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

Percentage Accurate: 99.8% → 100.0%

Time: 4.6s

Alternatives: 8

Speedup: 1.2×

• 20.9% 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

\[\begin{array}{l} \\ 4 \cdot \frac{x - y}{z} - 2 \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. associate-*l/ 99.7%

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

   2. sub-neg 99.7%

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

   3. distribute-rgt-neg-in 99.7%

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

   4. metadata-eval 99.7%

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

3. Simplified 99.7%

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

4. Taylor expanded in z around 0 100.0%

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

5. Final simplification 100.0%

   \[\leadsto 4 \cdot \frac{x - y}{z} - 2 \]

Alternative 2: 53.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{z} \cdot -4\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{-13}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-271}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-199}:\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+14}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ y z) -4.0)))
   (if (<= z -1.05e-13)
     -2.0
     (if (<= z 8e-271)
       t_0
       (if (<= z 1.9e-199) (* 4.0 (/ x z)) (if (<= z 7.5e+14) t_0 -2.0))))))

C

double code(double x, double y, double z) {
	double t_0 = (y / z) * -4.0;
	double tmp;
	if (z <= -1.05e-13) {
		tmp = -2.0;
	} else if (z <= 8e-271) {
		tmp = t_0;
	} else if (z <= 1.9e-199) {
		tmp = 4.0 * (x / z);
	} else if (z <= 7.5e+14) {
		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 = (y / z) * (-4.0d0)
    if (z <= (-1.05d-13)) then
        tmp = -2.0d0
    else if (z <= 8d-271) then
        tmp = t_0
    else if (z <= 1.9d-199) then
        tmp = 4.0d0 * (x / z)
    else if (z <= 7.5d+14) 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 = (y / z) * -4.0;
	double tmp;
	if (z <= -1.05e-13) {
		tmp = -2.0;
	} else if (z <= 8e-271) {
		tmp = t_0;
	} else if (z <= 1.9e-199) {
		tmp = 4.0 * (x / z);
	} else if (z <= 7.5e+14) {
		tmp = t_0;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y / z) * -4.0
	tmp = 0
	if z <= -1.05e-13:
		tmp = -2.0
	elif z <= 8e-271:
		tmp = t_0
	elif z <= 1.9e-199:
		tmp = 4.0 * (x / z)
	elif z <= 7.5e+14:
		tmp = t_0
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y / z) * -4.0)
	tmp = 0.0
	if (z <= -1.05e-13)
		tmp = -2.0;
	elseif (z <= 8e-271)
		tmp = t_0;
	elseif (z <= 1.9e-199)
		tmp = Float64(4.0 * Float64(x / z));
	elseif (z <= 7.5e+14)
		tmp = t_0;
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y / z) * -4.0;
	tmp = 0.0;
	if (z <= -1.05e-13)
		tmp = -2.0;
	elseif (z <= 8e-271)
		tmp = t_0;
	elseif (z <= 1.9e-199)
		tmp = 4.0 * (x / z);
	elseif (z <= 7.5e+14)
		tmp = t_0;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y / z), $MachinePrecision] * -4.0), $MachinePrecision]}, If[LessEqual[z, -1.05e-13], -2.0, If[LessEqual[z, 8e-271], t$95$0, If[LessEqual[z, 1.9e-199], N[(4.0 * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.5e+14], t$95$0, -2.0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.04999999999999994e-13 or 7.5e14 < z

   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. associate-*l/ 99.7%

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

      2. sub-neg 99.7%

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

      3. distribute-rgt-neg-in 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around inf 62.3%

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

   if -1.04999999999999994e-13 < z < 7.9999999999999997e-271 or 1.8999999999999999e-199 < z < 7.5e14

   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. associate-*l/ 99.8%

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

      2. sub-neg 99.8%

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

      3. distribute-rgt-neg-in 99.8%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 64.1%

