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

Percentage Accurate: 100.0% → 100.0%

Time: 7.6s

Alternatives: 10

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

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y - x}{y - z}\\ t_1 := \frac{x}{-y}\\ \mathbf{if}\;t\_0 \leq -4 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq -2 \cdot 10^{-222}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;t\_0 \leq 4 \cdot 10^{-8}:\\ \;\;\;\;\frac{-y}{z}\\ \mathbf{elif}\;t\_0 \leq 50:\\ \;\;\;\;1\\ \mathbf{elif}\;t\_0 \leq 10^{+170}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (- y x) (- y z))) (t_1 (/ x (- y))))
   (if (<= t_0 -4e+45)
     t_1
     (if (<= t_0 -2e-222)
       (/ x z)
       (if (<= t_0 4e-8)
         (/ (- y) z)
         (if (<= t_0 50.0) 1.0 (if (<= t_0 1e+170) t_1 (/ x z))))))))

C

double code(double x, double y, double z) {
	double t_0 = (y - x) / (y - z);
	double t_1 = x / -y;
	double tmp;
	if (t_0 <= -4e+45) {
		tmp = t_1;
	} else if (t_0 <= -2e-222) {
		tmp = x / z;
	} else if (t_0 <= 4e-8) {
		tmp = -y / z;
	} else if (t_0 <= 50.0) {
		tmp = 1.0;
	} else if (t_0 <= 1e+170) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = (y - x) / (y - z)
    t_1 = x / -y
    if (t_0 <= (-4d+45)) then
        tmp = t_1
    else if (t_0 <= (-2d-222)) then
        tmp = x / z
    else if (t_0 <= 4d-8) then
        tmp = -y / z
    else if (t_0 <= 50.0d0) then
        tmp = 1.0d0
    else if (t_0 <= 1d+170) then
        tmp = t_1
    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 t_1 = x / -y;
	double tmp;
	if (t_0 <= -4e+45) {
		tmp = t_1;
	} else if (t_0 <= -2e-222) {
		tmp = x / z;
	} else if (t_0 <= 4e-8) {
		tmp = -y / z;
	} else if (t_0 <= 50.0) {
		tmp = 1.0;
	} else if (t_0 <= 1e+170) {
		tmp = t_1;
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y - x) / (y - z)
	t_1 = x / -y
	tmp = 0
	if t_0 <= -4e+45:
		tmp = t_1
	elif t_0 <= -2e-222:
		tmp = x / z
	elif t_0 <= 4e-8:
		tmp = -y / z
	elif t_0 <= 50.0:
		tmp = 1.0
	elif t_0 <= 1e+170:
		tmp = t_1
	else:
		tmp = x / z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y - x) / Float64(y - z))
	t_1 = Float64(x / Float64(-y))
	tmp = 0.0
	if (t_0 <= -4e+45)
		tmp = t_1;
	elseif (t_0 <= -2e-222)
		tmp = Float64(x / z);
	elseif (t_0 <= 4e-8)
		tmp = Float64(Float64(-y) / z);
	elseif (t_0 <= 50.0)
		tmp = 1.0;
	elseif (t_0 <= 1e+170)
		tmp = t_1;
	else
		tmp = Float64(x / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y - x) / (y - z);
	t_1 = x / -y;
	tmp = 0.0;
	if (t_0 <= -4e+45)
		tmp = t_1;
	elseif (t_0 <= -2e-222)
		tmp = x / z;
	elseif (t_0 <= 4e-8)
		tmp = -y / z;
	elseif (t_0 <= 50.0)
		tmp = 1.0;
	elseif (t_0 <= 1e+170)
		tmp = t_1;
	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]}, Block[{t$95$1 = N[(x / (-y)), $MachinePrecision]}, If[LessEqual[t$95$0, -4e+45], t$95$1, If[LessEqual[t$95$0, -2e-222], N[(x / z), $MachinePrecision], If[LessEqual[t$95$0, 4e-8], N[((-y) / z), $MachinePrecision], If[LessEqual[t$95$0, 50.0], 1.0, If[LessEqual[t$95$0, 1e+170], t$95$1, N[(x / z), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -3.9999999999999997e45 or 50 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1.00000000000000003e170

   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 98.4

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

   5. Applied rewrites 98.4%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 63.1%

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

   if -3.9999999999999997e45 < (/.f64 (-.f64 x y) (-.f64 z y)) < -2.0000000000000001e-222 or 1.00000000000000003e170 < (/.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 74.0

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

   5. Applied rewrites 74.0%

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

   if -2.0000000000000001e-222 < (/.f64 (-.f64 x y) (-.f64 z y)) < 4.0000000000000001e-8

   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 99.2

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

   5. Applied rewrites 99.2%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 68.8%

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

   if 4.0000000000000001e-8 < (/.f64 (-.f64 x y) (-.f64 z y)) < 50

   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 93.9%

      \[\leadsto \color{blue}{1} \]
3. Recombined 4 regimes into one program.

