Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, B

Percentage Accurate: 99.8% → 100.0%

Time: 7.0s

Alternatives: 9

Speedup: 1.2×

• 22.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (* 4.0 (- (- x y) (* z 0.5))) z))

C

double code(double x, double y, double z) {
	return (4.0 * ((x - y) - (z * 0.5))) / 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 = (4.0d0 * ((x - y) - (z * 0.5d0))) / z
end function

Java

public static double code(double x, double y, double z) {
	return (4.0 * ((x - y) - (z * 0.5))) / z;
}

Python

def code(x, y, z):
	return (4.0 * ((x - y) - (z * 0.5))) / z

Julia

function code(x, y, z)
	return Float64(Float64(4.0 * Float64(Float64(x - y) - Float64(z * 0.5))) / z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (4.0 * ((x - y) - (z * 0.5))) / z;
end

Wolfram

code[x_, y_, z_] := N[(N[(4.0 * N[(N[(x - y), $MachinePrecision] - N[(z * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]

Initial Program: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (* 4.0 (- (- x y) (* z 0.5))) z))

C

double code(double x, double y, double z) {
	return (4.0 * ((x - y) - (z * 0.5))) / 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 = (4.0d0 * ((x - y) - (z * 0.5d0))) / z
end function

Java

public static double code(double x, double y, double z) {
	return (4.0 * ((x - y) - (z * 0.5))) / z;
}

Python

def code(x, y, z):
	return (4.0 * ((x - y) - (z * 0.5))) / z

Julia

function code(x, y, z)
	return Float64(Float64(4.0 * Float64(Float64(x - y) - Float64(z * 0.5))) / z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (4.0 * ((x - y) - (z * 0.5))) / z;
end

Wolfram

code[x_, y_, z_] := N[(N[(4.0 * N[(N[(x - y), $MachinePrecision] - N[(z * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ -4 \cdot \left(\frac{y - x}{z} - -0.5\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* -4.0 (- (/ (- y x) z) -0.5)))

C

double code(double x, double y, double z) {
	return -4.0 * (((y - x) / z) - -0.5);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (-4.0d0) * (((y - x) / z) - (-0.5d0))
end function

Java

public static double code(double x, double y, double z) {
	return -4.0 * (((y - x) / z) - -0.5);
}

Python

def code(x, y, z):
	return -4.0 * (((y - x) / z) - -0.5)

Julia

function code(x, y, z)
	return Float64(-4.0 * Float64(Float64(Float64(y - x) / z) - -0.5))
end

MATLAB

function tmp = code(x, y, z)
	tmp = -4.0 * (((y - x) / z) - -0.5);
end

Wolfram

code[x_, y_, z_] := N[(-4.0 * N[(N[(N[(y - x), $MachinePrecision] / z), $MachinePrecision] - -0.5), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.6%

   \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
2. Step-by-step derivation

   1. remove-double-neg 99.6%

      \[\leadsto \frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{\color{blue}{-\left(-z\right)}} \]

   2. neg-mul-1 99.6%

      \[\leadsto \frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{\color{blue}{-1 \cdot \left(-z\right)}} \]

   3. times-frac 100.0%

      \[\leadsto \color{blue}{\frac{4}{-1} \cdot \frac{\left(x - y\right) - z \cdot 0.5}{-z}} \]

   4. metadata-eval 100.0%

      \[\leadsto \color{blue}{-4} \cdot \frac{\left(x - y\right) - z \cdot 0.5}{-z} \]

   5. div-sub 100.0%

      \[\leadsto -4 \cdot \color{blue}{\left(\frac{x - y}{-z} - \frac{z \cdot 0.5}{-z}\right)} \]

   6. distribute-frac-neg2 100.0%

      \[\leadsto -4 \cdot \left(\color{blue}{\left(-\frac{x - y}{z}\right)} - \frac{z \cdot 0.5}{-z}\right) \]

   7. distribute-frac-neg 100.0%

      \[\leadsto -4 \cdot \left(\color{blue}{\frac{-\left(x - y\right)}{z}} - \frac{z \cdot 0.5}{-z}\right) \]

   8. sub-neg 100.0%

      \[\leadsto -4 \cdot \left(\frac{-\color{blue}{\left(x + \left(-y\right)\right)}}{z} - \frac{z \cdot 0.5}{-z}\right) \]

   9. +-commutative 100.0%

      \[\leadsto -4 \cdot \left(\frac{-\color{blue}{\left(\left(-y\right) + x\right)}}{z} - \frac{z \cdot 0.5}{-z}\right) \]

   10. distribute-neg-out 100.0%

       \[\leadsto -4 \cdot \left(\frac{\color{blue}{\left(-\left(-y\right)\right) + \left(-x\right)}}{z} - \frac{z \cdot 0.5}{-z}\right) \]

   11. remove-double-neg 100.0%

       \[\leadsto -4 \cdot \left(\frac{\color{blue}{y} + \left(-x\right)}{z} - \frac{z \cdot 0.5}{-z}\right) \]

   12. sub-neg 100.0%

       \[\leadsto -4 \cdot \left(\frac{\color{blue}{y - x}}{z} - \frac{z \cdot 0.5}{-z}\right) \]

   13. *-commutative 100.0%

       \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \frac{\color{blue}{0.5 \cdot z}}{-z}\right) \]

   14. neg-mul-1 100.0%

       \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \frac{0.5 \cdot z}{\color{blue}{-1 \cdot z}}\right) \]

   15. times-frac 100.0%

       \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \color{blue}{\frac{0.5}{-1} \cdot \frac{z}{z}}\right) \]

   16. metadata-eval 100.0%

       \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \color{blue}{-0.5} \cdot \frac{z}{z}\right) \]

   17. *-inverses 100.0%

       \[\leadsto -4 \cdot \left(\frac{y - x}{z} - -0.5 \cdot \color{blue}{1}\right) \]

   18. metadata-eval 100.0%

       \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \color{blue}{-0.5}\right) \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{-4 \cdot \left(\frac{y - x}{z} - -0.5\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 52.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-4 \cdot y}{z}\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{-42}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-171}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-53}:\\ \;\;\;\;\frac{x \cdot 4}{z}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+20}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* -4.0 y) z)))
   (if (<= z -5.2e-42)
     -2.0
     (if (<= z 5.8e-171)
       t_0
       (if (<= z 1.85e-53) (/ (* x 4.0) z) (if (<= z 5.5e+20) t_0 -2.0))))))

C

double code(double x, double y, double z) {
	double t_0 = (-4.0 * y) / z;
	double tmp;
	if (z <= -5.2e-42) {
		tmp = -2.0;
	} else if (z <= 5.8e-171) {
		tmp = t_0;
	} else if (z <= 1.85e-53) {
		tmp = (x * 4.0) / z;
	} else if (z <= 5.5e+20) {
		tmp = t_0;
	} else {
		tmp = -2.0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = ((-4.0d0) * y) / z
    if (z <= (-5.2d-42)) then
        tmp = -2.0d0
    else if (z <= 5.8d-171) then
        tmp = t_0
    else if (z <= 1.85d-53) then
        tmp = (x * 4.0d0) / z
    else if (z <= 5.5d+20) then
        tmp = t_0
    else
        tmp = -2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (-4.0 * y) / z;
	double tmp;
	if (z <= -5.2e-42) {
		tmp = -2.0;
	} else if (z <= 5.8e-171) {
		tmp = t_0;
	} else if (z <= 1.85e-53) {
		tmp = (x * 4.0) / z;
	} else if (z <= 5.5e+20) {
		tmp = t_0;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (-4.0 * y) / z
	tmp = 0
	if z <= -5.2e-42:
		tmp = -2.0
	elif z <= 5.8e-171:
		tmp = t_0
	elif z <= 1.85e-53:
		tmp = (x * 4.0) / z
	elif z <= 5.5e+20:
		tmp = t_0
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-4.0 * y) / z)
	tmp = 0.0
	if (z <= -5.2e-42)
		tmp = -2.0;
	elseif (z <= 5.8e-171)
		tmp = t_0;
	elseif (z <= 1.85e-53)
		tmp = Float64(Float64(x * 4.0) / z);
	elseif (z <= 5.5e+20)
		tmp = t_0;
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (-4.0 * y) / z;
	tmp = 0.0;
	if (z <= -5.2e-42)
		tmp = -2.0;
	elseif (z <= 5.8e-171)
		tmp = t_0;
	elseif (z <= 1.85e-53)
		tmp = (x * 4.0) / z;
	elseif (z <= 5.5e+20)
		tmp = t_0;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(-4.0 * y), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -5.2e-42], -2.0, If[LessEqual[z, 5.8e-171], t$95$0, If[LessEqual[z, 1.85e-53], N[(N[(x * 4.0), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 5.5e+20], t$95$0, -2.0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.2e-42 or 5.5e20 < z

