Main:bigenough2 from A

Percentage Accurate: 100.0% → 100.0%

Time: 5.2s

Alternatives: 8

Speedup: 1.0×

• 20.7% 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-def 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. Final simplification 100.0%

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

Alternative 2: 62.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+117}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -9.8 \cdot 10^{+30}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{-19}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+70}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -8.5e+117)
   (* y z)
   (if (<= y -9.8e+30)
     (* y x)
     (if (<= y -8.8e-19)
       (* y z)
       (if (<= y 1.2e-17) x (if (<= y 1.9e+70) (* y z) (* y x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -8.5e+117) {
		tmp = y * z;
	} else if (y <= -9.8e+30) {
		tmp = y * x;
	} else if (y <= -8.8e-19) {
		tmp = y * z;
	} else if (y <= 1.2e-17) {
		tmp = x;
	} else if (y <= 1.9e+70) {
		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 <= (-8.5d+117)) then
        tmp = y * z
    else if (y <= (-9.8d+30)) then
        tmp = y * x
    else if (y <= (-8.8d-19)) then
        tmp = y * z
    else if (y <= 1.2d-17) then
        tmp = x
    else if (y <= 1.9d+70) 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 <= -8.5e+117) {
		tmp = y * z;
	} else if (y <= -9.8e+30) {
		tmp = y * x;
	} else if (y <= -8.8e-19) {
		tmp = y * z;
	} else if (y <= 1.2e-17) {
		tmp = x;
	} else if (y <= 1.9e+70) {
		tmp = y * z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -8.5e+117:
		tmp = y * z
	elif y <= -9.8e+30:
		tmp = y * x
	elif y <= -8.8e-19:
		tmp = y * z
	elif y <= 1.2e-17:
		tmp = x
	elif y <= 1.9e+70:
		tmp = y * z
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -8.5e+117)
		tmp = Float64(y * z);
	elseif (y <= -9.8e+30)
		tmp = Float64(y * x);
	elseif (y <= -8.8e-19)
		tmp = Float64(y * z);
	elseif (y <= 1.2e-17)
		tmp = x;
	elseif (y <= 1.9e+70)
		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 <= -8.5e+117)
		tmp = y * z;
	elseif (y <= -9.8e+30)
		tmp = y * x;
	elseif (y <= -8.8e-19)
		tmp = y * z;
	elseif (y <= 1.2e-17)
		tmp = x;
	elseif (y <= 1.9e+70)
		tmp = y * z;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -8.5e+117], N[(y * z), $MachinePrecision], If[LessEqual[y, -9.8e+30], N[(y * x), $MachinePrecision], If[LessEqual[y, -8.8e-19], N[(y * z), $MachinePrecision], If[LessEqual[y, 1.2e-17], x, If[LessEqual[y, 1.9e+70], N[(y * z), $MachinePrecision], N[(y * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.49999999999999966e117 or -9.79999999999999969e30 < y < -8.7999999999999994e-19 or 1.19999999999999993e-17 < y < 1.8999999999999999e70

   1. Initial program 100.0%

      \[x + y \cdot \left(z + x\right) \]

   2. Taylor expanded in z around inf 69.8%

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

   3. Taylor expanded in x around 0 66.2%

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

   if -8.49999999999999966e117 < y < -9.79999999999999969e30 or 1.8999999999999999e70 < y

   1. Initial program 100.0%

      \[x + y \cdot \left(z + x\right) \]

   2. Taylor expanded in x around inf 66.3%

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

      1. +-commutative 66.3%

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

   4. Simplified 66.3%

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

   5. Taylor expanded in y around inf 66.3%

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

   if -8.7999999999999994e-19 < y < 1.19999999999999993e-17

   1. Initial program 100.0%

      \[x + y \cdot \left(z + x\right) \]

   2. Taylor expanded in y around 0 78.0%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+117}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -9.8 \cdot 10^{+30}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{-19}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+70}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 3: 75.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{-28} \lor \neg \left(x \leq 1.45 \cdot 10^{-126}\right):\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.1e-28) (not (<= x 1.45e-126))) (* x (+ y 1.0)) (* y z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.1e-28) || !(x <= 1.45e-126)) {
		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 <= (-3.1d-28)) .or. (.not. (x <= 1.45d-126))) 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 <= -3.1e-28) || !(x <= 1.45e-126)) {
		tmp = x * (y + 1.0);
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.1e-28) or not (x <= 1.45e-126):
		tmp = x * (y + 1.0)
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.1e-28) || !(x <= 1.45e-126))
		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 <= -3.1e-28) || ~((x <= 1.45e-126)))
		tmp = x * (y + 1.0);
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.1e-28], N[Not[LessEqual[x, 1.45e-126]], $MachinePrecision]], N[(x * N[(y + 1.0), $MachinePrecision]), $MachinePrecision], N[(y * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.09999999999999992e-28 or 1.44999999999999994e-126 < x

   1. Initial program 100.0%

      \[x + y \cdot \left(z + x\right) \]

   2. Taylor expanded in x around inf 83.6%

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

      1. +-commutative 83.6%

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

   4. Simplified 83.6%

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

   if -3.09999999999999992e-28 < x < 1.44999999999999994e-126

   1. Initial program 100.0%

      \[x + y \cdot \left(z + x\right) \]