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y - x}{y - z} \leq -4 \cdot 10^{+45}:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq -2 \cdot 10^{-222}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq 4 \cdot 10^{-8}:\\ \;\;\;\;\frac{-y}{z}\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq 50:\\ \;\;\;\;1\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq 10^{+170}:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 69.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y - x}{y - z}\\ \mathbf{if}\;t\_0 \leq -4 \cdot 10^{+45}:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{elif}\;t\_0 \leq -2 \cdot 10^{-222}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;t\_0 \leq 4 \cdot 10^{-8}:\\ \;\;\;\;\frac{-y}{z}\\ \mathbf{elif}\;t\_0 \leq 10^{+170}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (- y x) (- y z))))
   (if (<= t_0 -4e+45)
     (/ x (- y))
     (if (<= t_0 -2e-222)
       (/ x z)
       (if (<= t_0 4e-8)
         (/ (- y) z)
         (if (<= t_0 1e+170) (- 1.0 (/ x y)) (/ x z)))))))

C

double code(double x, double y, double z) {
	double t_0 = (y - x) / (y - z);
	double tmp;
	if (t_0 <= -4e+45) {
		tmp = x / -y;
	} else if (t_0 <= -2e-222) {
		tmp = x / z;
	} else if (t_0 <= 4e-8) {
		tmp = -y / z;
	} else if (t_0 <= 1e+170) {
		tmp = 1.0 - (x / y);
	} 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 <= (-4d+45)) then
        tmp = x / -y
    else if (t_0 <= (-2d-222)) then
        tmp = x / z
    else if (t_0 <= 4d-8) then
        tmp = -y / z
    else if (t_0 <= 1d+170) then
        tmp = 1.0d0 - (x / y)
    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 <= -4e+45) {
		tmp = x / -y;
	} else if (t_0 <= -2e-222) {
		tmp = x / z;
	} else if (t_0 <= 4e-8) {
		tmp = -y / z;
	} else if (t_0 <= 1e+170) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y - x) / (y - z)
	tmp = 0
	if t_0 <= -4e+45:
		tmp = x / -y
	elif t_0 <= -2e-222:
		tmp = x / z
	elif t_0 <= 4e-8:
		tmp = -y / z
	elif t_0 <= 1e+170:
		tmp = 1.0 - (x / y)
	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 <= -4e+45)
		tmp = Float64(x / Float64(-y));
	elseif (t_0 <= -2e-222)
		tmp = Float64(x / z);
	elseif (t_0 <= 4e-8)
		tmp = Float64(Float64(-y) / z);
	elseif (t_0 <= 1e+170)
		tmp = Float64(1.0 - Float64(x / y));
	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 <= -4e+45)
		tmp = x / -y;
	elseif (t_0 <= -2e-222)
		tmp = x / z;
	elseif (t_0 <= 4e-8)
		tmp = -y / z;
	elseif (t_0 <= 1e+170)
		tmp = 1.0 - (x / y);
	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, -4e+45], N[(x / (-y)), $MachinePrecision], If[LessEqual[t$95$0, -2e-222], N[(x / z), $MachinePrecision], If[LessEqual[t$95$0, 4e-8], N[((-y) / z), $MachinePrecision], If[LessEqual[t$95$0, 1e+170], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x / z), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -3.9999999999999997e45

   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 100.0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 65.1%

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

   if -3.9999999999999997e45 < (/.f64 (-.f64 x y) (-.f64 z y)) < -2.0000000000000001e-222 or 1.00000000000000003e170 < (/.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 74.0

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

   5. Applied rewrites 74.0%

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

   if -2.0000000000000001e-222 < (/.f64 (-.f64 x y) (-.f64 z y)) < 4.0000000000000001e-8

   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 99.2

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

   5. Applied rewrites 99.2%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 68.8%

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

   if 4.0000000000000001e-8 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1.00000000000000003e170

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\left(1 + -1 \cdot \frac{x}{y}\right) - -1 \cdot \frac{z}{y}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. associate--r+ N/A

