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

Percentage Accurate: 99.9% → 100.0%

Time: 9.2s

Alternatives: 8

Speedup: 1.2×

• 21.1% 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: 99.9% 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/ 99.4%

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

   2. sub-neg 99.4%

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

   3. distribute-rgt-neg-in 99.4%

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

   4. metadata-eval 99.4%

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

3. Simplified 99.4%

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

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: 86.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 4 \cdot \left(-0.5 - \frac{y}{z}\right)\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{+36}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+52}:\\ \;\;\;\;4 \cdot \frac{x}{z} + -2\\ \mathbf{elif}\;y \leq 3.25 \cdot 10^{+122}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 4.0 (- -0.5 (/ y z)))))
   (if (<= y -4.5e+36)
     t_0
     (if (<= y 3.8e+52)
       (+ (* 4.0 (/ x z)) -2.0)
       (if (<= y 3.25e+122) t_0 (* 4.0 (/ (- x y) z)))))))

C

double code(double x, double y, double z) {
	double t_0 = 4.0 * (-0.5 - (y / z));
	double tmp;
	if (y <= -4.5e+36) {
		tmp = t_0;
	} else if (y <= 3.8e+52) {
		tmp = (4.0 * (x / z)) + -2.0;
	} else if (y <= 3.25e+122) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = 4.0d0 * ((-0.5d0) - (y / z))
    if (y <= (-4.5d+36)) then
        tmp = t_0
    else if (y <= 3.8d+52) then
        tmp = (4.0d0 * (x / z)) + (-2.0d0)
    else if (y <= 3.25d+122) then
        tmp = t_0
    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 t_0 = 4.0 * (-0.5 - (y / z));
	double tmp;
	if (y <= -4.5e+36) {
		tmp = t_0;
	} else if (y <= 3.8e+52) {
		tmp = (4.0 * (x / z)) + -2.0;
	} else if (y <= 3.25e+122) {
		tmp = t_0;
	} else {
		tmp = 4.0 * ((x - y) / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 4.0 * (-0.5 - (y / z))
	tmp = 0
	if y <= -4.5e+36:
		tmp = t_0
	elif y <= 3.8e+52:
		tmp = (4.0 * (x / z)) + -2.0
	elif y <= 3.25e+122:
		tmp = t_0
	else:
		tmp = 4.0 * ((x - y) / z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(4.0 * Float64(-0.5 - Float64(y / z)))
	tmp = 0.0
	if (y <= -4.5e+36)
		tmp = t_0;
	elseif (y <= 3.8e+52)
		tmp = Float64(Float64(4.0 * Float64(x / z)) + -2.0);
	elseif (y <= 3.25e+122)
		tmp = t_0;
	else
		tmp = Float64(4.0 * Float64(Float64(x - y) / z));
	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 <= -4.5e+36)
		tmp = t_0;
	elseif (y <= 3.8e+52)
		tmp = (4.0 * (x / z)) + -2.0;
	elseif (y <= 3.25e+122)
		tmp = t_0;
	else
		tmp = 4.0 * ((x - y) / z);
	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, -4.5e+36], t$95$0, If[LessEqual[y, 3.8e+52], N[(N[(4.0 * N[(x / z), $MachinePrecision]), $MachinePrecision] + -2.0), $MachinePrecision], If[LessEqual[y, 3.25e+122], t$95$0, N[(4.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.49999999999999997e36 or 3.8e52 < y < 3.24999999999999982e122

   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 0 94.0%

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

      1. div-sub 94.0%

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

      2. *-commutative 94.0%

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

      3. *-lft-identity 94.0%

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

      4. associate-*l/ 94.0%

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

      5. associate-*r* 94.0%

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

      6. lft-mult-inverse 94.0%

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

      7. metadata-eval 94.0%

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

   6. Simplified 94.0%

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

   if -4.49999999999999997e36 < y < 3.8e52

   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/ 99.1%

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

      2. sub-neg 99.1%

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

      3. distribute-rgt-neg-in 99.1%

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

      4. metadata-eval 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in y around 0 89.9%

