Graphics.Rasterific.Shading:$sgradientColorAt from Rasterific-0.6.1

Percentage Accurate: 100.0% → 100.0%

Time: 5.6s

Alternatives: 8

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (y - x) / (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 = (y - x) / (y - z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\frac{x - y}{z - y} \]
2. Add Preprocessing

3. Final simplification 100.0%

   \[\leadsto \frac{y - x}{y - z} \]
4. Add Preprocessing

Alternative 2: 68.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-x}{y}\\ t_1 := \frac{y - x}{y - z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+262}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{+30}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 0.4:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;t\_1 \leq 2000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+155}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (- x) y)) (t_1 (/ (- y x) (- y z))))
   (if (<= t_1 -2e+262)
     (/ x z)
     (if (<= t_1 -1e+30)
       t_0
       (if (<= t_1 0.4)
         (/ x z)
         (if (<= t_1 2000000000.0) 1.0 (if (<= t_1 5e+155) (/ x z) t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = -x / y;
	double t_1 = (y - x) / (y - z);
	double tmp;
	if (t_1 <= -2e+262) {
		tmp = x / z;
	} else if (t_1 <= -1e+30) {
		tmp = t_0;
	} else if (t_1 <= 0.4) {
		tmp = x / z;
	} else if (t_1 <= 2000000000.0) {
		tmp = 1.0;
	} else if (t_1 <= 5e+155) {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_0 = -x / y
    t_1 = (y - x) / (y - z)
    if (t_1 <= (-2d+262)) then
        tmp = x / z
    else if (t_1 <= (-1d+30)) then
        tmp = t_0
    else if (t_1 <= 0.4d0) then
        tmp = x / z
    else if (t_1 <= 2000000000.0d0) then
        tmp = 1.0d0
    else if (t_1 <= 5d+155) then
        tmp = 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 = -x / y;
	double t_1 = (y - x) / (y - z);
	double tmp;
	if (t_1 <= -2e+262) {
		tmp = x / z;
	} else if (t_1 <= -1e+30) {
		tmp = t_0;
	} else if (t_1 <= 0.4) {
		tmp = x / z;
	} else if (t_1 <= 2000000000.0) {
		tmp = 1.0;
	} else if (t_1 <= 5e+155) {
		tmp = x / z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -x / y
	t_1 = (y - x) / (y - z)
	tmp = 0
	if t_1 <= -2e+262:
		tmp = x / z
	elif t_1 <= -1e+30:
		tmp = t_0
	elif t_1 <= 0.4:
		tmp = x / z
	elif t_1 <= 2000000000.0:
		tmp = 1.0
	elif t_1 <= 5e+155:
		tmp = x / z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-x) / y)
	t_1 = Float64(Float64(y - x) / Float64(y - z))
	tmp = 0.0
	if (t_1 <= -2e+262)
		tmp = Float64(x / z);
	elseif (t_1 <= -1e+30)
		tmp = t_0;
	elseif (t_1 <= 0.4)
		tmp = Float64(x / z);
	elseif (t_1 <= 2000000000.0)
		tmp = 1.0;
	elseif (t_1 <= 5e+155)
		tmp = Float64(x / z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -x / y;
	t_1 = (y - x) / (y - z);
	tmp = 0.0;
	if (t_1 <= -2e+262)
		tmp = x / z;
	elseif (t_1 <= -1e+30)
		tmp = t_0;
	elseif (t_1 <= 0.4)
		tmp = x / z;
	elseif (t_1 <= 2000000000.0)
		tmp = 1.0;
	elseif (t_1 <= 5e+155)
		tmp = x / z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[((-x) / y), $MachinePrecision]}, Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+262], N[(x / z), $MachinePrecision], If[LessEqual[t$95$1, -1e+30], t$95$0, If[LessEqual[t$95$1, 0.4], N[(x / z), $MachinePrecision], If[LessEqual[t$95$1, 2000000000.0], 1.0, If[LessEqual[t$95$1, 5e+155], N[(x / z), $MachinePrecision], t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -2e262 or -1e30 < (/.f64 (-.f64 x y) (-.f64 z y)) < 0.40000000000000002 or 2e9 < (/.f64 (-.f64 x y) (-.f64 z y)) < 4.9999999999999999e155