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

      4. mul-1-neg N/A

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

      5. sub-neg N/A

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

      6. div-sub N/A

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

      7. lower--.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower--.f64 89.3

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

   5. Applied rewrites 89.3%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 88.9%

      \[\leadsto 1 - \frac{x}{\color{blue}{y}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y - x}{y - z} \leq -4 \cdot 10^{+45}:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq -2 \cdot 10^{-222}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq 4 \cdot 10^{-8}:\\ \;\;\;\;\frac{-y}{z}\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq 10^{+170}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 67.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y - x}{y - z}\\ t_1 := \frac{x}{-y}\\ \mathbf{if}\;t\_0 \leq -4 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{-13}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;t\_0 \leq 50:\\ \;\;\;\;1\\ \mathbf{elif}\;t\_0 \leq 10^{+170}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (- y x) (- y z))) (t_1 (/ x (- y))))
   (if (<= t_0 -4e+45)
     t_1
     (if (<= t_0 2e-13)
       (/ x z)
       (if (<= t_0 50.0) 1.0 (if (<= t_0 1e+170) t_1 (/ x z)))))))

C

double code(double x, double y, double z) {
	double t_0 = (y - x) / (y - z);
	double t_1 = x / -y;
	double tmp;
	if (t_0 <= -4e+45) {
		tmp = t_1;
	} else if (t_0 <= 2e-13) {
		tmp = x / z;
	} else if (t_0 <= 50.0) {
		tmp = 1.0;
	} else if (t_0 <= 1e+170) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = (y - x) / (y - z)
    t_1 = x / -y
    if (t_0 <= (-4d+45)) then
        tmp = t_1
    else if (t_0 <= 2d-13) then
        tmp = x / z
    else if (t_0 <= 50.0d0) then
        tmp = 1.0d0
    else if (t_0 <= 1d+170) then
        tmp = t_1
    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 t_1 = x / -y;
	double tmp;
	if (t_0 <= -4e+45) {
		tmp = t_1;
	} else if (t_0 <= 2e-13) {
		tmp = x / z;
	} else if (t_0 <= 50.0) {
		tmp = 1.0;
	} else if (t_0 <= 1e+170) {
		tmp = t_1;
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y - x) / (y - z)
	t_1 = x / -y
	tmp = 0
	if t_0 <= -4e+45:
		tmp = t_1
	elif t_0 <= 2e-13:
		tmp = x / z
	elif t_0 <= 50.0:
		tmp = 1.0
	elif t_0 <= 1e+170:
		tmp = t_1
	else:
		tmp = x / z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y - x) / Float64(y - z))
	t_1 = Float64(x / Float64(-y))
	tmp = 0.0
	if (t_0 <= -4e+45)
		tmp = t_1;
	elseif (t_0 <= 2e-13)
		tmp = Float64(x / z);
	elseif (t_0 <= 50.0)
		tmp = 1.0;
	elseif (t_0 <= 1e+170)
		tmp = t_1;
	else
		tmp = Float64(x / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y - x) / (y - z);
	t_1 = x / -y;
	tmp = 0.0;
	if (t_0 <= -4e+45)
		tmp = t_1;
	elseif (t_0 <= 2e-13)
		tmp = x / z;
	elseif (t_0 <= 50.0)
		tmp = 1.0;
	elseif (t_0 <= 1e+170)
		tmp = t_1;
	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]}, Block[{t$95$1 = N[(x / (-y)), $MachinePrecision]}, If[LessEqual[t$95$0, -4e+45], t$95$1, If[LessEqual[t$95$0, 2e-13], N[(x / z), $MachinePrecision], If[LessEqual[t$95$0, 50.0], 1.0, If[LessEqual[t$95$0, 1e+170], t$95$1, N[(x / z), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -3.9999999999999997e45 or 50 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1.00000000000000003e170

   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 98.4

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

   5. Applied rewrites 98.4%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 63.1%

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

   if -3.9999999999999997e45 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2.0000000000000001e-13 or 1.00000000000000003e170 < (/.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 63.2