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

      1. metadata-eval 89.9%

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

      2. cancel-sign-sub-inv 89.9%

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

      3. div-sub 89.9%

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

      4. sub-neg 89.9%

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

      5. associate-/l* 89.9%

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

      6. *-lft-identity 89.9%

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

      7. associate-*l/ 89.8%

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

      8. lft-mult-inverse 89.9%

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

      9. metadata-eval 89.9%

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

      10. metadata-eval 89.9%

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

      11. distribute-lft-in 89.9%

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

      12. metadata-eval 89.9%

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

   6. Simplified 89.9%

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

   if 3.24999999999999982e122 < y

   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 0 100.0%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+36}:\\ \;\;\;\;4 \cdot \left(-0.5 - \frac{y}{z}\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+52}:\\ \;\;\;\;4 \cdot \frac{x}{z} + -2\\ \mathbf{elif}\;y \leq 3.25 \cdot 10^{+122}:\\ \;\;\;\;4 \cdot \left(-0.5 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - y}{z}\\ \end{array} \]

Alternative 3: 87.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+38}:\\ \;\;\;\;4 \cdot \frac{z \cdot -0.5 - y}{z}\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{+51}:\\ \;\;\;\;4 \cdot \frac{x}{z} + -2\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+124}:\\ \;\;\;\;4 \cdot \left(-0.5 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5e+38)
   (* 4.0 (/ (- (* z -0.5) y) z))
   (if (<= y 5.3e+51)
     (+ (* 4.0 (/ x z)) -2.0)
     (if (<= y 7.6e+124) (* 4.0 (- -0.5 (/ y z))) (* 4.0 (/ (- x y) z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5e+38) {
		tmp = 4.0 * (((z * -0.5) - y) / z);
	} else if (y <= 5.3e+51) {
		tmp = (4.0 * (x / z)) + -2.0;
	} else if (y <= 7.6e+124) {
		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 (y <= (-5d+38)) then
        tmp = 4.0d0 * (((z * (-0.5d0)) - y) / z)
    else if (y <= 5.3d+51) then
        tmp = (4.0d0 * (x / z)) + (-2.0d0)
    else if (y <= 7.6d+124) 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 (y <= -5e+38) {
		tmp = 4.0 * (((z * -0.5) - y) / z);
	} else if (y <= 5.3e+51) {
		tmp = (4.0 * (x / z)) + -2.0;
	} else if (y <= 7.6e+124) {
		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 y <= -5e+38:
		tmp = 4.0 * (((z * -0.5) - y) / z)
	elif y <= 5.3e+51:
		tmp = (4.0 * (x / z)) + -2.0
	elif y <= 7.6e+124:
		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 (y <= -5e+38)
		tmp = Float64(4.0 * Float64(Float64(Float64(z * -0.5) - y) / z));
	elseif (y <= 5.3e+51)
		tmp = Float64(Float64(4.0 * Float64(x / z)) + -2.0);
	elseif (y <= 7.6e+124)
		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 (y <= -5e+38)
		tmp = 4.0 * (((z * -0.5) - y) / z);
	elseif (y <= 5.3e+51)
		tmp = (4.0 * (x / z)) + -2.0;
	elseif (y <= 7.6e+124)
		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[LessEqual[y, -5e+38], N[(4.0 * N[(N[(N[(z * -0.5), $MachinePrecision] - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.3e+51], N[(N[(4.0 * N[(x / z), $MachinePrecision]), $MachinePrecision] + -2.0), $MachinePrecision], If[LessEqual[y, 7.6e+124], 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 4 regimes

2. if y < -4.9999999999999997e38

   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 0 92.6%

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

   if -4.9999999999999997e38 < y < 5.2999999999999997e51

   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/ 99.1%

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

      2. sub-neg 99.1%

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

      3. distribute-rgt-neg-in 99.1%

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

      4. metadata-eval 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in y around 0 89.9%

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

      1. metadata-eval 89.9%

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

      2. cancel-sign-sub-inv 89.9%

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

      3. div-sub 89.9%

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

      4. sub-neg 89.9%

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

      5. associate-/l* 89.9%

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

      6. *-lft-identity 89.9%

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

      7. associate-*l/ 89.8%

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

      8. lft-mult-inverse 89.9%

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

      9. metadata-eval 89.9%

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

      10. metadata-eval 89.9%

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

      11. distribute-lft-in 89.9%

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

      12. metadata-eval 89.9%

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

   6. Simplified 89.9%

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

   if 5.2999999999999997e51 < y < 7.5999999999999997e124

   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/ 99.9%

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

      2. sub-neg 99.9%

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

      3. distribute-rgt-neg-in 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 99.5%