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 67.9

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

   5. Applied rewrites 67.9%

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

   if -2e262 < (/.f64 (-.f64 x y) (-.f64 z y)) < -1e30 or 4.9999999999999999e155 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{-1 \cdot \frac{x - y}{y}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(\frac{x - y}{y}\right)} \]

      2. div-sub N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\frac{x}{y} - \frac{y}{y}\right)}\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\frac{x}{y} + \left(\mathsf{neg}\left(\frac{y}{y}\right)\right)\right)}\right) \]

      4. *-inverses N/A

         \[\leadsto \mathsf{neg}\left(\left(\frac{x}{y} + \left(\mathsf{neg}\left(\color{blue}{1}\right)\right)\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{neg}\left(\left(\frac{x}{y} + \color{blue}{-1}\right)\right) \]

      6. +-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(-1 + \frac{x}{y}\right)}\right) \]

      7. distribute-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(-1\right)\right) + \left(\mathsf{neg}\left(\frac{x}{y}\right)\right)} \]

      8. metadata-eval N/A

         \[\leadsto \color{blue}{1} + \left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \]

      9. unsub-neg N/A

         \[\leadsto \color{blue}{1 - \frac{x}{y}} \]

      10. lower--.f64 N/A

          \[\leadsto \color{blue}{1 - \frac{x}{y}} \]

      11. lower-/.f64 70.6

          \[\leadsto 1 - \color{blue}{\frac{x}{y}} \]

   5. Applied rewrites 70.6%

      \[\leadsto \color{blue}{1 - \frac{x}{y}} \]

   6. Taylor expanded in x around inf

      \[\leadsto -1 \cdot \color{blue}{\frac{x}{y}} \]
   7. Step-by-step derivation

   8. Applied rewrites 70.6%

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

   if 0.40000000000000002 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2e9

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Applied rewrites 97.4%

      \[\leadsto \color{blue}{1} \]
3. Recombined 3 regimes into one program.

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y - x}{y - z} \leq -2 \cdot 10^{+262}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq -1 \cdot 10^{+30}:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq 0.4:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq 2000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq 5 \cdot 10^{+155}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y - x}{y - z}\\ t_1 := \frac{x}{z - y}\\ \mathbf{if}\;t\_0 \leq -5000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 0.4:\\ \;\;\;\;\frac{x - y}{z}\\ \mathbf{elif}\;t\_0 \leq 2:\\ \;\;\;\;\frac{-y}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (- y x) (- y z))) (t_1 (/ x (- z y))))
   (if (<= t_0 -5000000.0)
     t_1
     (if (<= t_0 0.4) (/ (- x y) z) (if (<= t_0 2.0) (/ (- y) (- z y)) t_1)))))