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

   if 7.9999999999999997e-271 < z < 1.8999999999999999e-199

   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. associate-*l/ 99.8%

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

      2. sub-neg 99.8%

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

      3. distribute-rgt-neg-in 99.8%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 68.8%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-13}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-271}:\\ \;\;\;\;\frac{y}{z} \cdot -4\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-199}:\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+14}:\\ \;\;\;\;\frac{y}{z} \cdot -4\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]

Alternative 3: 85.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+26}:\\ \;\;\;\;\frac{4}{\frac{z}{x - y}}\\ \mathbf{elif}\;x \leq 8.4 \cdot 10^{-5}:\\ \;\;\;\;4 \cdot \frac{z \cdot -0.5 - y}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{4}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.3e+26)
   (/ 4.0 (/ z (- x y)))
   (if (<= x 8.4e-5) (* 4.0 (/ (- (* z -0.5) y) z)) (* (- x y) (/ 4.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.3e+26) {
		tmp = 4.0 / (z / (x - y));
	} else if (x <= 8.4e-5) {
		tmp = 4.0 * (((z * -0.5) - y) / z);
	} else {
		tmp = (x - y) * (4.0 / 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 <= (-1.3d+26)) then
        tmp = 4.0d0 / (z / (x - y))
    else if (x <= 8.4d-5) then
        tmp = 4.0d0 * (((z * (-0.5d0)) - y) / z)
    else
        tmp = (x - y) * (4.0d0 / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.3e+26) {
		tmp = 4.0 / (z / (x - y));
	} else if (x <= 8.4e-5) {
		tmp = 4.0 * (((z * -0.5) - y) / z);
	} else {
		tmp = (x - y) * (4.0 / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.3e+26:
		tmp = 4.0 / (z / (x - y))
	elif x <= 8.4e-5:
		tmp = 4.0 * (((z * -0.5) - y) / z)
	else:
		tmp = (x - y) * (4.0 / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.3e+26)
		tmp = Float64(4.0 / Float64(z / Float64(x - y)));
	elseif (x <= 8.4e-5)
		tmp = Float64(4.0 * Float64(Float64(Float64(z * -0.5) - y) / z));
	else
		tmp = Float64(Float64(x - y) * Float64(4.0 / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.3e+26)
		tmp = 4.0 / (z / (x - y));
	elseif (x <= 8.4e-5)
		tmp = 4.0 * (((z * -0.5) - y) / z);
	else
		tmp = (x - y) * (4.0 / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.3e+26], N[(4.0 / N[(z / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.4e-5], N[(4.0 * N[(N[(N[(z * -0.5), $MachinePrecision] - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(4.0 / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.30000000000000001e26

   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. associate-*l/ 99.7%

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

      2. sub-neg 99.7%

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

      3. distribute-rgt-neg-in 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around 0 84.3%

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

      1. associate-*r/ 84.3%

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

      2. associate-*l/ 84.1%

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

      3. *-commutative 84.1%

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

   6. Simplified 84.1%

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

      1. associate-*r/ 84.3%

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

      2. *-commutative 84.3%

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

      3. associate-/l* 84.3%

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

   8. Applied egg-rr 84.3%

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

   if -1.30000000000000001e26 < x < 8.39999999999999954e-5

   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. associate-*l/ 99.7%

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

      2. sub-neg 99.7%

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

      3. distribute-rgt-neg-in 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 92.7%

      \[\leadsto \color{blue}{4 \cdot \frac{-0.5 \cdot z - y}{z}} \]
   5. Step-by-step derivation

      1. *-commutative 92.7%

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

   6. Simplified 92.7%

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

   if 8.39999999999999954e-5 < x

   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. associate-*l/ 99.8%

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

      2. sub-neg 99.8%

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

      3. distribute-rgt-neg-in 99.8%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 89.1%

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

      1. associate-*r/ 89.1%

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

      2. associate-*l/ 88.9%

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

      3. *-commutative 88.9%

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

   6. Simplified 88.9%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+26}:\\ \;\;\;\;\frac{4}{\frac{z}{x - y}}\\ \mathbf{elif}\;x \leq 8.4 \cdot 10^{-5}:\\ \;\;\;\;4 \cdot \frac{z \cdot -0.5 - y}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{4}{z}\\ \end{array} \]

