simplified 94.8%

      \[\leadsto \color{blue}{x \cdot \left(y + 1\right)} \]

   if -3e15 < x < 2.10000000000000015e69

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

      \[\leadsto \color{blue}{x \cdot \left(1 + y\right) + y \cdot z} \]

   4. Taylor expanded in y around inf 80.7%

      \[\leadsto \color{blue}{y \cdot \left(x + z\right)} \]
   5. Step-by-step derivation

      1. +-commutative 80.7%

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

   6. Simplified 80.7%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+15} \lor \neg \left(x \leq 2.1 \cdot 10^{+69}\right):\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.1 \cdot 10^{-117} \lor \neg \left(x \leq 1.1 \cdot 10^{-104}\right):\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.1e-117) (not (<= x 1.1e-104))) (* x (+ y 1.0)) (* y z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.1e-117) || !(x <= 1.1e-104)) {
		tmp = x * (y + 1.0);
	} else {
		tmp = 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 ((x <= (-5.1d-117)) .or. (.not. (x <= 1.1d-104))) then
        tmp = x * (y + 1.0d0)
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.1e-117) || !(x <= 1.1e-104)) {
		tmp = x * (y + 1.0);
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.1e-117) or not (x <= 1.1e-104):
		tmp = x * (y + 1.0)
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.1e-117) || !(x <= 1.1e-104))
		tmp = Float64(x * Float64(y + 1.0));
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -5.1e-117) || ~((x <= 1.1e-104)))
		tmp = x * (y + 1.0);
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.1e-117], N[Not[LessEqual[x, 1.1e-104]], $MachinePrecision]], N[(x * N[(y + 1.0), $MachinePrecision]), $MachinePrecision], N[(y * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.1000000000000002e-117 or 1.10000000000000006e-104 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 81.6%

      \[\leadsto \color{blue}{x \cdot \left(1 + y\right)} \]
   4. Step-by-step derivation

      1. +-commutative 81.6%

         \[\leadsto x \cdot \color{blue}{\left(y + 1\right)} \]

   5. Simplified 81.6%

      \[\leadsto \color{blue}{x \cdot \left(y + 1\right)} \]

   if -5.1000000000000002e-117 < x < 1.10000000000000006e-104

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

      \[\leadsto \color{blue}{x \cdot \left(1 + y\right) + y \cdot z} \]

   4. Taylor expanded in x around 0 81.4%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.1 \cdot 10^{-117} \lor \neg \left(x \leq 1.1 \cdot 10^{-104}\right):\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+20} \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.6e+20) (not (<= y 1.0))) (* y x) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.6e+20) || !(y <= 1.0)) {
		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 <= (-2.6d+20)) .or. (.not. (y <= 1.0d0))) 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 <= -2.6e+20) || !(y <= 1.0)) {
		tmp = y * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.6e+20) or not (y <= 1.0):
		tmp = y * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.6e+20) || !(y <= 1.0))
		tmp = Float64(y * x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.6e+20) || ~((y <= 1.0)))
		tmp = y * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.6e+20], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(y * x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.6e20 or 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 97.7%

      \[\leadsto \color{blue}{x \cdot \left(1 + y\right) + y \cdot z} \]

   4. Taylor expanded in y around inf 99.8%

      \[\leadsto \color{blue}{y \cdot \left(x + z\right)} \]
   5. Step-by-step derivation

      1. +-commutative 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in z around 0 58.4%

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

      1. *-commutative 58.4%

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

   9. Simplified 58.4%

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

   if -2.6e20 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 64.6%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+20} \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
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. Taylor expanded in y around 0 34.0%

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

Reproduce

herbie shell --seed 2024086 
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))