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

      1. div-sub 99.5%

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

      2. *-commutative 99.5%

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

      3. *-lft-identity 99.5%

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

      4. associate-*l/ 99.5%

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

      5. associate-*r* 99.5%

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

      6. lft-mult-inverse 99.5%

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

      7. metadata-eval 99.5%

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

   6. Simplified 99.5%

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

   if 7.5999999999999997e124 < y

   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 0 100.0%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+38}:\\ \;\;\;\;4 \cdot \frac{z \cdot -0.5 - y}{z}\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{+51}:\\ \;\;\;\;4 \cdot \frac{x}{z} + -2\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+124}:\\ \;\;\;\;4 \cdot \left(-0.5 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - y}{z}\\ \end{array} \]

Alternative 4: 54.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y \cdot -4}{z}\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{+39}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-221}:\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+77}:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* y -4.0) z)))
   (if (<= y -2.4e+39)
     t_0
     (if (<= y -5.2e-221) (* 4.0 (/ x z)) (if (<= y 4e+77) -2.0 t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = (y * -4.0) / z;
	double tmp;
	if (y <= -2.4e+39) {
		tmp = t_0;
	} else if (y <= -5.2e-221) {
		tmp = 4.0 * (x / z);
	} else if (y <= 4e+77) {
		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 = (y * (-4.0d0)) / z
    if (y <= (-2.4d+39)) then
        tmp = t_0
    else if (y <= (-5.2d-221)) then
        tmp = 4.0d0 * (x / z)
    else if (y <= 4d+77) 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 = (y * -4.0) / z;
	double tmp;
	if (y <= -2.4e+39) {
		tmp = t_0;
	} else if (y <= -5.2e-221) {
		tmp = 4.0 * (x / z);
	} else if (y <= 4e+77) {
		tmp = -2.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y * -4.0) / z
	tmp = 0
	if y <= -2.4e+39:
		tmp = t_0
	elif y <= -5.2e-221:
		tmp = 4.0 * (x / z)
	elif y <= 4e+77:
		tmp = -2.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y * -4.0) / z)
	tmp = 0.0
	if (y <= -2.4e+39)
		tmp = t_0;
	elseif (y <= -5.2e-221)
		tmp = Float64(4.0 * Float64(x / z));
	elseif (y <= 4e+77)
		tmp = -2.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y * -4.0) / z;
	tmp = 0.0;
	if (y <= -2.4e+39)
		tmp = t_0;
	elseif (y <= -5.2e-221)
		tmp = 4.0 * (x / z);
	elseif (y <= 4e+77)
		tmp = -2.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y * -4.0), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[y, -2.4e+39], t$95$0, If[LessEqual[y, -5.2e-221], N[(4.0 * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e+77], -2.0, t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.4000000000000001e39 or 3.99999999999999993e77 < y

   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 76.9%

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

      1. *-commutative 76.9%

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

      2. associate-*l/ 76.9%

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

   6. Simplified 76.9%

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

   if -2.4000000000000001e39 < y < -5.2000000000000004e-221

   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 61.3%

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

   if -5.2000000000000004e-221 < y < 3.99999999999999993e77

   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/ 98.7%

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

      2. sub-neg 98.7%

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

      3. distribute-rgt-neg-in 98.7%

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

      4. metadata-eval 98.7%

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

   3. Simplified 98.7%

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

   4. Taylor expanded in z around inf 54.5%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+39}:\\ \;\;\;\;\frac{y \cdot -4}{z}\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-221}:\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+77}:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -4}{z}\\ \end{array} \]

Alternative 5: 80.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+62} \lor \neg \left(x \leq 1.05 \cdot 10^{+133}\right):\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \left(-0.5 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.8e+62) (not (<= x 1.05e+133)))
   (* 4.0 (/ x z))
   (* 4.0 (- -0.5 (/ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.8e+62) || !(x <= 1.05e+133)) {
		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 <= (-5.8d+62)) .or. (.not. (x <= 1.05d+133))) 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 <= -5.8e+62) || !(x <= 1.05e+133)) {
		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 <= -5.8e+62) or not (x <= 1.05e+133):
		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 <= -5.8e+62) || !(x <= 1.05e+133))
		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 <= -5.8e+62) || ~((x <= 1.05e+133)))
		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, -5.8e+62], N[Not[LessEqual[x, 1.05e+133]], $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 < -5.79999999999999968e62 or 1.05e133 < 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 79.7%