C

double code(double x, double y, double z) {
	double t_0 = (y - x) / (y - z);
	double t_1 = x / (z - y);
	double tmp;
	if (t_0 <= -5000000.0) {
		tmp = t_1;
	} else if (t_0 <= 0.4) {
		tmp = (x - y) / z;
	} else if (t_0 <= 2.0) {
		tmp = -y / (z - y);
	} else {
		tmp = t_1;
	}
	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 = (y - x) / (y - z)
    t_1 = x / (z - y)
    if (t_0 <= (-5000000.0d0)) then
        tmp = t_1
    else if (t_0 <= 0.4d0) then
        tmp = (x - y) / z
    else if (t_0 <= 2.0d0) then
        tmp = -y / (z - y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (y - x) / (y - z);
	double t_1 = x / (z - y);
	double tmp;
	if (t_0 <= -5000000.0) {
		tmp = t_1;
	} else if (t_0 <= 0.4) {
		tmp = (x - y) / z;
	} else if (t_0 <= 2.0) {
		tmp = -y / (z - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y - x) / (y - z)
	t_1 = x / (z - y)
	tmp = 0
	if t_0 <= -5000000.0:
		tmp = t_1
	elif t_0 <= 0.4:
		tmp = (x - y) / z
	elif t_0 <= 2.0:
		tmp = -y / (z - y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y - x) / Float64(y - z))
	t_1 = Float64(x / Float64(z - y))
	tmp = 0.0
	if (t_0 <= -5000000.0)
		tmp = t_1;
	elseif (t_0 <= 0.4)
		tmp = Float64(Float64(x - y) / z);
	elseif (t_0 <= 2.0)
		tmp = Float64(Float64(-y) / Float64(z - y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y - x) / (y - z);
	t_1 = x / (z - y);
	tmp = 0.0;
	if (t_0 <= -5000000.0)
		tmp = t_1;
	elseif (t_0 <= 0.4)
		tmp = (x - y) / z;
	elseif (t_0 <= 2.0)
		tmp = -y / (z - y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y - x), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -5000000.0], t$95$1, If[LessEqual[t$95$0, 0.4], N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$0, 2.0], N[((-y) / N[(z - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -5e6 or 2 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 98.5

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

   5. Applied rewrites 98.5%

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

   if -5e6 < (/.f64 (-.f64 x y) (-.f64 z y)) < 0.40000000000000002

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 98.2

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

   5. Applied rewrites 98.2%

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

   if 0.40000000000000002 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \frac{\color{blue}{-1 \cdot y}}{z - y} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. lower-neg.f64 99.1

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

   5. Applied rewrites 99.1%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y - x}{y - z} \leq -5000000:\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq 0.4:\\ \;\;\;\;\frac{x - y}{z}\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq 2:\\ \;\;\;\;\frac{-y}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y - x}{y - z}\\ t_1 := \frac{x}{z - y}\\ \mathbf{if}\;t\_0 \leq -5000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 0.4:\\ \;\;\;\;\frac{x - y}{z}\\ \mathbf{elif}\;t\_0 \leq 2000000000:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (- y x) (- y z))) (t_1 (/ x (- z y))))
   (if (<= t_0 -5000000.0)
     t_1
     (if (<= t_0 0.4)
       (/ (- x y) z)
       (if (<= t_0 2000000000.0) (- 1.0 (/ x y)) t_1)))))

C

double code(double x, double y, double z) {
	double t_0 = (y - x) / (y - z);
	double t_1 = x / (z - y);
	double tmp;
	if (t_0 <= -5000000.0) {
		tmp = t_1;
	} else if (t_0 <= 0.4) {
		tmp = (x - y) / z;
	} else if (t_0 <= 2000000000.0) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = t_1;
	}
	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 = (y - x) / (y - z)
    t_1 = x / (z - y)
    if (t_0 <= (-5000000.0d0)) then
        tmp = t_1
    else if (t_0 <= 0.4d0) then
        tmp = (x - y) / z
    else if (t_0 <= 2000000000.0d0) then
        tmp = 1.0d0 - (x / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (y - x) / (y - z);
	double t_1 = x / (z - y);
	double tmp;
	if (t_0 <= -5000000.0) {
		tmp = t_1;
	} else if (t_0 <= 0.4) {
		tmp = (x - y) / z;
	} else if (t_0 <= 2000000000.0) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y - x) / (y - z)
	t_1 = x / (z - y)
	tmp = 0
	if t_0 <= -5000000.0:
		tmp = t_1
	elif t_0 <= 0.4:
		tmp = (x - y) / z
	elif t_0 <= 2000000000.0:
		tmp = 1.0 - (x / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y - x) / Float64(y - z))
	t_1 = Float64(x / Float64(z - y))
	tmp = 0.0
	if (t_0 <= -5000000.0)
		tmp = t_1;
	elseif (t_0 <= 0.4)
		tmp = Float64(Float64(x - y) / z);
	elseif (t_0 <= 2000000000.0)
		tmp = Float64(1.0 - Float64(x / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y - x) / (y - z);
	t_1 = x / (z - y);
	tmp = 0.0;
	if (t_0 <= -5000000.0)
		tmp = t_1;
	elseif (t_0 <= 0.4)
		tmp = (x - y) / z;
	elseif (t_0 <= 2000000000.0)
		tmp = 1.0 - (x / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y - x), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -5000000.0], t$95$1, If[LessEqual[t$95$0, 0.4], N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$0, 2000000000.0], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -5e6 or 2e9 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 99.0