   1. Initial program 99.2%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Step-by-step derivation

      1. remove-double-neg 99.2%

         \[\leadsto \frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{\color{blue}{-\left(-z\right)}} \]

      2. neg-mul-1 99.2%

         \[\leadsto \frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{\color{blue}{-1 \cdot \left(-z\right)}} \]

      3. times-frac 100.0%

         \[\leadsto \color{blue}{\frac{4}{-1} \cdot \frac{\left(x - y\right) - z \cdot 0.5}{-z}} \]

      4. metadata-eval 100.0%

         \[\leadsto \color{blue}{-4} \cdot \frac{\left(x - y\right) - z \cdot 0.5}{-z} \]

      5. div-sub 100.0%

         \[\leadsto -4 \cdot \color{blue}{\left(\frac{x - y}{-z} - \frac{z \cdot 0.5}{-z}\right)} \]

      6. distribute-frac-neg2 100.0%

         \[\leadsto -4 \cdot \left(\color{blue}{\left(-\frac{x - y}{z}\right)} - \frac{z \cdot 0.5}{-z}\right) \]

      7. distribute-frac-neg 100.0%

         \[\leadsto -4 \cdot \left(\color{blue}{\frac{-\left(x - y\right)}{z}} - \frac{z \cdot 0.5}{-z}\right) \]

      8. sub-neg 100.0%

         \[\leadsto -4 \cdot \left(\frac{-\color{blue}{\left(x + \left(-y\right)\right)}}{z} - \frac{z \cdot 0.5}{-z}\right) \]

      9. +-commutative 100.0%

         \[\leadsto -4 \cdot \left(\frac{-\color{blue}{\left(\left(-y\right) + x\right)}}{z} - \frac{z \cdot 0.5}{-z}\right) \]

      10. distribute-neg-out 100.0%

          \[\leadsto -4 \cdot \left(\frac{\color{blue}{\left(-\left(-y\right)\right) + \left(-x\right)}}{z} - \frac{z \cdot 0.5}{-z}\right) \]

      11. remove-double-neg 100.0%

          \[\leadsto -4 \cdot \left(\frac{\color{blue}{y} + \left(-x\right)}{z} - \frac{z \cdot 0.5}{-z}\right) \]

      12. sub-neg 100.0%

          \[\leadsto -4 \cdot \left(\frac{\color{blue}{y - x}}{z} - \frac{z \cdot 0.5}{-z}\right) \]

      13. *-commutative 100.0%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \frac{\color{blue}{0.5 \cdot z}}{-z}\right) \]

      14. neg-mul-1 100.0%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \frac{0.5 \cdot z}{\color{blue}{-1 \cdot z}}\right) \]

      15. times-frac 100.0%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \color{blue}{\frac{0.5}{-1} \cdot \frac{z}{z}}\right) \]

      16. metadata-eval 100.0%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \color{blue}{-0.5} \cdot \frac{z}{z}\right) \]

      17. *-inverses 100.0%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - -0.5 \cdot \color{blue}{1}\right) \]

      18. metadata-eval 100.0%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \color{blue}{-0.5}\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{-4 \cdot \left(\frac{y - x}{z} - -0.5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 66.0%

      \[\leadsto \color{blue}{-2} \]

   if -5.2e-42 < z < 5.7999999999999997e-171 or 1.84999999999999991e-53 < z < 5.5e20

   1. Initial program 100.0%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 67.0%

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

      1. *-commutative 67.0%

         \[\leadsto \frac{\color{blue}{y \cdot -4}}{z} \]

   5. Simplified 67.0%

      \[\leadsto \frac{\color{blue}{y \cdot -4}}{z} \]

   if 5.7999999999999997e-171 < z < 1.84999999999999991e-53

   1. Initial program 99.8%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 62.2%

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

      1. *-commutative 62.2%

         \[\leadsto \frac{\color{blue}{x \cdot 4}}{z} \]

   5. Simplified 62.2%

      \[\leadsto \frac{\color{blue}{x \cdot 4}}{z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-42}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-171}:\\ \;\;\;\;\frac{-4 \cdot y}{z}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-53}:\\ \;\;\;\;\frac{x \cdot 4}{z}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+20}:\\ \;\;\;\;\frac{-4 \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 52.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-4}{\frac{z}{y}}\\ \mathbf{if}\;z \leq -4.7 \cdot 10^{-42}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{-170}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-53}:\\ \;\;\;\;\frac{x \cdot 4}{z}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+20}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ -4.0 (/ z y))))
   (if (<= z -4.7e-42)
     -2.0
     (if (<= z 1.26e-170)
       t_0
       (if (<= z 3.3e-53) (/ (* x 4.0) z) (if (<= z 1.8e+20) t_0 -2.0))))))

C

double code(double x, double y, double z) {
	double t_0 = -4.0 / (z / y);
	double tmp;
	if (z <= -4.7e-42) {
		tmp = -2.0;
	} else if (z <= 1.26e-170) {
		tmp = t_0;
	} else if (z <= 3.3e-53) {
		tmp = (x * 4.0) / z;
	} else if (z <= 1.8e+20) {
		tmp = t_0;
	} else {
		tmp = -2.0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = (-4.0d0) / (z / y)
    if (z <= (-4.7d-42)) then
        tmp = -2.0d0
    else if (z <= 1.26d-170) then
        tmp = t_0
    else if (z <= 3.3d-53) then
        tmp = (x * 4.0d0) / z
    else if (z <= 1.8d+20) then
        tmp = t_0
    else
        tmp = -2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -4.0 / (z / y);
	double tmp;
	if (z <= -4.7e-42) {
		tmp = -2.0;
	} else if (z <= 1.26e-170) {
		tmp = t_0;
	} else if (z <= 3.3e-53) {
		tmp = (x * 4.0) / z;
	} else if (z <= 1.8e+20) {
		tmp = t_0;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -4.0 / (z / y)
	tmp = 0
	if z <= -4.7e-42:
		tmp = -2.0
	elif z <= 1.26e-170:
		tmp = t_0
	elif z <= 3.3e-53:
		tmp = (x * 4.0) / z
	elif z <= 1.8e+20:
		tmp = t_0
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-4.0 / Float64(z / y))
	tmp = 0.0
	if (z <= -4.7e-42)
		tmp = -2.0;
	elseif (z <= 1.26e-170)
		tmp = t_0;
	elseif (z <= 3.3e-53)
		tmp = Float64(Float64(x * 4.0) / z);
	elseif (z <= 1.8e+20)
		tmp = t_0;
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -4.0 / (z / y);
	tmp = 0.0;
	if (z <= -4.7e-42)
		tmp = -2.0;
	elseif (z <= 1.26e-170)
		tmp = t_0;
	elseif (z <= 3.3e-53)
		tmp = (x * 4.0) / z;
	elseif (z <= 1.8e+20)
		tmp = t_0;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-4.0 / N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.7e-42], -2.0, If[LessEqual[z, 1.26e-170], t$95$0, If[LessEqual[z, 3.3e-53], N[(N[(x * 4.0), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 1.8e+20], t$95$0, -2.0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.7000000000000001e-42 or 1.8e20 < z

   1. Initial program 99.2%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Step-by-step derivation

      1. remove-double-neg 99.2%

         \[\leadsto \frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{\color{blue}{-\left(-z\right)}} \]

      2. neg-mul-1 99.2%

         \[\leadsto \frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{\color{blue}{-1 \cdot \left(-z\right)}} \]

      3. times-frac 100.0%

         \[\leadsto \color{blue}{\frac{4}{-1} \cdot \frac{\left(x - y\right) - z \cdot 0.5}{-z}} \]

      4. metadata-eval 100.0%

         \[\leadsto \color{blue}{-4} \cdot \frac{\left(x - y\right) - z \cdot 0.5}{-z} \]

      5. div-sub 100.0%

         \[\leadsto -4 \cdot \color{blue}{\left(\frac{x - y}{-z} - \frac{z \cdot 0.5}{-z}\right)} \]

      6. distribute-frac-neg2 100.0%

         \[\leadsto -4 \cdot \left(\color{blue}{\left(-\frac{x - y}{z}\right)} - \frac{z \cdot 0.5}{-z}\right) \]

      7. distribute-frac-neg 100.0%

         \[\leadsto -4 \cdot \left(\color{blue}{\frac{-\left(x - y\right)}{z}} - \frac{z \cdot 0.5}{-z}\right) \]