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

   if -5.79999999999999968e62 < x < 1.05e133

   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/ 99.2%

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

      2. sub-neg 99.2%

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

      3. distribute-rgt-neg-in 99.2%

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

      4. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in x around 0 83.8%

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

      1. div-sub 83.8%

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

      2. *-commutative 83.8%

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

      3. *-lft-identity 83.8%

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

      4. associate-*l/ 83.2%

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

      5. associate-*r* 83.2%

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

      6. lft-mult-inverse 83.8%

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

      7. metadata-eval 83.8%

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

   6. Simplified 83.8%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+62} \lor \neg \left(x \leq 1.05 \cdot 10^{+133}\right):\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \left(-0.5 - \frac{y}{z}\right)\\ \end{array} \]

Alternative 6: 85.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+49} \lor \neg \left(z \leq 1.35 \cdot 10^{+62}\right):\\ \;\;\;\;4 \cdot \left(-0.5 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5e+49) (not (<= z 1.35e+62)))
   (* 4.0 (- -0.5 (/ y z)))
   (* 4.0 (/ (- x y) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5e+49) || !(z <= 1.35e+62)) {
		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 <= (-5d+49)) .or. (.not. (z <= 1.35d+62))) 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 <= -5e+49) || !(z <= 1.35e+62)) {
		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 <= -5e+49) or not (z <= 1.35e+62):
		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 <= -5e+49) || !(z <= 1.35e+62))
		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 <= -5e+49) || ~((z <= 1.35e+62)))
		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, -5e+49], N[Not[LessEqual[z, 1.35e+62]], $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 < -5.0000000000000004e49 or 1.35e62 < 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/ 99.8%

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

      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 0 90.5%

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

      1. div-sub 90.5%

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

      2. *-commutative 90.5%

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

      3. *-lft-identity 90.5%

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

      4. associate-*l/ 90.4%

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

      5. associate-*r* 90.4%

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

      6. lft-mult-inverse 90.5%

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

      7. metadata-eval 90.5%

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

   6. Simplified 90.5%

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

   if -5.0000000000000004e49 < z < 1.35e62

   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/ 99.1%

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

      2. sub-neg 99.1%

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

      3. distribute-rgt-neg-in 99.1%

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

      4. metadata-eval 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in z around 0 90.8%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+49} \lor \neg \left(z \leq 1.35 \cdot 10^{+62}\right):\\ \;\;\;\;4 \cdot \left(-0.5 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - y}{z}\\ \end{array} \]

Alternative 7: 55.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.06 \cdot 10^{+44}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+62}:\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.06e+44) -2.0 (if (<= z 1.35e+62) (* 4.0 (/ x z)) -2.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.06e+44) {
		tmp = -2.0;
	} else if (z <= 1.35e+62) {
		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 <= (-1.06d+44)) then
        tmp = -2.0d0
    else if (z <= 1.35d+62) 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 <= -1.06e+44) {
		tmp = -2.0;
	} else if (z <= 1.35e+62) {
		tmp = 4.0 * (x / z);
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.06e+44:
		tmp = -2.0
	elif z <= 1.35e+62:
		tmp = 4.0 * (x / z)
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.06e+44)
		tmp = -2.0;
	elseif (z <= 1.35e+62)
		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 <= -1.06e+44)
		tmp = -2.0;
	elseif (z <= 1.35e+62)
		tmp = 4.0 * (x / z);
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.06e+44], -2.0, If[LessEqual[z, 1.35e+62], N[(4.0 * N[(x / z), $MachinePrecision]), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if z < -1.06e44 or 1.35e62 < 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/ 99.8%

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

      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 73.0%

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

   if -1.06e44 < z < 1.35e62

   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/ 99.1%

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

      2. sub-neg 99.1%

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

      3. distribute-rgt-neg-in 99.1%

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

      4. metadata-eval 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in x around inf 47.6%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.06 \cdot 10^{+44}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+62}:\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]

Alternative 8: 34.8% 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/ 99.4%

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

   2. sub-neg 99.4%

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

   3. distribute-rgt-neg-in 99.4%

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

   4. metadata-eval 99.4%

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

3. Simplified 99.4%

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

4. Taylor expanded in z around inf 33.3%

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

5. Final simplification 33.3%

   \[\leadsto -2 \]

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 2023279 
(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))