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

   5. Applied rewrites 99.0%

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

   if -5e6 < (/.f64 (-.f64 x y) (-.f64 z y)) < 0.40000000000000002

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 98.2

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

   5. Applied rewrites 98.2%

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

   if 0.40000000000000002 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2e9

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{-1 \cdot \frac{x - y}{y}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(\frac{x - y}{y}\right)} \]

      2. div-sub N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\frac{x}{y} - \frac{y}{y}\right)}\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\frac{x}{y} + \left(\mathsf{neg}\left(\frac{y}{y}\right)\right)\right)}\right) \]

      4. *-inverses N/A

         \[\leadsto \mathsf{neg}\left(\left(\frac{x}{y} + \left(\mathsf{neg}\left(\color{blue}{1}\right)\right)\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{neg}\left(\left(\frac{x}{y} + \color{blue}{-1}\right)\right) \]

      6. +-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(-1 + \frac{x}{y}\right)}\right) \]

      7. distribute-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(-1\right)\right) + \left(\mathsf{neg}\left(\frac{x}{y}\right)\right)} \]

      8. metadata-eval N/A

         \[\leadsto \color{blue}{1} + \left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \]

      9. unsub-neg N/A

         \[\leadsto \color{blue}{1 - \frac{x}{y}} \]

      10. lower--.f64 N/A

          \[\leadsto \color{blue}{1 - \frac{x}{y}} \]

      11. lower-/.f64 98.5

          \[\leadsto 1 - \color{blue}{\frac{x}{y}} \]

   5. Applied rewrites 98.5%

      \[\leadsto \color{blue}{1 - \frac{x}{y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y - x}{y - z} \leq -5000000:\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq 0.4:\\ \;\;\;\;\frac{x - y}{z}\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq 2000000000:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y - x}{y - z}\\ t_1 := \frac{x}{z - y}\\ \mathbf{if}\;t\_0 \leq 0.4:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 2000000000:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (- y x) (- y z))) (t_1 (/ x (- z y))))
   (if (<= t_0 0.4) t_1 (if (<= t_0 2000000000.0) (- 1.0 (/ x y)) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = (y - x) / (y - z);
	double t_1 = x / (z - y);
	double tmp;
	if (t_0 <= 0.4) {
		tmp = t_1;
	} else if (t_0 <= 2000000000.0) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = t_1;
	}
	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 = (y - x) / (y - z)
    t_1 = x / (z - y)
    if (t_0 <= 0.4d0) then
        tmp = t_1
    else if (t_0 <= 2000000000.0d0) then
        tmp = 1.0d0 - (x / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (y - x) / (y - z);
	double t_1 = x / (z - y);
	double tmp;
	if (t_0 <= 0.4) {
		tmp = t_1;
	} else if (t_0 <= 2000000000.0) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y - x) / (y - z)
	t_1 = x / (z - y)
	tmp = 0
	if t_0 <= 0.4:
		tmp = t_1
	elif t_0 <= 2000000000.0:
		tmp = 1.0 - (x / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y - x) / Float64(y - z))
	t_1 = Float64(x / Float64(z - y))
	tmp = 0.0
	if (t_0 <= 0.4)
		tmp = t_1;
	elseif (t_0 <= 2000000000.0)
		tmp = Float64(1.0 - Float64(x / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y - x) / (y - z);
	t_1 = x / (z - y);
	tmp = 0.0;
	if (t_0 <= 0.4)
		tmp = t_1;
	elseif (t_0 <= 2000000000.0)
		tmp = 1.0 - (x / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y - x), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 0.4], t$95$1, If[LessEqual[t$95$0, 2000000000.0], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 0.40000000000000002 or 2e9 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 80.3