Alternative 4: 80.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+115} \lor \neg \left(x \leq 1.85 \cdot 10^{+179}\right):\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \left(-0.5 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1e+115) (not (<= x 1.85e+179)))
   (* 4.0 (/ x z))
   (* 4.0 (- -0.5 (/ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1e+115) || !(x <= 1.85e+179)) {
		tmp = 4.0 * (x / z);
	} else {
		tmp = 4.0 * (-0.5 - (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 <= (-1d+115)) .or. (.not. (x <= 1.85d+179))) then
        tmp = 4.0d0 * (x / z)
    else
        tmp = 4.0d0 * ((-0.5d0) - (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1e+115) || !(x <= 1.85e+179)) {
		tmp = 4.0 * (x / z);
	} else {
		tmp = 4.0 * (-0.5 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1e+115) or not (x <= 1.85e+179):
		tmp = 4.0 * (x / z)
	else:
		tmp = 4.0 * (-0.5 - (y / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1e+115) || !(x <= 1.85e+179))
		tmp = Float64(4.0 * Float64(x / z));
	else
		tmp = Float64(4.0 * Float64(-0.5 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1e+115) || ~((x <= 1.85e+179)))
		tmp = 4.0 * (x / z);
	else
		tmp = 4.0 * (-0.5 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1e+115], N[Not[LessEqual[x, 1.85e+179]], $MachinePrecision]], N[(4.0 * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(4.0 * N[(-0.5 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1e115 or 1.85e179 < x

   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. associate-*l/ 99.7%

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

      2. sub-neg 99.7%

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

      3. distribute-rgt-neg-in 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 88.1%

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

   if -1e115 < x < 1.85e179

   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. associate-*l/ 99.7%

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

      2. sub-neg 99.7%

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

      3. distribute-rgt-neg-in 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 84.5%

      \[\leadsto \color{blue}{4 \cdot \frac{-0.5 \cdot z - y}{z}} \]
   5. Step-by-step derivation

      1. div-sub 84.5%

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

      2. associate-/l* 84.5%

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

      3. *-inverses 84.5%

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

      4. metadata-eval 84.5%

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

   6. Simplified 84.5%

      \[\leadsto \color{blue}{4 \cdot \left(-0.5 - \frac{y}{z}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+115} \lor \neg \left(x \leq 1.85 \cdot 10^{+179}\right):\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \left(-0.5 - \frac{y}{z}\right)\\ \end{array} \]

Alternative 5: 85.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+25} \lor \neg \left(x \leq 7.6 \cdot 10^{-9}\right):\\ \;\;\;\;\left(x - y\right) \cdot \frac{4}{z}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \left(-0.5 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5e+25) (not (<= x 7.6e-9)))
   (* (- x y) (/ 4.0 z))
   (* 4.0 (- -0.5 (/ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5e+25) || !(x <= 7.6e-9)) {
		tmp = (x - y) * (4.0 / z);
	} else {
		tmp = 4.0 * (-0.5 - (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 <= (-5d+25)) .or. (.not. (x <= 7.6d-9))) then
        tmp = (x - y) * (4.0d0 / z)
    else
        tmp = 4.0d0 * ((-0.5d0) - (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5e+25) || !(x <= 7.6e-9)) {
		tmp = (x - y) * (4.0 / z);
	} else {
		tmp = 4.0 * (-0.5 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5e+25) or not (x <= 7.6e-9):
		tmp = (x - y) * (4.0 / z)
	else:
		tmp = 4.0 * (-0.5 - (y / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5e+25) || !(x <= 7.6e-9))
		tmp = Float64(Float64(x - y) * Float64(4.0 / z));
	else
		tmp = Float64(4.0 * Float64(-0.5 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -5e+25) || ~((x <= 7.6e-9)))
		tmp = (x - y) * (4.0 / z);
	else
		tmp = 4.0 * (-0.5 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5e+25], N[Not[LessEqual[x, 7.6e-9]], $MachinePrecision]], N[(N[(x - y), $MachinePrecision] * N[(4.0 / z), $MachinePrecision]), $MachinePrecision], N[(4.0 * N[(-0.5 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.00000000000000024e25 or 7.60000000000000023e-9 < x

