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

Percentage Accurate: 100.0% → 100.0%

Time: 8.0s

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: 76.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{y - z}\\ \mathbf{if}\;y \leq -7.2 \cdot 10^{+71}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 0.00035:\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+167}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ y (- y z))))
   (if (<= y -7.2e+71)
     t_0
     (if (<= y 0.00035)
       (/ x (- z y))
       (if (<= y 1.35e+167) t_0 (- 1.0 (/ x y)))))))

C

double code(double x, double y, double z) {
	double t_0 = y / (y - z);
	double tmp;
	if (y <= -7.2e+71) {
		tmp = t_0;
	} else if (y <= 0.00035) {
		tmp = x / (z - y);
	} else if (y <= 1.35e+167) {
		tmp = t_0;
	} else {
		tmp = 1.0 - (x / y);
	}
	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 / (y - z)
    if (y <= (-7.2d+71)) then
        tmp = t_0
    else if (y <= 0.00035d0) then
        tmp = x / (z - y)
    else if (y <= 1.35d+167) then
        tmp = t_0
    else
        tmp = 1.0d0 - (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y / (y - z);
	double tmp;
	if (y <= -7.2e+71) {
		tmp = t_0;
	} else if (y <= 0.00035) {
		tmp = x / (z - y);
	} else if (y <= 1.35e+167) {
		tmp = t_0;
	} else {
		tmp = 1.0 - (x / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y / (y - z)
	tmp = 0
	if y <= -7.2e+71:
		tmp = t_0
	elif y <= 0.00035:
		tmp = x / (z - y)
	elif y <= 1.35e+167:
		tmp = t_0
	else:
		tmp = 1.0 - (x / y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y / Float64(y - z))
	tmp = 0.0
	if (y <= -7.2e+71)
		tmp = t_0;
	elseif (y <= 0.00035)
		tmp = Float64(x / Float64(z - y));
	elseif (y <= 1.35e+167)
		tmp = t_0;
	else
		tmp = Float64(1.0 - Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y / (y - z);
	tmp = 0.0;
	if (y <= -7.2e+71)
		tmp = t_0;
	elseif (y <= 0.00035)
		tmp = x / (z - y);
	elseif (y <= 1.35e+167)
		tmp = t_0;
	else
		tmp = 1.0 - (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.2e+71], t$95$0, If[LessEqual[y, 0.00035], N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.35e+167], t$95$0, N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.1999999999999999e71 or 3.49999999999999996e-4 < y < 1.35000000000000003e167

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 72.7%

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

      1. neg-mul-1 72.7%

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

      2. distribute-neg-frac2 72.7%

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

      3. sub-neg 72.7%

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

      4. +-commutative 72.7%

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

      5. distribute-neg-in 72.7%

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

      6. remove-double-neg 72.7%

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

      7. sub-neg 72.7%

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

   5. Simplified 72.7%

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

   if -7.1999999999999999e71 < y < 3.49999999999999996e-4

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 81.5%

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

   if 1.35000000000000003e167 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 89.0%

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

      1. associate-*r/ 89.0%

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

      2. neg-mul-1 89.0%

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

      3. sub-neg 89.0%

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

      4. +-commutative 89.0%

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

      5. distribute-neg-in 89.0%

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

      6. remove-double-neg 89.0%

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

      7. sub-neg 89.0%

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

      8. div-sub 89.0%

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

      9. *-inverses 89.0%

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

   5. Simplified 89.0%

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

Alternative 3: 76.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+65} \lor \neg \left(z \leq 3.8 \cdot 10^{-44}\right):\\ \;\;\;\;\frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.8e+65) (not (<= z 3.8e-44))) (/ (- x y) z) (- 1.0 (/ x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.8e+65) || !(z <= 3.8e-44)) {
		tmp = (x - y) / z;
	} else {
		tmp = 1.0 - (x / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-2.8d+65)) .or. (.not. (z <= 3.8d-44))) then
        tmp = (x - y) / z
    else
        tmp = 1.0d0 - (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.8e+65) || !(z <= 3.8e-44)) {
		tmp = (x - y) / z;
	} else {
		tmp = 1.0 - (x / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.8e+65) or not (z <= 3.8e-44):
		tmp = (x - y) / z
	else:
		tmp = 1.0 - (x / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.8e+65) || !(z <= 3.8e-44))
		tmp = Float64(Float64(x - y) / z);
	else
		tmp = Float64(1.0 - Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.8e+65) || ~((z <= 3.8e-44)))
		tmp = (x - y) / z;
	else
		tmp = 1.0 - (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.8e+65], N[Not[LessEqual[z, 3.8e-44]], $MachinePrecision]], N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.7999999999999999e65 or 3.8000000000000001e-44 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 78.4%