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

   5. Applied rewrites 80.3%

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

   if 0.40000000000000002 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2e9

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{-1 \cdot \frac{x - y}{y}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(\frac{x - y}{y}\right)} \]

      2. div-sub N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\frac{x}{y} - \frac{y}{y}\right)}\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\frac{x}{y} + \left(\mathsf{neg}\left(\frac{y}{y}\right)\right)\right)}\right) \]

      4. *-inverses N/A

         \[\leadsto \mathsf{neg}\left(\left(\frac{x}{y} + \left(\mathsf{neg}\left(\color{blue}{1}\right)\right)\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{neg}\left(\left(\frac{x}{y} + \color{blue}{-1}\right)\right) \]

      6. +-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(-1 + \frac{x}{y}\right)}\right) \]

      7. distribute-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(-1\right)\right) + \left(\mathsf{neg}\left(\frac{x}{y}\right)\right)} \]

      8. metadata-eval N/A

         \[\leadsto \color{blue}{1} + \left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \]

      9. unsub-neg N/A

         \[\leadsto \color{blue}{1 - \frac{x}{y}} \]

      10. lower--.f64 N/A

          \[\leadsto \color{blue}{1 - \frac{x}{y}} \]

      11. lower-/.f64 98.5

          \[\leadsto 1 - \color{blue}{\frac{x}{y}} \]

   5. Applied rewrites 98.5%

      \[\leadsto \color{blue}{1 - \frac{x}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y - x}{y - z} \leq 0.4:\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq 2000000000:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y - x}{y - z}\\ \mathbf{if}\;t\_0 \leq 0.4:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;t\_0 \leq 2000000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (- y x) (- y z))))
   (if (<= t_0 0.4) (/ x z) (if (<= t_0 2000000000.0) 1.0 (/ x z)))))

C

double code(double x, double y, double z) {
	double t_0 = (y - x) / (y - z);
	double tmp;
	if (t_0 <= 0.4) {
		tmp = x / z;
	} else if (t_0 <= 2000000000.0) {
		tmp = 1.0;
	} else {
		tmp = x / 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 = (y - x) / (y - z)
    if (t_0 <= 0.4d0) then
        tmp = x / z
    else if (t_0 <= 2000000000.0d0) then
        tmp = 1.0d0
    else
        tmp = x / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (y - x) / (y - z);
	double tmp;
	if (t_0 <= 0.4) {
		tmp = x / z;
	} else if (t_0 <= 2000000000.0) {
		tmp = 1.0;
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y - x) / (y - z)
	tmp = 0
	if t_0 <= 0.4:
		tmp = x / z
	elif t_0 <= 2000000000.0:
		tmp = 1.0
	else:
		tmp = x / z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y - x) / Float64(y - z))
	tmp = 0.0
	if (t_0 <= 0.4)
		tmp = Float64(x / z);
	elseif (t_0 <= 2000000000.0)
		tmp = 1.0;
	else
		tmp = Float64(x / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y - x) / (y - z);
	tmp = 0.0;
	if (t_0 <= 0.4)
		tmp = x / z;
	elseif (t_0 <= 2000000000.0)
		tmp = 1.0;
	else
		tmp = x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y - x), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 0.4], N[(x / z), $MachinePrecision], If[LessEqual[t$95$0, 2000000000.0], 1.0, N[(x / z), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 0.40000000000000002 or 2e9 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 57.8