   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. associate-*l/ 99.7%

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

      2. sub-neg 99.7%

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

      3. distribute-rgt-neg-in 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around 0 86.8%

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

      1. associate-*r/ 86.8%

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

      2. associate-*l/ 86.6%

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

      3. *-commutative 86.6%

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

   6. Simplified 86.6%

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

   if -5.00000000000000024e25 < x < 7.60000000000000023e-9

   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. associate-*l/ 99.7%

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

      2. sub-neg 99.7%

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

      3. distribute-rgt-neg-in 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 92.7%

      \[\leadsto \color{blue}{4 \cdot \frac{-0.5 \cdot z - y}{z}} \]
   5. Step-by-step derivation

      1. div-sub 92.7%

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

      2. associate-/l* 92.7%

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

      3. *-inverses 92.7%

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

      4. metadata-eval 92.7%

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

   6. Simplified 92.7%

      \[\leadsto \color{blue}{4 \cdot \left(-0.5 - \frac{y}{z}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+25} \lor \neg \left(x \leq 7.6 \cdot 10^{-9}\right):\\ \;\;\;\;\left(x - y\right) \cdot \frac{4}{z}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \left(-0.5 - \frac{y}{z}\right)\\ \end{array} \]

Alternative 6: 85.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.52 \cdot 10^{+26}:\\ \;\;\;\;\frac{4}{\frac{z}{x - y}}\\ \mathbf{elif}\;x \leq 7.1 \cdot 10^{-16}:\\ \;\;\;\;4 \cdot \left(-0.5 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{4}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.52e+26)
   (/ 4.0 (/ z (- x y)))
   (if (<= x 7.1e-16) (* 4.0 (- -0.5 (/ y z))) (* (- x y) (/ 4.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.52e+26) {
		tmp = 4.0 / (z / (x - y));
	} else if (x <= 7.1e-16) {
		tmp = 4.0 * (-0.5 - (y / z));
	} else {
		tmp = (x - y) * (4.0 / 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 <= (-1.52d+26)) then
        tmp = 4.0d0 / (z / (x - y))
    else if (x <= 7.1d-16) then
        tmp = 4.0d0 * ((-0.5d0) - (y / z))
    else
        tmp = (x - y) * (4.0d0 / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.52e+26) {
		tmp = 4.0 / (z / (x - y));
	} else if (x <= 7.1e-16) {
		tmp = 4.0 * (-0.5 - (y / z));
	} else {
		tmp = (x - y) * (4.0 / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.52e+26:
		tmp = 4.0 / (z / (x - y))
	elif x <= 7.1e-16:
		tmp = 4.0 * (-0.5 - (y / z))
	else:
		tmp = (x - y) * (4.0 / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.52e+26)
		tmp = Float64(4.0 / Float64(z / Float64(x - y)));
	elseif (x <= 7.1e-16)
		tmp = Float64(4.0 * Float64(-0.5 - Float64(y / z)));
	else
		tmp = Float64(Float64(x - y) * Float64(4.0 / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.52e+26)
		tmp = 4.0 / (z / (x - y));
	elseif (x <= 7.1e-16)
		tmp = 4.0 * (-0.5 - (y / z));
	else
		tmp = (x - y) * (4.0 / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.52e+26], N[(4.0 / N[(z / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.1e-16], N[(4.0 * N[(-0.5 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(4.0 / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.52e26

   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. associate-*l/ 99.7%

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

      2. sub-neg 99.7%

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

      3. distribute-rgt-neg-in 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around 0 84.3%

