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

Percentage Accurate: 99.8% → 100.0%

Time: 6.0s

Alternatives: 8

Speedup: 0.1×

• 20.8% 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, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

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. 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-lft-in 99.8%

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

   4. associate-*l/ 99.9%

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

   5. associate-*r/ 99.9%

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

   6. fma-def 99.9%

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

   7. associate-*l/ 99.2%

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

   8. *-commutative 99.2%

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

   9. distribute-rgt-neg-in 99.2%

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

   10. associate-*r* 99.2%

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

   11. remove-double-neg 99.2%

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

   12. neg-mul-1 99.2%

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

   13. times-frac 100.0%

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

   14. metadata-eval 100.0%

       \[\leadsto \mathsf{fma}\left(4, \frac{x - y}{z}, \frac{\color{blue}{2}}{-1} \cdot \frac{-z}{-z}\right) \]

   15. metadata-eval 100.0%

       \[\leadsto \mathsf{fma}\left(4, \frac{x - y}{z}, \color{blue}{-2} \cdot \frac{-z}{-z}\right) \]

   16. *-inverses 100.0%

       \[\leadsto \mathsf{fma}\left(4, \frac{x - y}{z}, -2 \cdot \color{blue}{1}\right) \]

   17. metadata-eval 100.0%

       \[\leadsto \mathsf{fma}\left(4, \frac{x - y}{z}, \color{blue}{-2}\right) \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(4, \frac{x - y}{z}, -2\right)} \]

4. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(4, \frac{x - y}{z}, -2\right) \]

Alternative 2: 85.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 4 \cdot \left(-0.5 - \frac{y}{z}\right)\\ \mathbf{if}\;y \leq -2.25 \cdot 10^{+60}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-36}:\\ \;\;\;\;4 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+41}:\\ \;\;\;\;-2 + 4 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 4.0 (- -0.5 (/ y z)))))
   (if (<= y -2.25e+60)
     t_0
     (if (<= y -2.05e-36)
       (* 4.0 (/ (- x y) z))
       (if (<= y 1.35e+41) (+ -2.0 (* 4.0 (/ x z))) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = 4.0 * (-0.5 - (y / z));
	double tmp;
	if (y <= -2.25e+60) {
		tmp = t_0;
	} else if (y <= -2.05e-36) {
		tmp = 4.0 * ((x - y) / z);
	} else if (y <= 1.35e+41) {
		tmp = -2.0 + (4.0 * (x / z));
	} else {
		tmp = t_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 * ((-0.5d0) - (y / z))
    if (y <= (-2.25d+60)) then
        tmp = t_0
    else if (y <= (-2.05d-36)) then
        tmp = 4.0d0 * ((x - y) / z)
    else if (y <= 1.35d+41) then
        tmp = (-2.0d0) + (4.0d0 * (x / z))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 4.0 * (-0.5 - (y / z));
	double tmp;
	if (y <= -2.25e+60) {
		tmp = t_0;
	} else if (y <= -2.05e-36) {
		tmp = 4.0 * ((x - y) / z);
	} else if (y <= 1.35e+41) {
		tmp = -2.0 + (4.0 * (x / z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 4.0 * (-0.5 - (y / z))
	tmp = 0
	if y <= -2.25e+60:
		tmp = t_0
	elif y <= -2.05e-36:
		tmp = 4.0 * ((x - y) / z)
	elif y <= 1.35e+41:
		tmp = -2.0 + (4.0 * (x / z))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(4.0 * Float64(-0.5 - Float64(y / z)))
	tmp = 0.0
	if (y <= -2.25e+60)
		tmp = t_0;
	elseif (y <= -2.05e-36)
		tmp = Float64(4.0 * Float64(Float64(x - y) / z));
	elseif (y <= 1.35e+41)
		tmp = Float64(-2.0 + Float64(4.0 * Float64(x / z)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 4.0 * (-0.5 - (y / z));
	tmp = 0.0;
	if (y <= -2.25e+60)
		tmp = t_0;
	elseif (y <= -2.05e-36)
		tmp = 4.0 * ((x - y) / z);
	elseif (y <= 1.35e+41)
		tmp = -2.0 + (4.0 * (x / z));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(4.0 * N[(-0.5 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.25e+60], t$95$0, If[LessEqual[y, -2.05e-36], N[(4.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.35e+41], N[(-2.0 + N[(4.0 * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.25000000000000006e60 or 1.35e41 < y

   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. 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 88.8%

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

      1. div-sub 88.8%

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

      2. *-commutative 88.8%

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

      3. *-lft-identity 88.8%

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

      4. associate-*l/ 88.7%

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

      5. associate-*r* 88.7%

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

      6. lft-mult-inverse 88.8%

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

      7. metadata-eval 88.8%

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

   6. Simplified 88.8%

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

   if -2.25000000000000006e60 < y < -2.05000000000000006e-36

   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 87.0%

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

   if -2.05000000000000006e-36 < y < 1.35e41

   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. 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 0 90.8%