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

   5. Applied rewrites 63.2%

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

   if 2.0000000000000001e-13 < (/.f64 (-.f64 x y) (-.f64 z y)) < 50

   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 93.0%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y - x}{y - z} \leq -4 \cdot 10^{+45}:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq 2 \cdot 10^{-13}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq 50:\\ \;\;\;\;1\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq 10^{+170}:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y - x}{y - z}\\ t_1 := \frac{x}{z - y}\\ \mathbf{if}\;t\_0 \leq -10000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 0.6:\\ \;\;\;\;\frac{x - y}{z}\\ \mathbf{elif}\;t\_0 \leq 20000000:\\ \;\;\;\;1 - \frac{x - z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (- y x) (- y z))) (t_1 (/ x (- z y))))
   (if (<= t_0 -10000000.0)
     t_1
     (if (<= t_0 0.6)
       (/ (- x y) z)
       (if (<= t_0 20000000.0) (- 1.0 (/ (- x 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 <= -10000000.0) {
		tmp = t_1;
	} else if (t_0 <= 0.6) {
		tmp = (x - y) / z;
	} else if (t_0 <= 20000000.0) {
		tmp = 1.0 - ((x - 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 <= (-10000000.0d0)) then
        tmp = t_1
    else if (t_0 <= 0.6d0) then
        tmp = (x - y) / z
    else if (t_0 <= 20000000.0d0) then
        tmp = 1.0d0 - ((x - 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 <= -10000000.0) {
		tmp = t_1;
	} else if (t_0 <= 0.6) {
		tmp = (x - y) / z;
	} else if (t_0 <= 20000000.0) {
		tmp = 1.0 - ((x - 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 <= -10000000.0:
		tmp = t_1
	elif t_0 <= 0.6:
		tmp = (x - y) / z
	elif t_0 <= 20000000.0:
		tmp = 1.0 - ((x - 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 <= -10000000.0)
		tmp = t_1;
	elseif (t_0 <= 0.6)
		tmp = Float64(Float64(x - y) / z);
	elseif (t_0 <= 20000000.0)
		tmp = Float64(1.0 - Float64(Float64(x - 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 <= -10000000.0)
		tmp = t_1;
	elseif (t_0 <= 0.6)
		tmp = (x - y) / z;
	elseif (t_0 <= 20000000.0)
		tmp = 1.0 - ((x - 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, -10000000.0], t$95$1, If[LessEqual[t$95$0, 0.6], N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$0, 20000000.0], N[(1.0 - N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -1e7 or 2e7 < (/.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 99.4

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

   5. Applied rewrites 99.4%

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

   if -1e7 < (/.f64 (-.f64 x y) (-.f64 z y)) < 0.599999999999999978

   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 97.5

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

   5. Applied rewrites 97.5%

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

   if 0.599999999999999978 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2e7

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\left(1 + -1 \cdot \frac{x}{y}\right) - -1 \cdot \frac{z}{y}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. associate--r+ N/A

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

      4. mul-1-neg N/A

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

      5. sub-neg N/A

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

      6. div-sub N/A

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

      7. lower--.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower--.f64 98.3

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

   5. Applied rewrites 98.3%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y - x}{y - z} \leq -10000000:\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq 0.6:\\ \;\;\;\;\frac{x - y}{z}\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq 20000000:\\ \;\;\;\;1 - \frac{x - z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 97.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y - x}{y - z}\\ t_1 := \frac{x}{z - y}\\ \mathbf{if}\;t\_0 \leq -10000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 4 \cdot 10^{-8}:\\ \;\;\;\;\frac{x - y}{z}\\ \mathbf{elif}\;t\_0 \leq 20000000:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (- y x) (- y z))) (t_1 (/ x (- z y))))
   (if (<= t_0 -10000000.0)
     t_1
     (if (<= t_0 4e-8)
       (/ (- x y) z)
       (if (<= t_0 20000000.0) (- 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 <= -10000000.0) {
		tmp = t_1;
	} else if (t_0 <= 4e-8) {
		tmp = (x - y) / z;
	} else if (t_0 <= 20000000.0) {
		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 <= (-10000000.0d0)) then
        tmp = t_1
    else if (t_0 <= 4d-8) then
        tmp = (x - y) / z
    else if (t_0 <= 20000000.0d0) 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 <= -10000000.0) {
		tmp = t_1;
	} else if (t_0 <= 4e-8) {
		tmp = (x - y) / z;
	} else if (t_0 <= 20000000.0) {
		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 <= -10000000.0:
		tmp = t_1
	elif t_0 <= 4e-8:
		tmp = (x - y) / z
	elif t_0 <= 20000000.0:
		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 <= -10000000.0)
		tmp = t_1;
	elseif (t_0 <= 4e-8)
		tmp = Float64(Float64(x - y) / z);
	elseif (t_0 <= 20000000.0)
		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 <= -10000000.0)
		tmp = t_1;
	elseif (t_0 <= 4e-8)
		tmp = (x - y) / z;
	elseif (t_0 <= 20000000.0)
		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, -10000000.0], t$95$1, If[LessEqual[t$95$0, 4e-8], N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$0, 20000000.0], 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)) < -1e7 or 2e7 < (/.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 99.4

