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

Percentage Accurate: 99.9% → 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: 99.9% 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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. remove-double-neg 100.0%

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

   2. neg-mul-1 100.0%

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

   3. times-frac 100.0%

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

   4. metadata-eval 100.0%

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

   5. div-sub 100.0%

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

   6. distribute-frac-neg2 100.0%

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

   7. distribute-frac-neg 100.0%

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

   8. sub-neg 100.0%

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

   9. +-commutative 100.0%

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

   10. distribute-neg-out 100.0%

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

   11. remove-double-neg 100.0%

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

   12. sub-neg 100.0%

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

   13. *-commutative 100.0%

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

   14. neg-mul-1 100.0%

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

   15. times-frac 100.0%

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

   16. metadata-eval 100.0%

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

   17. *-inverses 100.0%

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

   18. metadata-eval 100.0%

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

3. Simplified 100.0%

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

Alternative 2: 53.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -4 \cdot \frac{y}{z}\\ t_1 := \frac{x \cdot 4}{z}\\ \mathbf{if}\;y \leq -0.0022:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-241}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-300}:\\ \;\;\;\;-2\\ \mathbf{elif}\;y \leq 0.19:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+79}:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -4.0 (/ y z))) (t_1 (/ (* x 4.0) z)))
   (if (<= y -0.0022)
     t_0
     (if (<= y -3.9e-241)
       t_1
       (if (<= y 6.4e-300)
         -2.0
         (if (<= y 0.19) t_1 (if (<= y 4.8e+79) -2.0 t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = -4.0 * (y / z);
	double t_1 = (x * 4.0) / z;
	double tmp;
	if (y <= -0.0022) {
		tmp = t_0;
	} else if (y <= -3.9e-241) {
		tmp = t_1;
	} else if (y <= 6.4e-300) {
		tmp = -2.0;
	} else if (y <= 0.19) {
		tmp = t_1;
	} else if (y <= 4.8e+79) {
		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) :: t_1
    real(8) :: tmp
    t_0 = (-4.0d0) * (y / z)
    t_1 = (x * 4.0d0) / z
    if (y <= (-0.0022d0)) then
        tmp = t_0
    else if (y <= (-3.9d-241)) then
        tmp = t_1
    else if (y <= 6.4d-300) then
        tmp = -2.0d0
    else if (y <= 0.19d0) then
        tmp = t_1
    else if (y <= 4.8d+79) 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 * (y / z);
	double t_1 = (x * 4.0) / z;
	double tmp;
	if (y <= -0.0022) {
		tmp = t_0;
	} else if (y <= -3.9e-241) {
		tmp = t_1;
	} else if (y <= 6.4e-300) {
		tmp = -2.0;
	} else if (y <= 0.19) {
		tmp = t_1;
	} else if (y <= 4.8e+79) {
		tmp = -2.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -4.0 * (y / z)
	t_1 = (x * 4.0) / z
	tmp = 0
	if y <= -0.0022:
		tmp = t_0
	elif y <= -3.9e-241:
		tmp = t_1
	elif y <= 6.4e-300:
		tmp = -2.0
	elif y <= 0.19:
		tmp = t_1
	elif y <= 4.8e+79:
		tmp = -2.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-4.0 * Float64(y / z))
	t_1 = Float64(Float64(x * 4.0) / z)
	tmp = 0.0
	if (y <= -0.0022)
		tmp = t_0;
	elseif (y <= -3.9e-241)
		tmp = t_1;
	elseif (y <= 6.4e-300)
		tmp = -2.0;
	elseif (y <= 0.19)
		tmp = t_1;
	elseif (y <= 4.8e+79)
		tmp = -2.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -4.0 * (y / z);
	t_1 = (x * 4.0) / z;
	tmp = 0.0;
	if (y <= -0.0022)
		tmp = t_0;
	elseif (y <= -3.9e-241)
		tmp = t_1;
	elseif (y <= 6.4e-300)
		tmp = -2.0;
	elseif (y <= 0.19)
		tmp = t_1;
	elseif (y <= 4.8e+79)
		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[(y / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x * 4.0), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[y, -0.0022], t$95$0, If[LessEqual[y, -3.9e-241], t$95$1, If[LessEqual[y, 6.4e-300], -2.0, If[LessEqual[y, 0.19], t$95$1, If[LessEqual[y, 4.8e+79], -2.0, t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.00220000000000000013 or 4.79999999999999971e79 < 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. *-commutative 100.0%