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

      1. +-commutative 90.8%

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

      2. metadata-eval 90.8%

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

      3. cancel-sign-sub-inv 90.8%

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

      4. div-sub 90.8%

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

      5. sub-neg 90.8%

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

      6. associate-/l* 90.8%

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

      7. *-rgt-identity 90.8%

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

      8. *-commutative 90.8%

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

      9. associate-*l/ 90.7%

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

      10. lft-mult-inverse 90.8%

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

      11. metadata-eval 90.8%

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

      12. metadata-eval 90.8%

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

      13. distribute-lft-in 90.8%

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

      14. metadata-eval 90.8%

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

   6. Simplified 90.8%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{+60}:\\ \;\;\;\;4 \cdot \left(-0.5 - \frac{y}{z}\right)\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-36}:\\ \;\;\;\;4 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+41}:\\ \;\;\;\;-2 + 4 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \left(-0.5 - \frac{y}{z}\right)\\ \end{array} \]

Alternative 3: 53.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 4 \cdot \frac{x}{z}\\ \mathbf{if}\;x \leq -1.96 \cdot 10^{-25}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-9}:\\ \;\;\;\;\frac{y \cdot -4}{z}\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+92}:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 4.0 (/ x z))))
   (if (<= x -1.96e-25)
     t_0
     (if (<= x 1.75e-9) (/ (* y -4.0) z) (if (<= x 3.5e+92) -2.0 t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = 4.0 * (x / z);
	double tmp;
	if (x <= -1.96e-25) {
		tmp = t_0;
	} else if (x <= 1.75e-9) {
		tmp = (y * -4.0) / z;
	} else if (x <= 3.5e+92) {
		tmp = -2.0;
	} else {
		tmp = t_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 * (x / z)
    if (x <= (-1.96d-25)) then
        tmp = t_0
    else if (x <= 1.75d-9) then
        tmp = (y * (-4.0d0)) / z
    else if (x <= 3.5d+92) then
        tmp = -2.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 4.0 * (x / z);
	double tmp;
	if (x <= -1.96e-25) {
		tmp = t_0;
	} else if (x <= 1.75e-9) {
		tmp = (y * -4.0) / z;
	} else if (x <= 3.5e+92) {
		tmp = -2.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 4.0 * (x / z)
	tmp = 0
	if x <= -1.96e-25:
		tmp = t_0
	elif x <= 1.75e-9:
		tmp = (y * -4.0) / z
	elif x <= 3.5e+92:
		tmp = -2.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(4.0 * Float64(x / z))
	tmp = 0.0
	if (x <= -1.96e-25)
		tmp = t_0;
	elseif (x <= 1.75e-9)
		tmp = Float64(Float64(y * -4.0) / z);
	elseif (x <= 3.5e+92)
		tmp = -2.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 4.0 * (x / z);
	tmp = 0.0;
	if (x <= -1.96e-25)
		tmp = t_0;
	elseif (x <= 1.75e-9)
		tmp = (y * -4.0) / z;
	elseif (x <= 3.5e+92)
		tmp = -2.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(4.0 * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.96e-25], t$95$0, If[LessEqual[x, 1.75e-9], N[(N[(y * -4.0), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[x, 3.5e+92], -2.0, t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.96e-25 or 3.49999999999999986e92 < x

   1. Initial program 99.0%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   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 x around inf 62.3%

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

   if -1.96e-25 < x < 1.75e-9

   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. 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 y around inf 51.1%

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

      1. *-commutative 51.1%

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

      2. associate-*l/ 51.1%

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

   6. Simplified 51.1%

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

   if 1.75e-9 < x < 3.49999999999999986e92

   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 inf 49.8%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.96 \cdot 10^{-25}:\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-9}:\\ \;\;\;\;\frac{y \cdot -4}{z}\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+92}:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \end{array} \]

Alternative 4: 80.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+70} \lor \neg \left(x \leq 2.9 \cdot 10^{+141}\right):\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \left(-0.5 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.8e+70) (not (<= x 2.9e+141)))
   (* 4.0 (/ x z))
   (* 4.0 (- -0.5 (/ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.8e+70) || !(x <= 2.9e+141)) {
		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 <= (-3.8d+70)) .or. (.not. (x <= 2.9d+141))) 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 <= -3.8e+70) || !(x <= 2.9e+141)) {
		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 <= -3.8e+70) or not (x <= 2.9e+141):
		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 <= -3.8e+70) || !(x <= 2.9e+141))
		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 <= -3.8e+70) || ~((x <= 2.9e+141)))
		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, -3.8e+70], N[Not[LessEqual[x, 2.9e+141]], $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 < -3.7999999999999998e70 or 2.90000000000000007e141 < x