      8. sub-neg 100.0%

         \[\leadsto -4 \cdot \left(\frac{-\color{blue}{\left(x + \left(-y\right)\right)}}{z} - \frac{z \cdot 0.5}{-z}\right) \]

      9. +-commutative 100.0%

         \[\leadsto -4 \cdot \left(\frac{-\color{blue}{\left(\left(-y\right) + x\right)}}{z} - \frac{z \cdot 0.5}{-z}\right) \]

      10. distribute-neg-out 100.0%

          \[\leadsto -4 \cdot \left(\frac{\color{blue}{\left(-\left(-y\right)\right) + \left(-x\right)}}{z} - \frac{z \cdot 0.5}{-z}\right) \]

      11. remove-double-neg 100.0%

          \[\leadsto -4 \cdot \left(\frac{\color{blue}{y} + \left(-x\right)}{z} - \frac{z \cdot 0.5}{-z}\right) \]

      12. sub-neg 100.0%

          \[\leadsto -4 \cdot \left(\frac{\color{blue}{y - x}}{z} - \frac{z \cdot 0.5}{-z}\right) \]

      13. *-commutative 100.0%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \frac{\color{blue}{0.5 \cdot z}}{-z}\right) \]

      14. neg-mul-1 100.0%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \frac{0.5 \cdot z}{\color{blue}{-1 \cdot z}}\right) \]

      15. times-frac 100.0%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \color{blue}{\frac{0.5}{-1} \cdot \frac{z}{z}}\right) \]

      16. metadata-eval 100.0%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \color{blue}{-0.5} \cdot \frac{z}{z}\right) \]

      17. *-inverses 100.0%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - -0.5 \cdot \color{blue}{1}\right) \]

      18. metadata-eval 100.0%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \color{blue}{-0.5}\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{-4 \cdot \left(\frac{y - x}{z} - -0.5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 66.0%

      \[\leadsto \color{blue}{-2} \]

   if -4.7000000000000001e-42 < z < 1.26e-170 or 3.30000000000000004e-53 < z < 1.8e20

   1. Initial program 100.0%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 67.0%

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

      1. *-commutative 67.0%

         \[\leadsto \frac{\color{blue}{y \cdot -4}}{z} \]

   5. Simplified 67.0%

      \[\leadsto \frac{\color{blue}{y \cdot -4}}{z} \]

   6. Taylor expanded in y around 0 67.0%

      \[\leadsto \color{blue}{-4 \cdot \frac{y}{z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 67.0%

         \[\leadsto \color{blue}{\frac{-4 \cdot y}{z}} \]

      2. associate-*l/ 66.8%

         \[\leadsto \color{blue}{\frac{-4}{z} \cdot y} \]

      3. associate-/r/ 66.8%

         \[\leadsto \color{blue}{\frac{-4}{\frac{z}{y}}} \]

   8. Simplified 66.8%

      \[\leadsto \color{blue}{\frac{-4}{\frac{z}{y}}} \]

   if 1.26e-170 < z < 3.30000000000000004e-53

   1. Initial program 99.8%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 62.2%

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

      1. *-commutative 62.2%

         \[\leadsto \frac{\color{blue}{x \cdot 4}}{z} \]

   5. Simplified 62.2%

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

Alternative 4: 52.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-4}{\frac{z}{y}}\\ \mathbf{if}\;z \leq -5.6 \cdot 10^{-42}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-174}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-53}:\\ \;\;\;\;x \cdot \frac{4}{z}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+20}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ -4.0 (/ z y))))
   (if (<= z -5.6e-42)
     -2.0
     (if (<= z 6.4e-174)
       t_0
       (if (<= z 1.3e-53) (* x (/ 4.0 z)) (if (<= z 6.5e+20) t_0 -2.0))))))

C

double code(double x, double y, double z) {
	double t_0 = -4.0 / (z / y);
	double tmp;
	if (z <= -5.6e-42) {
		tmp = -2.0;
	} else if (z <= 6.4e-174) {
		tmp = t_0;
	} else if (z <= 1.3e-53) {
		tmp = x * (4.0 / z);
	} else if (z <= 6.5e+20) {
		tmp = t_0;
	} else {
		tmp = -2.0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = (-4.0d0) / (z / y)
    if (z <= (-5.6d-42)) then
        tmp = -2.0d0
    else if (z <= 6.4d-174) then
        tmp = t_0
    else if (z <= 1.3d-53) then
        tmp = x * (4.0d0 / z)
    else if (z <= 6.5d+20) then
        tmp = t_0
    else
        tmp = -2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -4.0 / (z / y);
	double tmp;
	if (z <= -5.6e-42) {
		tmp = -2.0;
	} else if (z <= 6.4e-174) {
		tmp = t_0;
	} else if (z <= 1.3e-53) {
		tmp = x * (4.0 / z);
	} else if (z <= 6.5e+20) {
		tmp = t_0;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -4.0 / (z / y)
	tmp = 0
	if z <= -5.6e-42:
		tmp = -2.0
	elif z <= 6.4e-174:
		tmp = t_0
	elif z <= 1.3e-53:
		tmp = x * (4.0 / z)
	elif z <= 6.5e+20:
		tmp = t_0
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-4.0 / Float64(z / y))
	tmp = 0.0
	if (z <= -5.6e-42)
		tmp = -2.0;
	elseif (z <= 6.4e-174)
		tmp = t_0;
	elseif (z <= 1.3e-53)
		tmp = Float64(x * Float64(4.0 / z));
	elseif (z <= 6.5e+20)
		tmp = t_0;
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -4.0 / (z / y);
	tmp = 0.0;
	if (z <= -5.6e-42)
		tmp = -2.0;
	elseif (z <= 6.4e-174)
		tmp = t_0;
	elseif (z <= 1.3e-53)
		tmp = x * (4.0 / z);
	elseif (z <= 6.5e+20)
		tmp = t_0;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-4.0 / N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.6e-42], -2.0, If[LessEqual[z, 6.4e-174], t$95$0, If[LessEqual[z, 1.3e-53], N[(x * N[(4.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e+20], t$95$0, -2.0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.59999999999999996e-42 or 6.5e20 < z

   1. Initial program 99.2%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Step-by-step derivation

      1. remove-double-neg 99.2%

         \[\leadsto \frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{\color{blue}{-\left(-z\right)}} \]

      2. neg-mul-1 99.2%

         \[\leadsto \frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{\color{blue}{-1 \cdot \left(-z\right)}} \]

      3. times-frac 100.0%

         \[\leadsto \color{blue}{\frac{4}{-1} \cdot \frac{\left(x - y\right) - z \cdot 0.5}{-z}} \]

      4. metadata-eval 100.0%

         \[\leadsto \color{blue}{-4} \cdot \frac{\left(x - y\right) - z \cdot 0.5}{-z} \]

      5. div-sub 100.0%

         \[\leadsto -4 \cdot \color{blue}{\left(\frac{x - y}{-z} - \frac{z \cdot 0.5}{-z}\right)} \]

      6. distribute-frac-neg2 100.0%

         \[\leadsto -4 \cdot \left(\color{blue}{\left(-\frac{x - y}{z}\right)} - \frac{z \cdot 0.5}{-z}\right) \]

      7. distribute-frac-neg 100.0%

         \[\leadsto -4 \cdot \left(\color{blue}{\frac{-\left(x - y\right)}{z}} - \frac{z \cdot 0.5}{-z}\right) \]

      8. sub-neg 100.0%

         \[\leadsto -4 \cdot \left(\frac{-\color{blue}{\left(x + \left(-y\right)\right)}}{z} - \frac{z \cdot 0.5}{-z}\right) \]

      9. +-commutative 100.0%

         \[\leadsto -4 \cdot \left(\frac{-\color{blue}{\left(\left(-y\right) + x\right)}}{z} - \frac{z \cdot 0.5}{-z}\right) \]

      10. distribute-neg-out 100.0%

          \[\leadsto -4 \cdot \left(\frac{\color{blue}{\left(-\left(-y\right)\right) + \left(-x\right)}}{z} - \frac{z \cdot 0.5}{-z}\right) \]

      11. remove-double-neg 100.0%

          \[\leadsto -4 \cdot \left(\frac{\color{blue}{y} + \left(-x\right)}{z} - \frac{z \cdot 0.5}{-z}\right) \]

      12. sub-neg 100.0%

          \[\leadsto -4 \cdot \left(\frac{\color{blue}{y - x}}{z} - \frac{z \cdot 0.5}{-z}\right) \]

      13. *-commutative 100.0%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \frac{\color{blue}{0.5 \cdot z}}{-z}\right) \]

      14. neg-mul-1 100.0%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \frac{0.5 \cdot z}{\color{blue}{-1 \cdot z}}\right) \]