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

      2. associate-/l* 99.7%

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

      3. associate--l- 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 68.4%

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

      1. *-commutative 68.4%

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

   7. Simplified 68.4%

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

   if -0.00220000000000000013 < y < -3.8999999999999999e-241 or 6.40000000000000043e-300 < y < 0.19

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-/l* 99.7%

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

      3. associate--l- 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 52.0%

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

      1. associate-*r/ 52.0%

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

      2. *-commutative 52.0%

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

   7. Simplified 52.0%

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

   if -3.8999999999999999e-241 < y < 6.40000000000000043e-300 or 0.19 < y < 4.79999999999999971e79

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-/l* 99.9%

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

      3. associate--l- 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 69.5%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0022:\\ \;\;\;\;-4 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-241}:\\ \;\;\;\;\frac{x \cdot 4}{z}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-300}:\\ \;\;\;\;-2\\ \mathbf{elif}\;y \leq 0.19:\\ \;\;\;\;\frac{x \cdot 4}{z}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+79}:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+118} \lor \neg \left(z \leq 1.22 \cdot 10^{+54}\right):\\ \;\;\;\;-4 \cdot \left(\frac{y}{z} - -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{4 \cdot \left(x - y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -6.5e+118) (not (<= z 1.22e+54)))
   (* -4.0 (- (/ y z) -0.5))
   (/ (* 4.0 (- x y)) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6.5e+118) || !(z <= 1.22e+54)) {
		tmp = -4.0 * ((y / z) - -0.5);
	} 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 <= (-6.5d+118)) .or. (.not. (z <= 1.22d+54))) then
        tmp = (-4.0d0) * ((y / z) - (-0.5d0))
    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 <= -6.5e+118) || !(z <= 1.22e+54)) {
		tmp = -4.0 * ((y / z) - -0.5);
	} else {
		tmp = (4.0 * (x - y)) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -6.5e+118) or not (z <= 1.22e+54):
		tmp = -4.0 * ((y / z) - -0.5)
	else:
		tmp = (4.0 * (x - y)) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -6.5e+118) || !(z <= 1.22e+54))
		tmp = Float64(-4.0 * Float64(Float64(y / z) - -0.5));
	else
		tmp = Float64(Float64(4.0 * Float64(x - y)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -6.5e+118) || ~((z <= 1.22e+54)))
		tmp = -4.0 * ((y / z) - -0.5);
	else
		tmp = (4.0 * (x - y)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -6.5e+118], N[Not[LessEqual[z, 1.22e+54]], $MachinePrecision]], N[(-4.0 * N[(N[(y / z), $MachinePrecision] - -0.5), $MachinePrecision]), $MachinePrecision], N[(N[(4.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.5e118 or 1.22e54 < 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. remove-double-neg 100.0%

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

      2. neg-mul-1 100.0%

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

      3. times-frac 100.0%

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

      4. metadata-eval 100.0%

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

      5. div-sub 100.0%

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

      6. distribute-frac-neg2 100.0%

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

      7. distribute-frac-neg 100.0%

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

      8. sub-neg 100.0%

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

      9. +-commutative 100.0%

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

      10. distribute-neg-out 100.0%

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

      11. remove-double-neg 100.0%

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

      12. sub-neg 100.0%

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

      13. *-commutative 100.0%

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

      14. neg-mul-1 100.0%

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

      15. times-frac 100.0%

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

      16. metadata-eval 100.0%

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

      17. *-inverses 100.0%

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

      18. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 90.9%

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

   if -6.5e118 < z < 1.22e54

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-/l* 99.7%

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

      3. associate--l- 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 87.8%

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

      1. associate-*r/ 87.8%

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

   7. Simplified 87.8%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+118} \lor \neg \left(z \leq 1.22 \cdot 10^{+54}\right):\\ \;\;\;\;-4 \cdot \left(\frac{y}{z} - -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{4 \cdot \left(x - y\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+118} \lor \neg \left(z \leq 3.8 \cdot 10^{+52}\right):\\ \;\;\;\;-4 \cdot \left(\frac{y}{z} - -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{4}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -6.5e+118) (not (<= z 3.8e+52)))
   (* -4.0 (- (/ y z) -0.5))
   (* (- x y) (/ 4.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6.5e+118) || !(z <= 3.8e+52)) {
		tmp = -4.0 * ((y / z) - -0.5);
	} 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 ((z <= (-6.5d+118)) .or. (.not. (z <= 3.8d+52))) then
        tmp = (-4.0d0) * ((y / z) - (-0.5d0))
    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 ((z <= -6.5e+118) || !(z <= 3.8e+52)) {
		tmp = -4.0 * ((y / z) - -0.5);
	} else {
		tmp = (x - y) * (4.0 / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -6.5e+118) or not (z <= 3.8e+52):
		tmp = -4.0 * ((y / z) - -0.5)
	else:
		tmp = (x - y) * (4.0 / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -6.5e+118) || !(z <= 3.8e+52))
		tmp = Float64(-4.0 * Float64(Float64(y / z) - -0.5));
	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 ((z <= -6.5e+118) || ~((z <= 3.8e+52)))
		tmp = -4.0 * ((y / z) - -0.5);
	else
		tmp = (x - y) * (4.0 / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -6.5e+118], N[Not[LessEqual[z, 3.8e+52]], $MachinePrecision]], N[(-4.0 * N[(N[(y / z), $MachinePrecision] - -0.5), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(4.0 / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.5e118 or 3.8e52 < 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. remove-double-neg 100.0%