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

   5. Applied rewrites 99.4%

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

   if -1e7 < (/.f64 (-.f64 x y) (-.f64 z y)) < 4.0000000000000001e-8

   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 98.4

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

   5. Applied rewrites 98.4%

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

   if 4.0000000000000001e-8 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2e7

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\left(1 + -1 \cdot \frac{x}{y}\right) - -1 \cdot \frac{z}{y}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. associate--r+ N/A

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

      4. mul-1-neg N/A

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

      5. sub-neg N/A

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

      6. div-sub N/A

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

      7. lower--.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower--.f64 97.3

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

   5. Applied rewrites 97.3%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 96.8%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y - x}{y - z} \leq -10000000:\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq 4 \cdot 10^{-8}:\\ \;\;\;\;\frac{x - y}{z}\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq 20000000:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y - x}{y - z}\\ t_1 := \frac{x}{z - y}\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{-222}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 4 \cdot 10^{-8}:\\ \;\;\;\;\frac{-y}{z}\\ \mathbf{elif}\;t\_0 \leq 20000000:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (- y x) (- y z))) (t_1 (/ x (- z y))))
   (if (<= t_0 -2e-222)
     t_1
     (if (<= t_0 4e-8)
       (/ (- y) z)
       (if (<= t_0 20000000.0) (- 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 <= -2e-222) {
		tmp = t_1;
	} else if (t_0 <= 4e-8) {
		tmp = -y / z;
	} else if (t_0 <= 20000000.0) {
		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 <= (-2d-222)) then
        tmp = t_1
    else if (t_0 <= 4d-8) then
        tmp = -y / z
    else if (t_0 <= 20000000.0d0) 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 <= -2e-222) {
		tmp = t_1;
	} else if (t_0 <= 4e-8) {
		tmp = -y / z;
	} else if (t_0 <= 20000000.0) {
		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 <= -2e-222:
		tmp = t_1
	elif t_0 <= 4e-8:
		tmp = -y / z
	elif t_0 <= 20000000.0:
		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 <= -2e-222)
		tmp = t_1;
	elseif (t_0 <= 4e-8)
		tmp = Float64(Float64(-y) / z);
	elseif (t_0 <= 20000000.0)
		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 <= -2e-222)
		tmp = t_1;
	elseif (t_0 <= 4e-8)
		tmp = -y / z;
	elseif (t_0 <= 20000000.0)
		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, -2e-222], t$95$1, If[LessEqual[t$95$0, 4e-8], N[((-y) / z), $MachinePrecision], If[LessEqual[t$95$0, 20000000.0], 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)) < -2.0000000000000001e-222 or 2e7 < (/.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 90.6

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

   5. Applied rewrites 90.6%

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

   if -2.0000000000000001e-222 < (/.f64 (-.f64 x y) (-.f64 z y)) < 4.0000000000000001e-8

   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 99.2

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

   5. Applied rewrites 99.2%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 68.8%

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

   if 4.0000000000000001e-8 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2e7

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\left(1 + -1 \cdot \frac{x}{y}\right) - -1 \cdot \frac{z}{y}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. associate--r+ N/A

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

      4. mul-1-neg N/A

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

      5. sub-neg N/A

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

      6. div-sub N/A

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

      7. lower--.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower--.f64 97.3

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

   5. Applied rewrites 97.3%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 96.8%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y - x}{y - z} \leq -2 \cdot 10^{-222}:\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq 4 \cdot 10^{-8}:\\ \;\;\;\;\frac{-y}{z}\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq 20000000:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y - x}{y - z}\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{-222} \lor \neg \left(t\_0 \leq 2\right):\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (- y x) (- y z))))
   (if (or (<= t_0 -2e-222) (not (<= t_0 2.0))) (/ x (- z y)) (/ y (- y z)))))