      15. times-frac 100.0%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \color{blue}{\frac{0.5}{-1} \cdot \frac{z}{z}}\right) \]

      16. metadata-eval 100.0%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \color{blue}{-0.5} \cdot \frac{z}{z}\right) \]

      17. *-inverses 100.0%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - -0.5 \cdot \color{blue}{1}\right) \]

      18. metadata-eval 100.0%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \color{blue}{-0.5}\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{-4 \cdot \left(\frac{y - x}{z} - -0.5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 66.0%

      \[\leadsto \color{blue}{-2} \]

   if -5.59999999999999996e-42 < z < 6.4e-174 or 1.29999999999999998e-53 < z < 6.5e20

   1. Initial program 100.0%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 67.0%

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

      1. *-commutative 67.0%

         \[\leadsto \frac{\color{blue}{y \cdot -4}}{z} \]

   5. Simplified 67.0%

      \[\leadsto \frac{\color{blue}{y \cdot -4}}{z} \]

   6. Taylor expanded in y around 0 67.0%

      \[\leadsto \color{blue}{-4 \cdot \frac{y}{z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 67.0%

         \[\leadsto \color{blue}{\frac{-4 \cdot y}{z}} \]

      2. associate-*l/ 66.8%

         \[\leadsto \color{blue}{\frac{-4}{z} \cdot y} \]

      3. associate-/r/ 66.8%

         \[\leadsto \color{blue}{\frac{-4}{\frac{z}{y}}} \]

   8. Simplified 66.8%

      \[\leadsto \color{blue}{\frac{-4}{\frac{z}{y}}} \]

   if 6.4e-174 < z < 1.29999999999999998e-53

   1. Initial program 99.8%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Step-by-step derivation

      1. remove-double-neg 99.8%

         \[\leadsto \frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{\color{blue}{-\left(-z\right)}} \]

      2. neg-mul-1 99.8%

         \[\leadsto \frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{\color{blue}{-1 \cdot \left(-z\right)}} \]

      3. times-frac 99.8%

         \[\leadsto \color{blue}{\frac{4}{-1} \cdot \frac{\left(x - y\right) - z \cdot 0.5}{-z}} \]

      4. metadata-eval 99.8%

         \[\leadsto \color{blue}{-4} \cdot \frac{\left(x - y\right) - z \cdot 0.5}{-z} \]

      5. div-sub 99.9%

         \[\leadsto -4 \cdot \color{blue}{\left(\frac{x - y}{-z} - \frac{z \cdot 0.5}{-z}\right)} \]

      6. distribute-frac-neg2 99.9%

         \[\leadsto -4 \cdot \left(\color{blue}{\left(-\frac{x - y}{z}\right)} - \frac{z \cdot 0.5}{-z}\right) \]

      7. distribute-frac-neg 99.9%

         \[\leadsto -4 \cdot \left(\color{blue}{\frac{-\left(x - y\right)}{z}} - \frac{z \cdot 0.5}{-z}\right) \]

      8. sub-neg 99.9%

         \[\leadsto -4 \cdot \left(\frac{-\color{blue}{\left(x + \left(-y\right)\right)}}{z} - \frac{z \cdot 0.5}{-z}\right) \]

      9. +-commutative 99.9%

         \[\leadsto -4 \cdot \left(\frac{-\color{blue}{\left(\left(-y\right) + x\right)}}{z} - \frac{z \cdot 0.5}{-z}\right) \]

      10. distribute-neg-out 99.9%

          \[\leadsto -4 \cdot \left(\frac{\color{blue}{\left(-\left(-y\right)\right) + \left(-x\right)}}{z} - \frac{z \cdot 0.5}{-z}\right) \]

      11. remove-double-neg 99.9%

          \[\leadsto -4 \cdot \left(\frac{\color{blue}{y} + \left(-x\right)}{z} - \frac{z \cdot 0.5}{-z}\right) \]

      12. sub-neg 99.9%

          \[\leadsto -4 \cdot \left(\frac{\color{blue}{y - x}}{z} - \frac{z \cdot 0.5}{-z}\right) \]

      13. *-commutative 99.9%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \frac{\color{blue}{0.5 \cdot z}}{-z}\right) \]

      14. neg-mul-1 99.9%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \frac{0.5 \cdot z}{\color{blue}{-1 \cdot z}}\right) \]

      15. times-frac 99.9%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \color{blue}{\frac{0.5}{-1} \cdot \frac{z}{z}}\right) \]

      16. metadata-eval 99.9%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \color{blue}{-0.5} \cdot \frac{z}{z}\right) \]

      17. *-inverses 99.9%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - -0.5 \cdot \color{blue}{1}\right) \]

      18. metadata-eval 99.9%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \color{blue}{-0.5}\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{-4 \cdot \left(\frac{y - x}{z} - -0.5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 62.2%

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

      1. associate-*r/ 62.2%

         \[\leadsto \color{blue}{\frac{4 \cdot x}{z}} \]

      2. associate-*l/ 62.0%

         \[\leadsto \color{blue}{\frac{4}{z} \cdot x} \]

      3. *-commutative 62.0%

         \[\leadsto \color{blue}{x \cdot \frac{4}{z}} \]

   7. Simplified 62.0%

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

Alternative 5: 86.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+112} \lor \neg \left(x \leq 3.1 \cdot 10^{+49}\right):\\ \;\;\;\;x \cdot \frac{4}{z} + -2\\ \mathbf{else}:\\ \;\;\;\;-2 + -4 \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.5e+112) (not (<= x 3.1e+49)))
   (+ (* x (/ 4.0 z)) -2.0)
   (+ -2.0 (* -4.0 (/ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.5e+112) || !(x <= 3.1e+49)) {
		tmp = (x * (4.0 / z)) + -2.0;
	} else {
		tmp = -2.0 + (-4.0 * (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 <= (-2.5d+112)) .or. (.not. (x <= 3.1d+49))) then
        tmp = (x * (4.0d0 / z)) + (-2.0d0)
    else
        tmp = (-2.0d0) + ((-4.0d0) * (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.5e+112) || !(x <= 3.1e+49)) {
		tmp = (x * (4.0 / z)) + -2.0;
	} else {
		tmp = -2.0 + (-4.0 * (y / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.5e+112) or not (x <= 3.1e+49):
		tmp = (x * (4.0 / z)) + -2.0
	else:
		tmp = -2.0 + (-4.0 * (y / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.5e+112) || !(x <= 3.1e+49))
		tmp = Float64(Float64(x * Float64(4.0 / z)) + -2.0);
	else
		tmp = Float64(-2.0 + Float64(-4.0 * Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.5e+112) || ~((x <= 3.1e+49)))
		tmp = (x * (4.0 / z)) + -2.0;
	else
		tmp = -2.0 + (-4.0 * (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.5e+112], N[Not[LessEqual[x, 3.1e+49]], $MachinePrecision]], N[(N[(x * N[(4.0 / z), $MachinePrecision]), $MachinePrecision] + -2.0), $MachinePrecision], N[(-2.0 + N[(-4.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.5e112 or 3.09999999999999992e49 < x

   1. Initial program 98.9%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Step-by-step derivation

      1. remove-double-neg 98.9%

         \[\leadsto \frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{\color{blue}{-\left(-z\right)}} \]

      2. neg-mul-1 98.9%

         \[\leadsto \frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{\color{blue}{-1 \cdot \left(-z\right)}} \]

      3. times-frac 99.9%

         \[\leadsto \color{blue}{\frac{4}{-1} \cdot \frac{\left(x - y\right) - z \cdot 0.5}{-z}} \]

      4. metadata-eval 99.9%

         \[\leadsto \color{blue}{-4} \cdot \frac{\left(x - y\right) - z \cdot 0.5}{-z} \]

      5. div-sub 99.9%

         \[\leadsto -4 \cdot \color{blue}{\left(\frac{x - y}{-z} - \frac{z \cdot 0.5}{-z}\right)} \]

      6. distribute-frac-neg2 99.9%

         \[\leadsto -4 \cdot \left(\color{blue}{\left(-\frac{x - y}{z}\right)} - \frac{z \cdot 0.5}{-z}\right) \]

      7. distribute-frac-neg 99.9%

         \[\leadsto -4 \cdot \left(\color{blue}{\frac{-\left(x - y\right)}{z}} - \frac{z \cdot 0.5}{-z}\right) \]

      8. sub-neg 99.9%

         \[\leadsto -4 \cdot \left(\frac{-\color{blue}{\left(x + \left(-y\right)\right)}}{z} - \frac{z \cdot 0.5}{-z}\right) \]

      9. +-commutative 99.9%

         \[\leadsto -4 \cdot \left(\frac{-\color{blue}{\left(\left(-y\right) + x\right)}}{z} - \frac{z \cdot 0.5}{-z}\right) \]