   2. Taylor expanded in z around inf 92.6%

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

   3. Taylor expanded in x around 0 78.7%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{-28} \lor \neg \left(x \leq 1.45 \cdot 10^{-126}\right):\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 4: 75.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{-28}:\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-126}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.95e-28)
   (* x (+ y 1.0))
   (if (<= x 1.6e-126) (* y z) (+ x (* y x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.95e-28) {
		tmp = x * (y + 1.0);
	} else if (x <= 1.6e-126) {
		tmp = y * z;
	} else {
		tmp = x + (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 (x <= (-1.95d-28)) then
        tmp = x * (y + 1.0d0)
    else if (x <= 1.6d-126) then
        tmp = y * z
    else
        tmp = x + (y * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.95e-28) {
		tmp = x * (y + 1.0);
	} else if (x <= 1.6e-126) {
		tmp = y * z;
	} else {
		tmp = x + (y * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.95e-28:
		tmp = x * (y + 1.0)
	elif x <= 1.6e-126:
		tmp = y * z
	else:
		tmp = x + (y * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.95e-28)
		tmp = Float64(x * Float64(y + 1.0));
	elseif (x <= 1.6e-126)
		tmp = Float64(y * z);
	else
		tmp = Float64(x + Float64(y * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.95e-28)
		tmp = x * (y + 1.0);
	elseif (x <= 1.6e-126)
		tmp = y * z;
	else
		tmp = x + (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.95e-28], N[(x * N[(y + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.6e-126], N[(y * z), $MachinePrecision], N[(x + N[(y * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.94999999999999999e-28

   1. Initial program 100.0%

      \[x + y \cdot \left(z + x\right) \]

   2. Taylor expanded in x around inf 85.9%

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

      1. +-commutative 85.9%

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

   4. Simplified 85.9%

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

   if -1.94999999999999999e-28 < x < 1.6e-126

   1. Initial program 100.0%

      \[x + y \cdot \left(z + x\right) \]

   2. Taylor expanded in z around inf 92.6%

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

   3. Taylor expanded in x around 0 78.7%

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

   if 1.6e-126 < x

   1. Initial program 100.0%

      \[x + y \cdot \left(z + x\right) \]

   2. Taylor expanded in z around 0 81.6%

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

      1. *-commutative 81.6%

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

   4. Simplified 81.6%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{-28}:\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-126}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot x\\ \end{array} \]

Alternative 5: 86.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-39}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -8.2e+18)
   (* x (+ y 1.0))
   (if (<= x 7e-39) (+ x (* y z)) (+ x (* y x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -8.2e+18) {
		tmp = x * (y + 1.0);
	} else if (x <= 7e-39) {
		tmp = x + (y * z);
	} else {
		tmp = x + (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 (x <= (-8.2d+18)) then
        tmp = x * (y + 1.0d0)
    else if (x <= 7d-39) then
        tmp = x + (y * z)
    else
        tmp = x + (y * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -8.2e+18) {
		tmp = x * (y + 1.0);
	} else if (x <= 7e-39) {
		tmp = x + (y * z);
	} else {
		tmp = x + (y * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -8.2e+18:
		tmp = x * (y + 1.0)
	elif x <= 7e-39:
		tmp = x + (y * z)
	else:
		tmp = x + (y * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -8.2e+18)
		tmp = Float64(x * Float64(y + 1.0));
	elseif (x <= 7e-39)
		tmp = Float64(x + Float64(y * z));
	else
		tmp = Float64(x + Float64(y * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -8.2e+18)
		tmp = x * (y + 1.0);
	elseif (x <= 7e-39)
		tmp = x + (y * z);
	else
		tmp = x + (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -8.2e+18], N[(x * N[(y + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7e-39], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.2e18

   1. Initial program 100.0%

      \[x + y \cdot \left(z + x\right) \]

   2. Taylor expanded in x around inf 89.4%

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

      1. +-commutative 89.4%

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

   4. Simplified 89.4%

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

   if -8.2e18 < x < 6.99999999999999999e-39

   1. Initial program 100.0%

      \[x + y \cdot \left(z + x\right) \]

   2. Taylor expanded in z around inf 86.6%

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

   if 6.99999999999999999e-39 < x

   1. Initial program 100.0%

      \[x + y \cdot \left(z + x\right) \]

   2. Taylor expanded in z around 0 89.6%

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

      1. *-commutative 89.6%

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

   4. Simplified 89.6%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-39}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot x\\ \end{array} \]

Alternative 6: 61.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -56:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 0.0004:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -56.0) (* y x) (if (<= y 0.0004) x (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -56.0) {
		tmp = y * x;
	} else if (y <= 0.0004) {
		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 <= (-56.0d0)) then
        tmp = y * x
    else if (y <= 0.0004d0) 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 <= -56.0) {
		tmp = y * x;
	} else if (y <= 0.0004) {
		tmp = x;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -56.0:
		tmp = y * x
	elif y <= 0.0004:
		tmp = x
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -56.0)
		tmp = Float64(y * x);
	elseif (y <= 0.0004)
		tmp = x;
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -56.0)
		tmp = y * x;
	elseif (y <= 0.0004)
		tmp = x;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -56.0], N[(y * x), $MachinePrecision], If[LessEqual[y, 0.0004], x, N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -56 or 4.00000000000000019e-4 < y

   1. Initial program 100.0%

      \[x + y \cdot \left(z + x\right) \]

   2. Taylor expanded in x around inf 52.9%

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

      1. +-commutative 52.9%

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

   4. Simplified 52.9%

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

   5. Taylor expanded in y around inf 52.6%

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

   if -56 < y < 4.00000000000000019e-4

   1. Initial program 100.0%

      \[x + y \cdot \left(z + x\right) \]

   2. Taylor expanded in y around 0 72.8%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -56:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 0.0004:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

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. Final simplification 100.0%

   \[\leadsto x + y \cdot \left(x + z\right) \]

Alternative 8: 37.3% 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. Taylor expanded in y around 0 38.9%

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

3. Final simplification 38.9%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023275 
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))