C

double code(double x, double y, double z) {
	double t_0 = (y - x) / (y - z);
	double tmp;
	if ((t_0 <= -2e-222) || !(t_0 <= 2.0)) {
		tmp = x / (z - y);
	} else {
		tmp = y / (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 = (y - x) / (y - z)
    if ((t_0 <= (-2d-222)) .or. (.not. (t_0 <= 2.0d0))) then
        tmp = x / (z - y)
    else
        tmp = y / (y - 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 <= -2e-222) || !(t_0 <= 2.0)) {
		tmp = x / (z - y);
	} else {
		tmp = y / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y - x) / (y - z)
	tmp = 0
	if (t_0 <= -2e-222) or not (t_0 <= 2.0):
		tmp = x / (z - y)
	else:
		tmp = y / (y - z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y - x) / Float64(y - z))
	tmp = 0.0
	if ((t_0 <= -2e-222) || !(t_0 <= 2.0))
		tmp = Float64(x / Float64(z - y));
	else
		tmp = Float64(y / Float64(y - 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 <= -2e-222) || ~((t_0 <= 2.0)))
		tmp = x / (z - y);
	else
		tmp = y / (y - 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[Or[LessEqual[t$95$0, -2e-222], N[Not[LessEqual[t$95$0, 2.0]], $MachinePrecision]], N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision], N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -2.0000000000000001e-222 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 90.0

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

   5. Applied rewrites 90.0%

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

   if -2.0000000000000001e-222 < (/.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

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. lower-/.f64 N/A

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

      4. sub-neg N/A

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

      5. +-commutative N/A

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

      6. distribute-neg-in N/A

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

      7. remove-double-neg N/A

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

      8. *-rgt-identity N/A

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

      9. distribute-lft-neg-in N/A

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

      10. *-inverses N/A

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

      11. associate-/l* N/A

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

      12. distribute-lft-neg-out N/A

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

      13. distribute-rgt-neg-out N/A

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

      14. associate-*l/ N/A

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

      15. distribute-rgt-neg-in N/A

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

      16. unsub-neg N/A

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

      17. remove-double-neg N/A

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

      18. mul-1-neg N/A

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

      19. distribute-lft-neg-in N/A

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

      20. associate-*r/ N/A

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

      21. mul-1-neg N/A

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

      22. associate-*l/ N/A

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

      23. associate-/l* N/A

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

      24. *-inverses N/A

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

      25. distribute-lft-neg-out N/A

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

      26. remove-double-neg N/A

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

      27. *-rgt-identity N/A

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

   5. Applied rewrites 86.3%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y - x}{y - z} \leq -2 \cdot 10^{-222} \lor \neg \left(\frac{y - x}{y - z} \leq 2\right):\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 68.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y - x}{y - z}\\ \mathbf{if}\;t\_0 \leq 2 \cdot 10^{-13} \lor \neg \left(t\_0 \leq 2\right):\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (- y x) (- y z))))
   (if (or (<= t_0 2e-13) (not (<= t_0 2.0))) (/ x z) 1.0)))

C

double code(double x, double y, double z) {
	double t_0 = (y - x) / (y - z);
	double tmp;
	if ((t_0 <= 2e-13) || !(t_0 <= 2.0)) {
		tmp = x / z;
	} else {
		tmp = 1.0;
	}
	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 - x) / (y - z)
    if ((t_0 <= 2d-13) .or. (.not. (t_0 <= 2.0d0))) then
        tmp = x / z
    else
        tmp = 1.0d0
    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 <= 2e-13) || !(t_0 <= 2.0)) {
		tmp = x / z;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y - x) / (y - z)
	tmp = 0
	if (t_0 <= 2e-13) or not (t_0 <= 2.0):
		tmp = x / z
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y - x) / Float64(y - z))
	tmp = 0.0
	if ((t_0 <= 2e-13) || !(t_0 <= 2.0))
		tmp = Float64(x / z);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y - x) / (y - z);
	tmp = 0.0;
	if ((t_0 <= 2e-13) || ~((t_0 <= 2.0)))
		tmp = x / z;
	else
		tmp = 1.0;
	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[Or[LessEqual[t$95$0, 2e-13], N[Not[LessEqual[t$95$0, 2.0]], $MachinePrecision]], N[(x / z), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 2.0000000000000001e-13 or 2 < (/.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 55.3

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

   5. Applied rewrites 55.3%

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

   if 2.0000000000000001e-13 < (/.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 y around inf

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

   5. Applied rewrites 93.9%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y - x}{y - z} \leq 2 \cdot 10^{-13} \lor \neg \left(\frac{y - x}{y - z} \leq 2\right):\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 34.7% 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 33.6%

   \[\leadsto \color{blue}{1} \]
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 2024271 
(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)))