      10. distribute-neg-out 99.9%

          \[\leadsto -4 \cdot \left(\frac{\color{blue}{\left(-\left(-y\right)\right) + \left(-x\right)}}{z} - \frac{z \cdot 0.5}{-z}\right) \]

      11. remove-double-neg 99.9%

          \[\leadsto -4 \cdot \left(\frac{\color{blue}{y} + \left(-x\right)}{z} - \frac{z \cdot 0.5}{-z}\right) \]

      12. sub-neg 99.9%

          \[\leadsto -4 \cdot \left(\frac{\color{blue}{y - x}}{z} - \frac{z \cdot 0.5}{-z}\right) \]

      13. *-commutative 99.9%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \frac{\color{blue}{0.5 \cdot z}}{-z}\right) \]

      14. neg-mul-1 99.9%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \frac{0.5 \cdot z}{\color{blue}{-1 \cdot z}}\right) \]

      15. times-frac 99.9%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \color{blue}{\frac{0.5}{-1} \cdot \frac{z}{z}}\right) \]

      16. metadata-eval 99.9%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \color{blue}{-0.5} \cdot \frac{z}{z}\right) \]

      17. *-inverses 99.9%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - -0.5 \cdot \color{blue}{1}\right) \]

      18. metadata-eval 99.9%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \color{blue}{-0.5}\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{-4 \cdot \left(\frac{y - x}{z} - -0.5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 91.2%

      \[\leadsto \color{blue}{-4 \cdot \left(0.5 - \frac{x}{z}\right)} \]
   6. Step-by-step derivation

      1. sub-neg 91.2%

         \[\leadsto -4 \cdot \color{blue}{\left(0.5 + \left(-\frac{x}{z}\right)\right)} \]

      2. +-commutative 91.2%

         \[\leadsto -4 \cdot \color{blue}{\left(\left(-\frac{x}{z}\right) + 0.5\right)} \]

      3. distribute-lft-in 91.2%

         \[\leadsto \color{blue}{-4 \cdot \left(-\frac{x}{z}\right) + -4 \cdot 0.5} \]

      4. metadata-eval 91.2%

         \[\leadsto \color{blue}{\frac{4}{-1}} \cdot \left(-\frac{x}{z}\right) + -4 \cdot 0.5 \]

      5. distribute-neg-frac2 91.2%

         \[\leadsto \frac{4}{-1} \cdot \color{blue}{\frac{x}{-z}} + -4 \cdot 0.5 \]

      6. times-frac 91.2%

         \[\leadsto \color{blue}{\frac{4 \cdot x}{-1 \cdot \left(-z\right)}} + -4 \cdot 0.5 \]

      7. neg-mul-1 91.2%

         \[\leadsto \frac{4 \cdot x}{\color{blue}{-\left(-z\right)}} + -4 \cdot 0.5 \]

      8. remove-double-neg 91.2%

         \[\leadsto \frac{4 \cdot x}{\color{blue}{z}} + -4 \cdot 0.5 \]

      9. associate-*l/ 91.1%

         \[\leadsto \color{blue}{\frac{4}{z} \cdot x} + -4 \cdot 0.5 \]

      10. *-commutative 91.1%

          \[\leadsto \color{blue}{x \cdot \frac{4}{z}} + -4 \cdot 0.5 \]

      11. metadata-eval 91.1%

          \[\leadsto x \cdot \frac{4}{z} + \color{blue}{-2} \]

   7. Simplified 91.1%

      \[\leadsto \color{blue}{x \cdot \frac{4}{z} + -2} \]

   if -2.5e112 < x < 3.09999999999999992e49

   1. Initial program 100.0%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Step-by-step derivation

      1. remove-double-neg 100.0%

         \[\leadsto \frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{\color{blue}{-\left(-z\right)}} \]

      2. neg-mul-1 100.0%

         \[\leadsto \frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{\color{blue}{-1 \cdot \left(-z\right)}} \]

      3. times-frac 100.0%

         \[\leadsto \color{blue}{\frac{4}{-1} \cdot \frac{\left(x - y\right) - z \cdot 0.5}{-z}} \]

      4. metadata-eval 100.0%

         \[\leadsto \color{blue}{-4} \cdot \frac{\left(x - y\right) - z \cdot 0.5}{-z} \]

      5. div-sub 100.0%

         \[\leadsto -4 \cdot \color{blue}{\left(\frac{x - y}{-z} - \frac{z \cdot 0.5}{-z}\right)} \]

      6. distribute-frac-neg2 100.0%

         \[\leadsto -4 \cdot \left(\color{blue}{\left(-\frac{x - y}{z}\right)} - \frac{z \cdot 0.5}{-z}\right) \]

      7. distribute-frac-neg 100.0%

         \[\leadsto -4 \cdot \left(\color{blue}{\frac{-\left(x - y\right)}{z}} - \frac{z \cdot 0.5}{-z}\right) \]

      8. sub-neg 100.0%

         \[\leadsto -4 \cdot \left(\frac{-\color{blue}{\left(x + \left(-y\right)\right)}}{z} - \frac{z \cdot 0.5}{-z}\right) \]

      9. +-commutative 100.0%

         \[\leadsto -4 \cdot \left(\frac{-\color{blue}{\left(\left(-y\right) + x\right)}}{z} - \frac{z \cdot 0.5}{-z}\right) \]

      10. distribute-neg-out 100.0%

          \[\leadsto -4 \cdot \left(\frac{\color{blue}{\left(-\left(-y\right)\right) + \left(-x\right)}}{z} - \frac{z \cdot 0.5}{-z}\right) \]

      11. remove-double-neg 100.0%

          \[\leadsto -4 \cdot \left(\frac{\color{blue}{y} + \left(-x\right)}{z} - \frac{z \cdot 0.5}{-z}\right) \]

      12. sub-neg 100.0%

          \[\leadsto -4 \cdot \left(\frac{\color{blue}{y - x}}{z} - \frac{z \cdot 0.5}{-z}\right) \]

      13. *-commutative 100.0%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \frac{\color{blue}{0.5 \cdot z}}{-z}\right) \]

      14. neg-mul-1 100.0%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \frac{0.5 \cdot z}{\color{blue}{-1 \cdot z}}\right) \]

      15. times-frac 100.0%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \color{blue}{\frac{0.5}{-1} \cdot \frac{z}{z}}\right) \]

      16. metadata-eval 100.0%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \color{blue}{-0.5} \cdot \frac{z}{z}\right) \]

      17. *-inverses 100.0%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - -0.5 \cdot \color{blue}{1}\right) \]

      18. metadata-eval 100.0%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \color{blue}{-0.5}\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{-4 \cdot \left(\frac{y - x}{z} - -0.5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 90.3%

      \[\leadsto \color{blue}{-4 \cdot \left(0.5 + \frac{y}{z}\right)} \]
   6. Step-by-step derivation

      1. +-commutative 90.3%

         \[\leadsto -4 \cdot \color{blue}{\left(\frac{y}{z} + 0.5\right)} \]

      2. distribute-rgt-in 90.3%

         \[\leadsto \color{blue}{\frac{y}{z} \cdot -4 + 0.5 \cdot -4} \]

      3. metadata-eval 90.3%

         \[\leadsto \frac{y}{z} \cdot -4 + \color{blue}{-2} \]

   7. Simplified 90.3%

      \[\leadsto \color{blue}{\frac{y}{z} \cdot -4 + -2} \]
3. Recombined 2 regimes into one program.