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

   if -2.7999999999999999e65 < z < 3.8000000000000001e-44

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 77.8%

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

      1. associate-*r/ 77.8%

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

      2. neg-mul-1 77.8%

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

      3. sub-neg 77.8%

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

      4. +-commutative 77.8%

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

      5. distribute-neg-in 77.8%

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

      6. remove-double-neg 77.8%

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

      7. sub-neg 77.8%

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

      8. div-sub 77.8%

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

      9. *-inverses 77.8%

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

   5. Simplified 77.8%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+65} \lor \neg \left(z \leq 3.8 \cdot 10^{-44}\right):\\ \;\;\;\;\frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+71} \lor \neg \left(y \leq 1.35 \cdot 10^{-9}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.5e+71) (not (<= y 1.35e-9))) (- 1.0 (/ x y)) (/ x (- z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.5e+71) || !(y <= 1.35e-9)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x / (z - y);
	}
	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 <= (-5.5d+71)) .or. (.not. (y <= 1.35d-9))) then
        tmp = 1.0d0 - (x / y)
    else
        tmp = x / (z - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.5e+71) || !(y <= 1.35e-9)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x / (z - y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5.5e+71) or not (y <= 1.35e-9):
		tmp = 1.0 - (x / y)
	else:
		tmp = x / (z - y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.5e+71) || !(y <= 1.35e-9))
		tmp = Float64(1.0 - Float64(x / y));
	else
		tmp = Float64(x / Float64(z - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -5.5e+71) || ~((y <= 1.35e-9)))
		tmp = 1.0 - (x / y);
	else
		tmp = x / (z - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5.5e+71], N[Not[LessEqual[y, 1.35e-9]], $MachinePrecision]], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.5e71 or 1.3500000000000001e-9 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 70.0%

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

      1. associate-*r/ 70.0%

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

      2. neg-mul-1 70.0%

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

      3. sub-neg 70.0%

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

      4. +-commutative 70.0%

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

      5. distribute-neg-in 70.0%

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

      6. remove-double-neg 70.0%

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

      7. sub-neg 70.0%

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

      8. div-sub 70.1%

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

      9. *-inverses 70.1%

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

   5. Simplified 70.1%

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

   if -5.5e71 < y < 1.3500000000000001e-9

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 81.2%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+71} \lor \neg \left(y \leq 1.35 \cdot 10^{-9}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 70.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.95 \cdot 10^{-7} \lor \neg \left(y \leq 1.9 \cdot 10^{-7}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.95e-7) (not (<= y 1.9e-7))) (- 1.0 (/ x y)) (/ x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.95e-7) || !(y <= 1.9e-7)) {
		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) :: tmp
    if ((y <= (-2.95d-7)) .or. (.not. (y <= 1.9d-7))) 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 tmp;
	if ((y <= -2.95e-7) || !(y <= 1.9e-7)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.95e-7) or not (y <= 1.9e-7):
		tmp = 1.0 - (x / y)
	else:
		tmp = x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.95e-7) || !(y <= 1.9e-7))
		tmp = Float64(1.0 - Float64(x / y));
	else
		tmp = Float64(x / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.95e-7) || ~((y <= 1.9e-7)))
		tmp = 1.0 - (x / y);
	else
		tmp = x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.95e-7], N[Not[LessEqual[y, 1.9e-7]], $MachinePrecision]], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.94999999999999981e-7 or 1.90000000000000007e-7 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 67.8%

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

      1. associate-*r/ 67.8%

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

      2. neg-mul-1 67.8%

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

      3. sub-neg 67.8%

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

      4. +-commutative 67.8%

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

      5. distribute-neg-in 67.8%

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

      6. remove-double-neg 67.8%

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

      7. sub-neg 67.8%

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

      8. div-sub 67.9%

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

      9. *-inverses 67.9%

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

   5. Simplified 67.9%

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

   if -2.94999999999999981e-7 < y < 1.90000000000000007e-7

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 71.8%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.95 \cdot 10^{-7} \lor \neg \left(y \leq 1.9 \cdot 10^{-7}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+70}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-46}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4e+70) 1.0 (if (<= y 2.3e-46) (/ x z) 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4e+70) {
		tmp = 1.0;
	} else if (y <= 2.3e-46) {
		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 <= (-4d+70)) then
        tmp = 1.0d0
    else if (y <= 2.3d-46) 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 <= -4e+70) {
		tmp = 1.0;
	} else if (y <= 2.3e-46) {
		tmp = x / z;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4e+70:
		tmp = 1.0
	elif y <= 2.3e-46:
		tmp = x / z
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4e+70)
		tmp = 1.0;
	elseif (y <= 2.3e-46)
		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 <= -4e+70)
		tmp = 1.0;
	elseif (y <= 2.3e-46)
		tmp = x / z;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4e+70], 1.0, If[LessEqual[y, 2.3e-46], N[(x / z), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -4.00000000000000029e70 or 2.2999999999999999e-46 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 55.7%

      \[\leadsto \color{blue}{1} \]

   if -4.00000000000000029e70 < y < 2.2999999999999999e-46

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 69.2%

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

Alternative 7: 34.3% 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%

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

3. Taylor expanded in y around inf 33.7%

   \[\leadsto \color{blue}{1} \]
4. 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 2024137 
(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)))