   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. 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 74.6%

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

   if -3.7999999999999998e70 < x < 2.90000000000000007e141

   1. Initial program 99.5%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   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 82.8%

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

      1. div-sub 82.8%

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

      2. *-commutative 82.8%

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

      3. *-lft-identity 82.8%

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

      4. associate-*l/ 82.7%

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

      5. associate-*r* 82.7%

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

      6. lft-mult-inverse 82.8%

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

      7. metadata-eval 82.8%

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

   6. Simplified 82.8%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+70} \lor \neg \left(x \leq 2.9 \cdot 10^{+141}\right):\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \left(-0.5 - \frac{y}{z}\right)\\ \end{array} \]

Alternative 5: 85.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.175 \lor \neg \left(z \leq 1.1 \cdot 10^{+119}\right):\\ \;\;\;\;4 \cdot \left(-0.5 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.175) (not (<= z 1.1e+119)))
   (* 4.0 (- -0.5 (/ y z)))
   (* 4.0 (/ (- x y) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.175) || !(z <= 1.1e+119)) {
		tmp = 4.0 * (-0.5 - (y / z));
	} else {
		tmp = 4.0 * ((x - y) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-0.175d0)) .or. (.not. (z <= 1.1d+119))) then
        tmp = 4.0d0 * ((-0.5d0) - (y / z))
    else
        tmp = 4.0d0 * ((x - y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.175) || !(z <= 1.1e+119)) {
		tmp = 4.0 * (-0.5 - (y / z));
	} else {
		tmp = 4.0 * ((x - y) / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.175) or not (z <= 1.1e+119):
		tmp = 4.0 * (-0.5 - (y / z))
	else:
		tmp = 4.0 * ((x - y) / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.175) || !(z <= 1.1e+119))
		tmp = Float64(4.0 * Float64(-0.5 - Float64(y / z)));
	else
		tmp = Float64(4.0 * Float64(Float64(x - y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.175) || ~((z <= 1.1e+119)))
		tmp = 4.0 * (-0.5 - (y / z));
	else
		tmp = 4.0 * ((x - y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.175], N[Not[LessEqual[z, 1.1e+119]], $MachinePrecision]], N[(4.0 * N[(-0.5 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(4.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.17499999999999999 or 1.1000000000000001e119 < z

   1. Initial program 98.0%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   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 87.0%

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

      1. div-sub 87.0%

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

      2. *-commutative 87.0%

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

      3. *-lft-identity 87.0%

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

      4. associate-*l/ 86.8%

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

      5. associate-*r* 86.8%

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

      6. lft-mult-inverse 87.0%

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

      7. metadata-eval 87.0%

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

   6. Simplified 87.0%

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

   if -0.17499999999999999 < z < 1.1000000000000001e119

   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 85.7%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.175 \lor \neg \left(z \leq 1.1 \cdot 10^{+119}\right):\\ \;\;\;\;4 \cdot \left(-0.5 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - y}{z}\\ \end{array} \]

Alternative 6: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. 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. Final simplification 99.7%

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

Alternative 7: 53.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.0155:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+133}:\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.0155) -2.0 (if (<= z 3.4e+133) (* 4.0 (/ x z)) -2.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.0155) {
		tmp = -2.0;
	} else if (z <= 3.4e+133) {
		tmp = 4.0 * (x / 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 <= (-0.0155d0)) then
        tmp = -2.0d0
    else if (z <= 3.4d+133) then
        tmp = 4.0d0 * (x / 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 <= -0.0155) {
		tmp = -2.0;
	} else if (z <= 3.4e+133) {
		tmp = 4.0 * (x / z);
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.0155:
		tmp = -2.0
	elif z <= 3.4e+133:
		tmp = 4.0 * (x / z)
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.0155)
		tmp = -2.0;
	elseif (z <= 3.4e+133)
		tmp = Float64(4.0 * Float64(x / z));
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.0155)
		tmp = -2.0;
	elseif (z <= 3.4e+133)
		tmp = 4.0 * (x / z);
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.0155], -2.0, If[LessEqual[z, 3.4e+133], N[(4.0 * N[(x / z), $MachinePrecision]), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if z < -0.0155 or 3.39999999999999987e133 < z

   1. Initial program 98.0%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   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 66.9%

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

   if -0.0155 < z < 3.39999999999999987e133

   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 x around inf 44.5%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0155:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+133}:\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]

Alternative 8: 34.2% 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 99.2%

   \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
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 34.4%

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

5. Final simplification 34.4%

   \[\leadsto -2 \]

Developer target: 97.8% 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 2023175 
(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))