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+112} \lor \neg \left(x \leq 3.1 \cdot 10^{+49}\right):\\ \;\;\;\;x \cdot \frac{4}{z} + -2\\ \mathbf{else}:\\ \;\;\;\;-2 + -4 \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{-42} \lor \neg \left(z \leq 2.7 \cdot 10^{+20}\right):\\ \;\;\;\;x \cdot \frac{4}{z} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{4}{z} \cdot \left(x - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.6e-42) (not (<= z 2.7e+20)))
   (+ (* x (/ 4.0 z)) -2.0)
   (* (/ 4.0 z) (- x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.6e-42) || !(z <= 2.7e+20)) {
		tmp = (x * (4.0 / z)) + -2.0;
	} else {
		tmp = (4.0 / z) * (x - y);
	}
	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 ((z <= (-5.6d-42)) .or. (.not. (z <= 2.7d+20))) then
        tmp = (x * (4.0d0 / z)) + (-2.0d0)
    else
        tmp = (4.0d0 / z) * (x - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.6e-42) || !(z <= 2.7e+20)) {
		tmp = (x * (4.0 / z)) + -2.0;
	} else {
		tmp = (4.0 / z) * (x - y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.6e-42) or not (z <= 2.7e+20):
		tmp = (x * (4.0 / z)) + -2.0
	else:
		tmp = (4.0 / z) * (x - y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.6e-42) || !(z <= 2.7e+20))
		tmp = Float64(Float64(x * Float64(4.0 / z)) + -2.0);
	else
		tmp = Float64(Float64(4.0 / z) * Float64(x - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -5.6e-42) || ~((z <= 2.7e+20)))
		tmp = (x * (4.0 / z)) + -2.0;
	else
		tmp = (4.0 / z) * (x - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.6e-42], N[Not[LessEqual[z, 2.7e+20]], $MachinePrecision]], N[(N[(x * N[(4.0 / z), $MachinePrecision]), $MachinePrecision] + -2.0), $MachinePrecision], N[(N[(4.0 / z), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.59999999999999996e-42 or 2.7e20 < z

   1. Initial program 99.2%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Step-by-step derivation

      1. remove-double-neg 99.2%

         \[\leadsto \frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{\color{blue}{-\left(-z\right)}} \]

      2. neg-mul-1 99.2%

         \[\leadsto \frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{\color{blue}{-1 \cdot \left(-z\right)}} \]

      3. times-frac 100.0%

         \[\leadsto \color{blue}{\frac{4}{-1} \cdot \frac{\left(x - y\right) - z \cdot 0.5}{-z}} \]

      4. metadata-eval 100.0%

         \[\leadsto \color{blue}{-4} \cdot \frac{\left(x - y\right) - z \cdot 0.5}{-z} \]

      5. div-sub 100.0%

         \[\leadsto -4 \cdot \color{blue}{\left(\frac{x - y}{-z} - \frac{z \cdot 0.5}{-z}\right)} \]

      6. distribute-frac-neg2 100.0%

         \[\leadsto -4 \cdot \left(\color{blue}{\left(-\frac{x - y}{z}\right)} - \frac{z \cdot 0.5}{-z}\right) \]

      7. distribute-frac-neg 100.0%

         \[\leadsto -4 \cdot \left(\color{blue}{\frac{-\left(x - y\right)}{z}} - \frac{z \cdot 0.5}{-z}\right) \]

      8. sub-neg 100.0%

         \[\leadsto -4 \cdot \left(\frac{-\color{blue}{\left(x + \left(-y\right)\right)}}{z} - \frac{z \cdot 0.5}{-z}\right) \]

      9. +-commutative 100.0%

         \[\leadsto -4 \cdot \left(\frac{-\color{blue}{\left(\left(-y\right) + x\right)}}{z} - \frac{z \cdot 0.5}{-z}\right) \]

      10. distribute-neg-out 100.0%

          \[\leadsto -4 \cdot \left(\frac{\color{blue}{\left(-\left(-y\right)\right) + \left(-x\right)}}{z} - \frac{z \cdot 0.5}{-z}\right) \]

      11. remove-double-neg 100.0%

          \[\leadsto -4 \cdot \left(\frac{\color{blue}{y} + \left(-x\right)}{z} - \frac{z \cdot 0.5}{-z}\right) \]

      12. sub-neg 100.0%

          \[\leadsto -4 \cdot \left(\frac{\color{blue}{y - x}}{z} - \frac{z \cdot 0.5}{-z}\right) \]

      13. *-commutative 100.0%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \frac{\color{blue}{0.5 \cdot z}}{-z}\right) \]

      14. neg-mul-1 100.0%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \frac{0.5 \cdot z}{\color{blue}{-1 \cdot z}}\right) \]

      15. times-frac 100.0%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \color{blue}{\frac{0.5}{-1} \cdot \frac{z}{z}}\right) \]

      16. metadata-eval 100.0%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \color{blue}{-0.5} \cdot \frac{z}{z}\right) \]

      17. *-inverses 100.0%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - -0.5 \cdot \color{blue}{1}\right) \]

      18. metadata-eval 100.0%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \color{blue}{-0.5}\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{-4 \cdot \left(\frac{y - x}{z} - -0.5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 83.2%

      \[\leadsto \color{blue}{-4 \cdot \left(0.5 - \frac{x}{z}\right)} \]
   6. Step-by-step derivation

      1. sub-neg 83.2%

         \[\leadsto -4 \cdot \color{blue}{\left(0.5 + \left(-\frac{x}{z}\right)\right)} \]

      2. +-commutative 83.2%

         \[\leadsto -4 \cdot \color{blue}{\left(\left(-\frac{x}{z}\right) + 0.5\right)} \]

      3. distribute-lft-in 83.2%

         \[\leadsto \color{blue}{-4 \cdot \left(-\frac{x}{z}\right) + -4 \cdot 0.5} \]

      4. metadata-eval 83.2%

         \[\leadsto \color{blue}{\frac{4}{-1}} \cdot \left(-\frac{x}{z}\right) + -4 \cdot 0.5 \]

      5. distribute-neg-frac2 83.2%

         \[\leadsto \frac{4}{-1} \cdot \color{blue}{\frac{x}{-z}} + -4 \cdot 0.5 \]

      6. times-frac 83.2%

         \[\leadsto \color{blue}{\frac{4 \cdot x}{-1 \cdot \left(-z\right)}} + -4 \cdot 0.5 \]

      7. neg-mul-1 83.2%

         \[\leadsto \frac{4 \cdot x}{\color{blue}{-\left(-z\right)}} + -4 \cdot 0.5 \]

      8. remove-double-neg 83.2%

         \[\leadsto \frac{4 \cdot x}{\color{blue}{z}} + -4 \cdot 0.5 \]

      9. associate-*l/ 83.1%

         \[\leadsto \color{blue}{\frac{4}{z} \cdot x} + -4 \cdot 0.5 \]

      10. *-commutative 83.1%

          \[\leadsto \color{blue}{x \cdot \frac{4}{z}} + -4 \cdot 0.5 \]

      11. metadata-eval 83.1%

          \[\leadsto x \cdot \frac{4}{z} + \color{blue}{-2} \]

   7. Simplified 83.1%

      \[\leadsto \color{blue}{x \cdot \frac{4}{z} + -2} \]

   if -5.59999999999999996e-42 < z < 2.7e20

   1. Initial program 99.9%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Step-by-step derivation

      1. *-commutative 99.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x - y\right) - z \cdot 0.5\right) \cdot 4}}{z} \]

      2. associate-/l* 99.8%

         \[\leadsto \color{blue}{\left(\left(x - y\right) - z \cdot 0.5\right) \cdot \frac{4}{z}} \]

      3. associate--l- 99.8%

         \[\leadsto \color{blue}{\left(x - \left(y + z \cdot 0.5\right)\right)} \cdot \frac{4}{z} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\left(x - \left(y + z \cdot 0.5\right)\right) \cdot \frac{4}{z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 94.2%

      \[\leadsto \color{blue}{\left(x - y\right)} \cdot \frac{4}{z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{-42} \lor \neg \left(z \leq 2.7 \cdot 10^{+20}\right):\\ \;\;\;\;x \cdot \frac{4}{z} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{4}{z} \cdot \left(x - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 80.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+179}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+122}:\\ \;\;\;\;\frac{4}{z} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.1e+179) -2.0 (if (<= z 2.7e+122) (* (/ 4.0 z) (- x y)) -2.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.1e+179) {
		tmp = -2.0;
	} else if (z <= 2.7e+122) {
		tmp = (4.0 / z) * (x - y);
	} else {
		tmp = -2.0;
	}
	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 (z <= (-1.1d+179)) then
        tmp = -2.0d0
    else if (z <= 2.7d+122) then
        tmp = (4.0d0 / z) * (x - y)
    else
        tmp = -2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.1e+179) {
		tmp = -2.0;
	} else if (z <= 2.7e+122) {
		tmp = (4.0 / z) * (x - y);
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.1e+179:
		tmp = -2.0
	elif z <= 2.7e+122:
		tmp = (4.0 / z) * (x - y)
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.1e+179)
		tmp = -2.0;
	elseif (z <= 2.7e+122)
		tmp = Float64(Float64(4.0 / z) * Float64(x - y));
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.1e+179)
		tmp = -2.0;
	elseif (z <= 2.7e+122)
		tmp = (4.0 / z) * (x - y);
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.1e+179], -2.0, If[LessEqual[z, 2.7e+122], N[(N[(4.0 / z), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1e179 or 2.6999999999999998e122 < z

   1. Initial program 98.6%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Step-by-step derivation

      1. remove-double-neg 98.6%

         \[\leadsto \frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{\color{blue}{-\left(-z\right)}} \]