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

   5. Applied rewrites 57.8%

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

   if 0.40000000000000002 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2e9

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Applied rewrites 97.4%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y - x}{y - z} \leq 0.4:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq 2000000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 71.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -1.15 \cdot 10^{-32}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-39}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ x y))))
   (if (<= y -1.15e-32) t_0 (if (<= y 1.8e-39) (/ x z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (x / y);
	double tmp;
	if (y <= -1.15e-32) {
		tmp = t_0;
	} else if (y <= 1.8e-39) {
		tmp = 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 = 1.0d0 - (x / y)
    if (y <= (-1.15d-32)) then
        tmp = t_0
    else if (y <= 1.8d-39) then
        tmp = 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 = 1.0 - (x / y);
	double tmp;
	if (y <= -1.15e-32) {
		tmp = t_0;
	} else if (y <= 1.8e-39) {
		tmp = x / z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (x / y)
	tmp = 0
	if y <= -1.15e-32:
		tmp = t_0
	elif y <= 1.8e-39:
		tmp = x / z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(x / y))
	tmp = 0.0
	if (y <= -1.15e-32)
		tmp = t_0;
	elseif (y <= 1.8e-39)
		tmp = Float64(x / z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (x / y);
	tmp = 0.0;
	if (y <= -1.15e-32)
		tmp = t_0;
	elseif (y <= 1.8e-39)
		tmp = x / z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.15e-32], t$95$0, If[LessEqual[y, 1.8e-39], N[(x / z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.15e-32 or 1.8e-39 < y

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{-1 \cdot \frac{x - y}{y}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(\frac{x - y}{y}\right)} \]

      2. div-sub N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\frac{x}{y} - \frac{y}{y}\right)}\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\frac{x}{y} + \left(\mathsf{neg}\left(\frac{y}{y}\right)\right)\right)}\right) \]

      4. *-inverses N/A

         \[\leadsto \mathsf{neg}\left(\left(\frac{x}{y} + \left(\mathsf{neg}\left(\color{blue}{1}\right)\right)\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{neg}\left(\left(\frac{x}{y} + \color{blue}{-1}\right)\right) \]

      6. +-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(-1 + \frac{x}{y}\right)}\right) \]

      7. distribute-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(-1\right)\right) + \left(\mathsf{neg}\left(\frac{x}{y}\right)\right)} \]

      8. metadata-eval N/A

         \[\leadsto \color{blue}{1} + \left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \]

      9. unsub-neg N/A

         \[\leadsto \color{blue}{1 - \frac{x}{y}} \]

      10. lower--.f64 N/A

          \[\leadsto \color{blue}{1 - \frac{x}{y}} \]

      11. lower-/.f64 78.4

          \[\leadsto 1 - \color{blue}{\frac{x}{y}} \]

   5. Applied rewrites 78.4%

      \[\leadsto \color{blue}{1 - \frac{x}{y}} \]

   if -1.15e-32 < y < 1.8e-39

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 74.5

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

   5. Applied rewrites 74.5%

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

Alternative 8: 34.2% accurate, 18.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 1.0)

C

double code(double x, double y, double z) {
	return 1.0;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0
end function

Java

public static double code(double x, double y, double z) {
	return 1.0;
}

Python

def code(x, y, z):
	return 1.0

Julia

function code(x, y, z)
	return 1.0
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0;
end

Wolfram

code[x_, y_, z_] := 1.0

Derivation

1. Initial program 100.0%

   \[\frac{x - y}{z - y} \]
2. Add Preprocessing

3. Taylor expanded in y around inf

   \[\leadsto \color{blue}{1} \]
4. Step-by-step derivation

5. Applied rewrites 35.4%

   \[\leadsto \color{blue}{1} \]
6. Add Preprocessing

Developer Target 1: 100.0% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024298 
(FPCore (x y z)
  :name "Graphics.Rasterific.Shading:$sgradientColorAt from Rasterific-0.6.1"
  :precision binary64

  :alt
  (! :herbie-platform default (- (/ x (- z y)) (/ y (- z y))))

  (/ (- x y) (- z y)))