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

      1. associate-*r/ 84.3%

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

      2. associate-*l/ 84.1%

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

      3. *-commutative 84.1%

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

   6. Simplified 84.1%

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

      1. associate-*r/ 84.3%

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

      2. *-commutative 84.3%

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

      3. associate-/l* 84.3%

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

   8. Applied egg-rr 84.3%

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

   if -1.52e26 < x < 7.1e-16

   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. associate-*l/ 99.7%

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

      2. sub-neg 99.7%

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

      3. distribute-rgt-neg-in 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 92.7%

      \[\leadsto \color{blue}{4 \cdot \frac{-0.5 \cdot z - y}{z}} \]
   5. Step-by-step derivation

      1. div-sub 92.7%

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

      2. associate-/l* 92.7%

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

      3. *-inverses 92.7%

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

      4. metadata-eval 92.7%

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

   6. Simplified 92.7%

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

   if 7.1e-16 < x

   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. associate-*l/ 99.8%

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

      2. sub-neg 99.8%

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

      3. distribute-rgt-neg-in 99.8%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 89.1%

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

      1. associate-*r/ 89.1%

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

      2. associate-*l/ 88.9%

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

      3. *-commutative 88.9%

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

   6. Simplified 88.9%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.52 \cdot 10^{+26}:\\ \;\;\;\;\frac{4}{\frac{z}{x - y}}\\ \mathbf{elif}\;x \leq 7.1 \cdot 10^{-16}:\\ \;\;\;\;4 \cdot \left(-0.5 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{4}{z}\\ \end{array} \]

Alternative 7: 53.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-12}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq 65000000000000:\\ \;\;\;\;\frac{y}{z} \cdot -4\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1e-12) -2.0 (if (<= z 65000000000000.0) (* (/ y z) -4.0) -2.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1e-12) {
		tmp = -2.0;
	} else if (z <= 65000000000000.0) {
		tmp = (y / z) * -4.0;
	} 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) :: tmp
    if (z <= (-1d-12)) then
        tmp = -2.0d0
    else if (z <= 65000000000000.0d0) then
        tmp = (y / z) * (-4.0d0)
    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 <= -1e-12) {
		tmp = -2.0;
	} else if (z <= 65000000000000.0) {
		tmp = (y / z) * -4.0;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1e-12:
		tmp = -2.0
	elif z <= 65000000000000.0:
		tmp = (y / z) * -4.0
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1e-12)
		tmp = -2.0;
	elseif (z <= 65000000000000.0)
		tmp = Float64(Float64(y / z) * -4.0);
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1e-12)
		tmp = -2.0;
	elseif (z <= 65000000000000.0)
		tmp = (y / z) * -4.0;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1e-12], -2.0, If[LessEqual[z, 65000000000000.0], N[(N[(y / z), $MachinePrecision] * -4.0), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if z < -9.9999999999999998e-13 or 6.5e13 < z

   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. associate-*l/ 99.7%

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

      2. sub-neg 99.7%

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

      3. distribute-rgt-neg-in 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around inf 62.3%

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

   if -9.9999999999999998e-13 < z < 6.5e13

   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. associate-*l/ 99.8%

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

      2. sub-neg 99.8%

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

      3. distribute-rgt-neg-in 99.8%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 61.3%

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

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-12}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq 65000000000000:\\ \;\;\;\;\frac{y}{z} \cdot -4\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]

Alternative 8: 34.0% 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 100.0%

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

   1. associate-*l/ 99.7%

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

   2. sub-neg 99.7%

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

   3. distribute-rgt-neg-in 99.7%

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

   4. metadata-eval 99.7%

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

3. Simplified 99.7%

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

4. Taylor expanded in z around inf 33.0%

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

5. Final simplification 33.0%

   \[\leadsto -2 \]

Developer target: 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 2023312 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, B"
  :precision binary64

  :herbie-target
  (- (* 4.0 (/ x z)) (+ 2.0 (* 4.0 (/ y z))))

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