      2. neg-mul-1 98.6%

         \[\leadsto \frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{\color{blue}{-1 \cdot \left(-z\right)}} \]

      3. times-frac 100.0%

         \[\leadsto \color{blue}{\frac{4}{-1} \cdot \frac{\left(x - y\right) - z \cdot 0.5}{-z}} \]

      4. metadata-eval 100.0%

         \[\leadsto \color{blue}{-4} \cdot \frac{\left(x - y\right) - z \cdot 0.5}{-z} \]

      5. div-sub 100.0%

         \[\leadsto -4 \cdot \color{blue}{\left(\frac{x - y}{-z} - \frac{z \cdot 0.5}{-z}\right)} \]

      6. distribute-frac-neg2 100.0%

         \[\leadsto -4 \cdot \left(\color{blue}{\left(-\frac{x - y}{z}\right)} - \frac{z \cdot 0.5}{-z}\right) \]

      7. distribute-frac-neg 100.0%

         \[\leadsto -4 \cdot \left(\color{blue}{\frac{-\left(x - y\right)}{z}} - \frac{z \cdot 0.5}{-z}\right) \]

      8. sub-neg 100.0%

         \[\leadsto -4 \cdot \left(\frac{-\color{blue}{\left(x + \left(-y\right)\right)}}{z} - \frac{z \cdot 0.5}{-z}\right) \]

      9. +-commutative 100.0%

         \[\leadsto -4 \cdot \left(\frac{-\color{blue}{\left(\left(-y\right) + x\right)}}{z} - \frac{z \cdot 0.5}{-z}\right) \]

      10. distribute-neg-out 100.0%

          \[\leadsto -4 \cdot \left(\frac{\color{blue}{\left(-\left(-y\right)\right) + \left(-x\right)}}{z} - \frac{z \cdot 0.5}{-z}\right) \]

      11. remove-double-neg 100.0%

          \[\leadsto -4 \cdot \left(\frac{\color{blue}{y} + \left(-x\right)}{z} - \frac{z \cdot 0.5}{-z}\right) \]

      12. sub-neg 100.0%

          \[\leadsto -4 \cdot \left(\frac{\color{blue}{y - x}}{z} - \frac{z \cdot 0.5}{-z}\right) \]

      13. *-commutative 100.0%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \frac{\color{blue}{0.5 \cdot z}}{-z}\right) \]

      14. neg-mul-1 100.0%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \frac{0.5 \cdot z}{\color{blue}{-1 \cdot z}}\right) \]

      15. times-frac 100.0%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \color{blue}{\frac{0.5}{-1} \cdot \frac{z}{z}}\right) \]

      16. metadata-eval 100.0%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \color{blue}{-0.5} \cdot \frac{z}{z}\right) \]

      17. *-inverses 100.0%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - -0.5 \cdot \color{blue}{1}\right) \]

      18. metadata-eval 100.0%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \color{blue}{-0.5}\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{-4 \cdot \left(\frac{y - x}{z} - -0.5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 85.1%

      \[\leadsto \color{blue}{-2} \]

   if -1.1e179 < z < 2.6999999999999998e122

   1. Initial program 100.0%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x - y\right) - z \cdot 0.5\right) \cdot 4}}{z} \]

      2. associate-/l* 99.8%

         \[\leadsto \color{blue}{\left(\left(x - y\right) - z \cdot 0.5\right) \cdot \frac{4}{z}} \]

      3. associate--l- 99.8%

         \[\leadsto \color{blue}{\left(x - \left(y + z \cdot 0.5\right)\right)} \cdot \frac{4}{z} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\left(x - \left(y + z \cdot 0.5\right)\right) \cdot \frac{4}{z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 84.5%

      \[\leadsto \color{blue}{\left(x - y\right)} \cdot \frac{4}{z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+179}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+122}:\\ \;\;\;\;\frac{4}{z} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 52.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-45}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+110}:\\ \;\;\;\;x \cdot \frac{4}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -6.5e-45) -2.0 (if (<= z 1.45e+110) (* x (/ 4.0 z)) -2.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -6.5e-45) {
		tmp = -2.0;
	} else if (z <= 1.45e+110) {
		tmp = x * (4.0 / z);
	} else {
		tmp = -2.0;
	}
	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 (z <= (-6.5d-45)) then
        tmp = -2.0d0
    else if (z <= 1.45d+110) then
        tmp = x * (4.0d0 / z)
    else
        tmp = -2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -6.5e-45) {
		tmp = -2.0;
	} else if (z <= 1.45e+110) {
		tmp = x * (4.0 / z);
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -6.5e-45:
		tmp = -2.0
	elif z <= 1.45e+110:
		tmp = x * (4.0 / z)
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -6.5e-45)
		tmp = -2.0;
	elseif (z <= 1.45e+110)
		tmp = Float64(x * Float64(4.0 / z));
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -6.5e-45)
		tmp = -2.0;
	elseif (z <= 1.45e+110)
		tmp = x * (4.0 / z);
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -6.5e-45], -2.0, If[LessEqual[z, 1.45e+110], N[(x * N[(4.0 / z), $MachinePrecision]), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if z < -6.4999999999999995e-45 or 1.45e110 < z

   1. Initial program 99.1%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Step-by-step derivation

      1. remove-double-neg 99.1%

         \[\leadsto \frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{\color{blue}{-\left(-z\right)}} \]

      2. neg-mul-1 99.1%

         \[\leadsto \frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{\color{blue}{-1 \cdot \left(-z\right)}} \]

      3. times-frac 100.0%

         \[\leadsto \color{blue}{\frac{4}{-1} \cdot \frac{\left(x - y\right) - z \cdot 0.5}{-z}} \]

      4. metadata-eval 100.0%

         \[\leadsto \color{blue}{-4} \cdot \frac{\left(x - y\right) - z \cdot 0.5}{-z} \]

      5. div-sub 100.0%

         \[\leadsto -4 \cdot \color{blue}{\left(\frac{x - y}{-z} - \frac{z \cdot 0.5}{-z}\right)} \]

      6. distribute-frac-neg2 100.0%

         \[\leadsto -4 \cdot \left(\color{blue}{\left(-\frac{x - y}{z}\right)} - \frac{z \cdot 0.5}{-z}\right) \]

      7. distribute-frac-neg 100.0%

         \[\leadsto -4 \cdot \left(\color{blue}{\frac{-\left(x - y\right)}{z}} - \frac{z \cdot 0.5}{-z}\right) \]

      8. sub-neg 100.0%

         \[\leadsto -4 \cdot \left(\frac{-\color{blue}{\left(x + \left(-y\right)\right)}}{z} - \frac{z \cdot 0.5}{-z}\right) \]

      9. +-commutative 100.0%

         \[\leadsto -4 \cdot \left(\frac{-\color{blue}{\left(\left(-y\right) + x\right)}}{z} - \frac{z \cdot 0.5}{-z}\right) \]

      10. distribute-neg-out 100.0%

          \[\leadsto -4 \cdot \left(\frac{\color{blue}{\left(-\left(-y\right)\right) + \left(-x\right)}}{z} - \frac{z \cdot 0.5}{-z}\right) \]

      11. remove-double-neg 100.0%

          \[\leadsto -4 \cdot \left(\frac{\color{blue}{y} + \left(-x\right)}{z} - \frac{z \cdot 0.5}{-z}\right) \]

      12. sub-neg 100.0%

          \[\leadsto -4 \cdot \left(\frac{\color{blue}{y - x}}{z} - \frac{z \cdot 0.5}{-z}\right) \]

      13. *-commutative 100.0%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \frac{\color{blue}{0.5 \cdot z}}{-z}\right) \]

      14. neg-mul-1 100.0%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \frac{0.5 \cdot z}{\color{blue}{-1 \cdot z}}\right) \]

      15. times-frac 100.0%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \color{blue}{\frac{0.5}{-1} \cdot \frac{z}{z}}\right) \]

      16. metadata-eval 100.0%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \color{blue}{-0.5} \cdot \frac{z}{z}\right) \]

      17. *-inverses 100.0%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - -0.5 \cdot \color{blue}{1}\right) \]

      18. metadata-eval 100.0%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \color{blue}{-0.5}\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{-4 \cdot \left(\frac{y - x}{z} - -0.5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 68.3%

      \[\leadsto \color{blue}{-2} \]

   if -6.4999999999999995e-45 < z < 1.45e110

   1. Initial program 99.9%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Step-by-step derivation

      1. remove-double-neg 99.9%

         \[\leadsto \frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{\color{blue}{-\left(-z\right)}} \]

      2. neg-mul-1 99.9%

         \[\leadsto \frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{\color{blue}{-1 \cdot \left(-z\right)}} \]