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

      2. neg-mul-1 100.0%

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

      3. times-frac 100.0%

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

      4. metadata-eval 100.0%

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

      5. div-sub 100.0%

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

      6. distribute-frac-neg2 100.0%

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

      7. distribute-frac-neg 100.0%

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

      8. sub-neg 100.0%

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

      9. +-commutative 100.0%

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

      10. distribute-neg-out 100.0%

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

      11. remove-double-neg 100.0%

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

      12. sub-neg 100.0%

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

      13. *-commutative 100.0%

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

      14. neg-mul-1 100.0%

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

      15. times-frac 100.0%

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

      16. metadata-eval 100.0%

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

      17. *-inverses 100.0%

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

      18. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 90.9%

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

   if -6.5e118 < z < 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. *-commutative 100.0%

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

      2. associate-/l* 99.7%

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

      3. associate--l- 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 87.5%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+118} \lor \neg \left(z \leq 3.8 \cdot 10^{+52}\right):\\ \;\;\;\;-4 \cdot \left(\frac{y}{z} - -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{4}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 80.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+88} \lor \neg \left(x \leq 5 \cdot 10^{+142}\right):\\ \;\;\;\;\frac{x \cdot 4}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(\frac{y}{z} - -0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -9e+88) (not (<= x 5e+142)))
   (/ (* x 4.0) z)
   (* -4.0 (- (/ y z) -0.5))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -9e+88) || !(x <= 5e+142)) {
		tmp = (x * 4.0) / z;
	} else {
		tmp = -4.0 * ((y / z) - -0.5);
	}
	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 <= (-9d+88)) .or. (.not. (x <= 5d+142))) then
        tmp = (x * 4.0d0) / z
    else
        tmp = (-4.0d0) * ((y / z) - (-0.5d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -9e+88) || !(x <= 5e+142)) {
		tmp = (x * 4.0) / z;
	} else {
		tmp = -4.0 * ((y / z) - -0.5);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -9e+88) or not (x <= 5e+142):
		tmp = (x * 4.0) / z
	else:
		tmp = -4.0 * ((y / z) - -0.5)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -9e+88) || !(x <= 5e+142))
		tmp = Float64(Float64(x * 4.0) / z);
	else
		tmp = Float64(-4.0 * Float64(Float64(y / z) - -0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -9e+88) || ~((x <= 5e+142)))
		tmp = (x * 4.0) / z;
	else
		tmp = -4.0 * ((y / z) - -0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -9e+88], N[Not[LessEqual[x, 5e+142]], $MachinePrecision]], N[(N[(x * 4.0), $MachinePrecision] / z), $MachinePrecision], N[(-4.0 * N[(N[(y / z), $MachinePrecision] - -0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9e88 or 5.0000000000000001e142 < 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. *-commutative 100.0%

