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

Percentage Accurate: 100.0% → 100.0%

Time: 11.4s

Alternatives: 7

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

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

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]

Derivation

1. Initial program 100.0%

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

Alternative 2: 74.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x - y}{z}\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{-8}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-100}:\\ \;\;\;\;\frac{y}{y - z}\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-126}:\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+29}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (- x y) z)))
   (if (<= z -9.5e-8)
     t_0
     (if (<= z -4.1e-100)
       (/ y (- y z))
       (if (<= z -7.6e-126)
         (/ x (- z y))
         (if (<= z 2.1e+29) (- 1.0 (/ x y)) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = (x - y) / z;
	double tmp;
	if (z <= -9.5e-8) {
		tmp = t_0;
	} else if (z <= -4.1e-100) {
		tmp = y / (y - z);
	} else if (z <= -7.6e-126) {
		tmp = x / (z - y);
	} else if (z <= 2.1e+29) {
		tmp = 1.0 - (x / y);
	} 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 = (x - y) / z
    if (z <= (-9.5d-8)) then
        tmp = t_0
    else if (z <= (-4.1d-100)) then
        tmp = y / (y - z)
    else if (z <= (-7.6d-126)) then
        tmp = x / (z - y)
    else if (z <= 2.1d+29) then
        tmp = 1.0d0 - (x / y)
    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) / z;
	double tmp;
	if (z <= -9.5e-8) {
		tmp = t_0;
	} else if (z <= -4.1e-100) {
		tmp = y / (y - z);
	} else if (z <= -7.6e-126) {
		tmp = x / (z - y);
	} else if (z <= 2.1e+29) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x - y) / z
	tmp = 0
	if z <= -9.5e-8:
		tmp = t_0
	elif z <= -4.1e-100:
		tmp = y / (y - z)
	elif z <= -7.6e-126:
		tmp = x / (z - y)
	elif z <= 2.1e+29:
		tmp = 1.0 - (x / y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x - y) / z)
	tmp = 0.0
	if (z <= -9.5e-8)
		tmp = t_0;
	elseif (z <= -4.1e-100)
		tmp = Float64(y / Float64(y - z));
	elseif (z <= -7.6e-126)
		tmp = Float64(x / Float64(z - y));
	elseif (z <= 2.1e+29)
		tmp = Float64(1.0 - Float64(x / y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x - y) / z;
	tmp = 0.0;
	if (z <= -9.5e-8)
		tmp = t_0;
	elseif (z <= -4.1e-100)
		tmp = y / (y - z);
	elseif (z <= -7.6e-126)
		tmp = x / (z - y);
	elseif (z <= 2.1e+29)
		tmp = 1.0 - (x / y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -9.5e-8], t$95$0, If[LessEqual[z, -4.1e-100], N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.6e-126], N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e+29], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.50000000000000036e-8 or 2.1000000000000002e29 < z

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -9.50000000000000036e-8 < z < -4.0999999999999999e-100

   1. Initial program 99.9%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -4.0999999999999999e-100 < z < -7.5999999999999997e-126

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -7.5999999999999997e-126 < z < 2.1000000000000002e29

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 3: 77.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{z - y}\\ \mathbf{if}\;x \leq -2.4 \cdot 10^{+53}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 490000:\\ \;\;\;\;\frac{y}{y - z}\\ \mathbf{elif}\;x \leq 6.1 \cdot 10^{+71}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 9.4 \cdot 10^{+104}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ x (- z y))))
   (if (<= x -2.4e+53)
     t_0
     (if (<= x 490000.0)
       (/ y (- y z))
       (if (<= x 6.1e+71) t_0 (if (<= x 9.4e+104) (- 1.0 (/ x y)) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x / (z - y);
	double tmp;
	if (x <= -2.4e+53) {
		tmp = t_0;
	} else if (x <= 490000.0) {
		tmp = y / (y - z);
	} else if (x <= 6.1e+71) {
		tmp = t_0;
	} else if (x <= 9.4e+104) {
		tmp = 1.0 - (x / y);
	} 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 = x / (z - y)
    if (x <= (-2.4d+53)) then
        tmp = t_0
    else if (x <= 490000.0d0) then
        tmp = y / (y - z)
    else if (x <= 6.1d+71) then
        tmp = t_0
    else if (x <= 9.4d+104) then
        tmp = 1.0d0 - (x / y)
    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 / (z - y);
	double tmp;
	if (x <= -2.4e+53) {
		tmp = t_0;
	} else if (x <= 490000.0) {
		tmp = y / (y - z);
	} else if (x <= 6.1e+71) {
		tmp = t_0;
	} else if (x <= 9.4e+104) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x / (z - y)
	tmp = 0
	if x <= -2.4e+53:
		tmp = t_0
	elif x <= 490000.0:
		tmp = y / (y - z)
	elif x <= 6.1e+71:
		tmp = t_0
	elif x <= 9.4e+104:
		tmp = 1.0 - (x / y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x / Float64(z - y))
	tmp = 0.0
	if (x <= -2.4e+53)
		tmp = t_0;
	elseif (x <= 490000.0)
		tmp = Float64(y / Float64(y - z));
	elseif (x <= 6.1e+71)
		tmp = t_0;
	elseif (x <= 9.4e+104)
		tmp = Float64(1.0 - Float64(x / y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x / (z - y);
	tmp = 0.0;
	if (x <= -2.4e+53)
		tmp = t_0;
	elseif (x <= 490000.0)
		tmp = y / (y - z);
	elseif (x <= 6.1e+71)
		tmp = t_0;
	elseif (x <= 9.4e+104)
		tmp = 1.0 - (x / y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.4e+53], t$95$0, If[LessEqual[x, 490000.0], N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.1e+71], t$95$0, If[LessEqual[x, 9.4e+104], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.4e53 or 4.9e5 < x < 6.1000000000000003e71 or 9.40000000000000034e104 < x