      3. times-frac 99.9%

         \[\leadsto \color{blue}{\frac{4}{-1} \cdot \frac{\left(x - y\right) - z \cdot 0.5}{-z}} \]

      4. metadata-eval 99.9%

         \[\leadsto \color{blue}{-4} \cdot \frac{\left(x - y\right) - z \cdot 0.5}{-z} \]

      5. div-sub 100.0%

         \[\leadsto -4 \cdot \color{blue}{\left(\frac{x - y}{-z} - \frac{z \cdot 0.5}{-z}\right)} \]

      6. distribute-frac-neg2 100.0%

         \[\leadsto -4 \cdot \left(\color{blue}{\left(-\frac{x - y}{z}\right)} - \frac{z \cdot 0.5}{-z}\right) \]

      7. distribute-frac-neg 100.0%

         \[\leadsto -4 \cdot \left(\color{blue}{\frac{-\left(x - y\right)}{z}} - \frac{z \cdot 0.5}{-z}\right) \]

      8. sub-neg 100.0%

         \[\leadsto -4 \cdot \left(\frac{-\color{blue}{\left(x + \left(-y\right)\right)}}{z} - \frac{z \cdot 0.5}{-z}\right) \]

      9. +-commutative 100.0%

         \[\leadsto -4 \cdot \left(\frac{-\color{blue}{\left(\left(-y\right) + x\right)}}{z} - \frac{z \cdot 0.5}{-z}\right) \]

      10. distribute-neg-out 100.0%

          \[\leadsto -4 \cdot \left(\frac{\color{blue}{\left(-\left(-y\right)\right) + \left(-x\right)}}{z} - \frac{z \cdot 0.5}{-z}\right) \]

      11. remove-double-neg 100.0%

          \[\leadsto -4 \cdot \left(\frac{\color{blue}{y} + \left(-x\right)}{z} - \frac{z \cdot 0.5}{-z}\right) \]

      12. sub-neg 100.0%

          \[\leadsto -4 \cdot \left(\frac{\color{blue}{y - x}}{z} - \frac{z \cdot 0.5}{-z}\right) \]

      13. *-commutative 100.0%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \frac{\color{blue}{0.5 \cdot z}}{-z}\right) \]

      14. neg-mul-1 100.0%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \frac{0.5 \cdot z}{\color{blue}{-1 \cdot z}}\right) \]

      15. times-frac 100.0%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \color{blue}{\frac{0.5}{-1} \cdot \frac{z}{z}}\right) \]

      16. metadata-eval 100.0%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \color{blue}{-0.5} \cdot \frac{z}{z}\right) \]

      17. *-inverses 100.0%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - -0.5 \cdot \color{blue}{1}\right) \]

      18. metadata-eval 100.0%

          \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \color{blue}{-0.5}\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{-4 \cdot \left(\frac{y - x}{z} - -0.5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 42.0%

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

      1. associate-*r/ 42.0%

         \[\leadsto \color{blue}{\frac{4 \cdot x}{z}} \]

      2. associate-*l/ 41.9%

         \[\leadsto \color{blue}{\frac{4}{z} \cdot x} \]

      3. *-commutative 41.9%

         \[\leadsto \color{blue}{x \cdot \frac{4}{z}} \]

   7. Simplified 41.9%

      \[\leadsto \color{blue}{x \cdot \frac{4}{z}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 34.1% accurate, 11.0× speedup

Math

\[\begin{array}{l} \\ -2 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 -2.0)

C

double code(double x, double y, double z) {
	return -2.0;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = -2.0d0
end function

Java

public static double code(double x, double y, double z) {
	return -2.0;
}

Python

def code(x, y, z):
	return -2.0

Julia

function code(x, y, z)
	return -2.0
end

MATLAB

function tmp = code(x, y, z)
	tmp = -2.0;
end

Wolfram

code[x_, y_, z_] := -2.0

Derivation

1. Initial program 99.6%

   \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
2. Step-by-step derivation

   1. remove-double-neg 99.6%

      \[\leadsto \frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{\color{blue}{-\left(-z\right)}} \]

   2. neg-mul-1 99.6%

      \[\leadsto \frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{\color{blue}{-1 \cdot \left(-z\right)}} \]

   3. times-frac 100.0%

      \[\leadsto \color{blue}{\frac{4}{-1} \cdot \frac{\left(x - y\right) - z \cdot 0.5}{-z}} \]

   4. metadata-eval 100.0%

      \[\leadsto \color{blue}{-4} \cdot \frac{\left(x - y\right) - z \cdot 0.5}{-z} \]

   5. div-sub 100.0%

      \[\leadsto -4 \cdot \color{blue}{\left(\frac{x - y}{-z} - \frac{z \cdot 0.5}{-z}\right)} \]

   6. distribute-frac-neg2 100.0%

      \[\leadsto -4 \cdot \left(\color{blue}{\left(-\frac{x - y}{z}\right)} - \frac{z \cdot 0.5}{-z}\right) \]

   7. distribute-frac-neg 100.0%

      \[\leadsto -4 \cdot \left(\color{blue}{\frac{-\left(x - y\right)}{z}} - \frac{z \cdot 0.5}{-z}\right) \]

   8. sub-neg 100.0%

      \[\leadsto -4 \cdot \left(\frac{-\color{blue}{\left(x + \left(-y\right)\right)}}{z} - \frac{z \cdot 0.5}{-z}\right) \]

   9. +-commutative 100.0%

      \[\leadsto -4 \cdot \left(\frac{-\color{blue}{\left(\left(-y\right) + x\right)}}{z} - \frac{z \cdot 0.5}{-z}\right) \]

   10. distribute-neg-out 100.0%

       \[\leadsto -4 \cdot \left(\frac{\color{blue}{\left(-\left(-y\right)\right) + \left(-x\right)}}{z} - \frac{z \cdot 0.5}{-z}\right) \]

   11. remove-double-neg 100.0%

       \[\leadsto -4 \cdot \left(\frac{\color{blue}{y} + \left(-x\right)}{z} - \frac{z \cdot 0.5}{-z}\right) \]

   12. sub-neg 100.0%

       \[\leadsto -4 \cdot \left(\frac{\color{blue}{y - x}}{z} - \frac{z \cdot 0.5}{-z}\right) \]

   13. *-commutative 100.0%

       \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \frac{\color{blue}{0.5 \cdot z}}{-z}\right) \]

   14. neg-mul-1 100.0%

       \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \frac{0.5 \cdot z}{\color{blue}{-1 \cdot z}}\right) \]

   15. times-frac 100.0%

       \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \color{blue}{\frac{0.5}{-1} \cdot \frac{z}{z}}\right) \]

   16. metadata-eval 100.0%

       \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \color{blue}{-0.5} \cdot \frac{z}{z}\right) \]

   17. *-inverses 100.0%

       \[\leadsto -4 \cdot \left(\frac{y - x}{z} - -0.5 \cdot \color{blue}{1}\right) \]

   18. metadata-eval 100.0%

       \[\leadsto -4 \cdot \left(\frac{y - x}{z} - \color{blue}{-0.5}\right) \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{-4 \cdot \left(\frac{y - x}{z} - -0.5\right)} \]
4. Add Preprocessing

5. Taylor expanded in z around inf 34.9%

   \[\leadsto \color{blue}{-2} \]
6. Add Preprocessing

Developer Target 1: 98.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ 4 \cdot \frac{x}{z} - \left(2 + 4 \cdot \frac{y}{z}\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (- (* 4.0 (/ x z)) (+ 2.0 (* 4.0 (/ y z)))))

C

double code(double x, double y, double z) {
	return (4.0 * (x / z)) - (2.0 + (4.0 * (y / 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 = (4.0d0 * (x / z)) - (2.0d0 + (4.0d0 * (y / z)))
end function

Java

public static double code(double x, double y, double z) {
	return (4.0 * (x / z)) - (2.0 + (4.0 * (y / z)));
}

Python

def code(x, y, z):
	return (4.0 * (x / z)) - (2.0 + (4.0 * (y / z)))

Julia

function code(x, y, z)
	return Float64(Float64(4.0 * Float64(x / z)) - Float64(2.0 + Float64(4.0 * Float64(y / z))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (4.0 * (x / z)) - (2.0 + (4.0 * (y / z)));
end

Wolfram

code[x_, y_, z_] := N[(N[(4.0 * N[(x / z), $MachinePrecision]), $MachinePrecision] - N[(2.0 + N[(4.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024132 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, B"
  :precision binary64

  :alt
  (! :herbie-platform default (- (* 4 (/ x z)) (+ 2 (* 4 (/ y z)))))

  (/ (* 4.0 (- (- x y) (* z 0.5))) z))