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

      2. associate-/l* 99.8%

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

      3. associate--l- 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 75.6%

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

      1. associate-*r/ 75.6%

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

      2. *-commutative 75.6%

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

   7. Simplified 75.6%

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

   if -9e88 < x < 5.0000000000000001e142

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. neg-mul-1 100.0%

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

      3. times-frac 100.0%

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

      4. metadata-eval 100.0%

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

      5. div-sub 100.0%

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

      6. distribute-frac-neg2 100.0%

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

      7. distribute-frac-neg 100.0%

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

      8. sub-neg 100.0%

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

      9. +-commutative 100.0%

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

      10. distribute-neg-out 100.0%

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

      11. remove-double-neg 100.0%

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

      12. sub-neg 100.0%

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

      13. *-commutative 100.0%

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

      14. neg-mul-1 100.0%

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

      15. times-frac 100.0%

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

      16. metadata-eval 100.0%

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

      17. *-inverses 100.0%

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

      18. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 83.7%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+88} \lor \neg \left(x \leq 5 \cdot 10^{+142}\right):\\ \;\;\;\;\frac{x \cdot 4}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(\frac{y}{z} - -0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 53.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+46}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+102}:\\ \;\;\;\;-4 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.3e+46) -2.0 (if (<= z 2.2e+102) (* -4.0 (/ y z)) -2.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.3e+46) {
		tmp = -2.0;
	} else if (z <= 2.2e+102) {
		tmp = -4.0 * (y / 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 <= (-1.3d+46)) then
        tmp = -2.0d0
    else if (z <= 2.2d+102) then
        tmp = (-4.0d0) * (y / 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 <= -1.3e+46) {
		tmp = -2.0;
	} else if (z <= 2.2e+102) {
		tmp = -4.0 * (y / z);
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.3e+46:
		tmp = -2.0
	elif z <= 2.2e+102:
		tmp = -4.0 * (y / z)
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.3e+46)
		tmp = -2.0;
	elseif (z <= 2.2e+102)
		tmp = Float64(-4.0 * Float64(y / z));
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.3e+46)
		tmp = -2.0;
	elseif (z <= 2.2e+102)
		tmp = -4.0 * (y / z);
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.3e+46], -2.0, If[LessEqual[z, 2.2e+102], N[(-4.0 * N[(y / z), $MachinePrecision]), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if z < -1.30000000000000007e46 or 2.20000000000000007e102 < 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. *-commutative 100.0%

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

      2. associate-/l* 99.7%

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

      3. associate--l- 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 69.2%

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

   if -1.30000000000000007e46 < z < 2.20000000000000007e102

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-/l* 99.7%

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

      3. associate--l- 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 51.1%

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

      1. *-commutative 51.1%

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

   7. Simplified 51.1%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+46}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+102}:\\ \;\;\;\;-4 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 52.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+45}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+104}:\\ \;\;\;\;y \cdot \frac{-4}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5.8e+45) -2.0 (if (<= z 8.8e+104) (* y (/ -4.0 z)) -2.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.8e+45) {
		tmp = -2.0;
	} else if (z <= 8.8e+104) {
		tmp = y * (-4.0 / z);
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-5.8d+45)) then
        tmp = -2.0d0
    else if (z <= 8.8d+104) then
        tmp = y * ((-4.0d0) / z)
    else
        tmp = -2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.8e+45) {
		tmp = -2.0;
	} else if (z <= 8.8e+104) {
		tmp = y * (-4.0 / z);
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5.8e+45:
		tmp = -2.0
	elif z <= 8.8e+104:
		tmp = y * (-4.0 / z)
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5.8e+45)
		tmp = -2.0;
	elseif (z <= 8.8e+104)
		tmp = Float64(y * Float64(-4.0 / z));
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -5.8e+45)
		tmp = -2.0;
	elseif (z <= 8.8e+104)
		tmp = y * (-4.0 / z);
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5.8e+45], -2.0, If[LessEqual[z, 8.8e+104], N[(y * N[(-4.0 / z), $MachinePrecision]), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if z < -5.7999999999999994e45 or 8.80000000000000002e104 < 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. *-commutative 100.0%

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

      2. associate-/l* 99.7%

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

      3. associate--l- 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 69.2%

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

   if -5.7999999999999994e45 < z < 8.80000000000000002e104

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-/l* 99.7%

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

      3. associate--l- 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 51.1%

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

      1. metadata-eval 51.1%

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

      2. distribute-lft-neg-in 51.1%

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

      3. *-lft-identity 51.1%

         \[\leadsto -4 \cdot \frac{\color{blue}{1 \cdot y}}{z} \]

      4. associate-*l/ 50.9%

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

      5. associate-*l* 50.9%

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

      6. associate-*r/ 50.9%

         \[\leadsto -\color{blue}{\frac{4 \cdot 1}{z}} \cdot y \]

      7. metadata-eval 50.9%

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

      8. *-commutative 50.9%

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

      9. distribute-rgt-neg-in 50.9%

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

      10. distribute-neg-frac 50.9%

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

      11. metadata-eval 50.9%

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

   7. Simplified 50.9%

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

Alternative 8: 33.1% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. *-commutative 100.0%

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

   2. associate-/l* 99.7%

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

   3. associate--l- 99.7%

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

3. Simplified 99.7%

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

5. Taylor expanded in z around inf 33.7%

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

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 2024089 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, B"
  :precision binary64

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

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