   1. Initial program 99.9%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -2.4e53 < x < 4.9e5

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if 6.1000000000000003e71 < x < 9.40000000000000034e104

   1. Initial program 99.8%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 76.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -5 \cdot 10^{-82}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 0.000116:\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ x y))))
   (if (<= y -5e-82) t_0 (if (<= y 0.000116) (/ x (- z y)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (x / y);
	double tmp;
	if (y <= -5e-82) {
		tmp = t_0;
	} else if (y <= 0.000116) {
		tmp = x / (z - y);
	} 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 <= (-5d-82)) then
        tmp = t_0
    else if (y <= 0.000116d0) then
        tmp = x / (z - y)
    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 <= -5e-82) {
		tmp = t_0;
	} else if (y <= 0.000116) {
		tmp = x / (z - y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (x / y)
	tmp = 0
	if y <= -5e-82:
		tmp = t_0
	elif y <= 0.000116:
		tmp = x / (z - y)
	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 <= -5e-82)
		tmp = t_0;
	elseif (y <= 0.000116)
		tmp = Float64(x / Float64(z - y));
	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 <= -5e-82)
		tmp = t_0;
	elseif (y <= 0.000116)
		tmp = x / (z - y);
	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, -5e-82], t$95$0, If[LessEqual[y, 0.000116], N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.9999999999999998e-82 or 1.16e-4 < y

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -4.9999999999999998e-82 < y < 1.16e-4

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 70.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{-124}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-92}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ x y))))
   (if (<= y -1.2e-124) t_0 (if (<= y 2.6e-92) (/ x z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (x / y);
	double tmp;
	if (y <= -1.2e-124) {
		tmp = t_0;
	} else if (y <= 2.6e-92) {
		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 <= (-1.2d-124)) then
        tmp = t_0
    else if (y <= 2.6d-92) 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 <= -1.2e-124) {
		tmp = t_0;
	} else if (y <= 2.6e-92) {
		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 <= -1.2e-124:
		tmp = t_0
	elif y <= 2.6e-92:
		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 <= -1.2e-124)
		tmp = t_0;
	elseif (y <= 2.6e-92)
		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 <= -1.2e-124)
		tmp = t_0;
	elseif (y <= 2.6e-92)
		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, -1.2e-124], t$95$0, If[LessEqual[y, 2.6e-92], N[(x / z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.19999999999999996e-124 or 2.6e-92 < y

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -1.19999999999999996e-124 < y < 2.6e-92

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 61.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{-74}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-10}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.55e-74) 1.0 (if (<= y 6.8e-10) (/ x z) 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.55e-74) {
		tmp = 1.0;
	} else if (y <= 6.8e-10) {
		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) :: tmp
    if (y <= (-2.55d-74)) then
        tmp = 1.0d0
    else if (y <= 6.8d-10) 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 tmp;
	if (y <= -2.55e-74) {
		tmp = 1.0;
	} else if (y <= 6.8e-10) {
		tmp = x / z;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.55e-74:
		tmp = 1.0
	elif y <= 6.8e-10:
		tmp = x / z
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.55e-74)
		tmp = 1.0;
	elseif (y <= 6.8e-10)
		tmp = Float64(x / z);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.55e-74)
		tmp = 1.0;
	elseif (y <= 6.8e-10)
		tmp = x / z;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.55e-74], 1.0, If[LessEqual[y, 6.8e-10], N[(x / z), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -2.5499999999999998e-74 or 6.8000000000000003e-10 < y

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -2.5499999999999998e-74 < y < 6.8000000000000003e-10

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 35.2% accurate, 7.0× 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%

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

3. Simplified 0

   \[\leadsto expr\]
4. Add Preprocessing

5. Taylor expanded in y around inf 0

   \[\leadsto expr\]

7. Simplified 0

   \[\leadsto expr\]
8. Add Preprocessing

Developer target: 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 2024110 
(FPCore (x y z)
  :name "Graphics.Rasterific.Shading:$sgradientColorAt from Rasterific-0.6.1"
  :precision binary64

  :alt
  (- (/ x (- z y)) (/ y (- z y)))

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