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

Percentage Accurate: 100.0% → 100.0%

Time: 5.5s

Alternatives: 8

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

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. Final simplification 100.0%

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

Alternative 2: 61.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+127}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{+82}:\\ \;\;\;\;\frac{y}{-z}\\ \mathbf{elif}\;y \leq -17500000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+43}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.55e+127)
   1.0
   (if (<= y -1.1e+82)
     (/ y (- z))
     (if (<= y -17500000.0) 1.0 (if (<= y 1.9e+43) (/ x z) 1.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.55e+127) {
		tmp = 1.0;
	} else if (y <= -1.1e+82) {
		tmp = y / -z;
	} else if (y <= -17500000.0) {
		tmp = 1.0;
	} else if (y <= 1.9e+43) {
		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 <= (-1.55d+127)) then
        tmp = 1.0d0
    else if (y <= (-1.1d+82)) then
        tmp = y / -z
    else if (y <= (-17500000.0d0)) then
        tmp = 1.0d0
    else if (y <= 1.9d+43) 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 <= -1.55e+127) {
		tmp = 1.0;
	} else if (y <= -1.1e+82) {
		tmp = y / -z;
	} else if (y <= -17500000.0) {
		tmp = 1.0;
	} else if (y <= 1.9e+43) {
		tmp = x / z;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.55e+127:
		tmp = 1.0
	elif y <= -1.1e+82:
		tmp = y / -z
	elif y <= -17500000.0:
		tmp = 1.0
	elif y <= 1.9e+43:
		tmp = x / z
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.55e+127)
		tmp = 1.0;
	elseif (y <= -1.1e+82)
		tmp = Float64(y / Float64(-z));
	elseif (y <= -17500000.0)
		tmp = 1.0;
	elseif (y <= 1.9e+43)
		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 <= -1.55e+127)
		tmp = 1.0;
	elseif (y <= -1.1e+82)
		tmp = y / -z;
	elseif (y <= -17500000.0)
		tmp = 1.0;
	elseif (y <= 1.9e+43)
		tmp = x / z;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.55e+127], 1.0, If[LessEqual[y, -1.1e+82], N[(y / (-z)), $MachinePrecision], If[LessEqual[y, -17500000.0], 1.0, If[LessEqual[y, 1.9e+43], N[(x / z), $MachinePrecision], 1.0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.5500000000000001e127 or -1.1000000000000001e82 < y < -1.75e7 or 1.90000000000000004e43 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 67.8%

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

   if -1.5500000000000001e127 < y < -1.1000000000000001e82

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 93.4%

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

      1. +-commutative 93.4%

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

      2. mul-1-neg 93.4%

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

      3. unsub-neg 93.4%

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

      4. *-commutative 93.4%

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

   5. Simplified 93.4%

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

   6. Taylor expanded in z around inf 45.9%

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

   7. Taylor expanded in x around 0 41.7%

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

      1. neg-mul-1 41.7%

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

   9. Simplified 41.7%

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

   if -1.75e7 < y < 1.90000000000000004e43

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 67.5%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+127}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{+82}:\\ \;\;\;\;\frac{y}{-z}\\ \mathbf{elif}\;y \leq -17500000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+43}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 70.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.85 \cdot 10^{-76} \lor \neg \left(y \leq 1.22 \cdot 10^{-113}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.85e-76) (not (<= y 1.22e-113))) (- 1.0 (/ x y)) (/ x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.85e-76) || !(y <= 1.22e-113)) {
		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 <= (-3.85d-76)) .or. (.not. (y <= 1.22d-113))) 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 <= -3.85e-76) || !(y <= 1.22e-113)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.85e-76) or not (y <= 1.22e-113):
		tmp = 1.0 - (x / y)
	else:
		tmp = x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.85e-76) || !(y <= 1.22e-113))
		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 <= -3.85e-76) || ~((y <= 1.22e-113)))
		tmp = 1.0 - (x / y);
	else
		tmp = x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.85e-76], N[Not[LessEqual[y, 1.22e-113]], $MachinePrecision]], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.84999999999999991e-76 or 1.21999999999999995e-113 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 71.3%

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

      1. div-sub 71.3%

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

      2. sub-neg 71.3%

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

      3. *-inverses 71.3%

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

      4. metadata-eval 71.3%

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

      5. distribute-lft-in 71.3%

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

      6. metadata-eval 71.3%

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

      7. +-commutative 71.3%

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

      8. mul-1-neg 71.3%

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

      9. unsub-neg 71.3%

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

   5. Simplified 71.3%

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

   if -3.84999999999999991e-76 < y < 1.21999999999999995e-113

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 78.9%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.85 \cdot 10^{-76} \lor \neg \left(y \leq 1.22 \cdot 10^{-113}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+19} \lor \neg \left(y \leq 1.95 \cdot 10^{+40}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -7.2e+19) (not (<= y 1.95e+40))) (- 1.0 (/ x y)) (/ x (- z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7.2e+19) || !(y <= 1.95e+40)) {
		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 <= (-7.2d+19)) .or. (.not. (y <= 1.95d+40))) 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 <= -7.2e+19) || !(y <= 1.95e+40)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x / (z - y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -7.2e+19) or not (y <= 1.95e+40):
		tmp = 1.0 - (x / y)
	else:
		tmp = x / (z - y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -7.2e+19) || !(y <= 1.95e+40))
		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 <= -7.2e+19) || ~((y <= 1.95e+40)))
		tmp = 1.0 - (x / y);
	else
		tmp = x / (z - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -7.2e+19], N[Not[LessEqual[y, 1.95e+40]], $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 < -7.2e19 or 1.95e40 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 76.9%

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

      1. div-sub 76.9%

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

      2. sub-neg 76.9%

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

      3. *-inverses 76.9%

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

      4. metadata-eval 76.9%

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

      5. distribute-lft-in 76.9%

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

      6. metadata-eval 76.9%

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

      7. +-commutative 76.9%

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

      8. mul-1-neg 76.9%

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

      9. unsub-neg 76.9%

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

   5. Simplified 76.9%

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

   if -7.2e19 < y < 1.95e40

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 80.7%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+19} \lor \neg \left(y \leq 1.95 \cdot 10^{+40}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-31} \lor \neg \left(z \leq 1.55 \cdot 10^{+92}\right):\\ \;\;\;\;\frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.55e-31) (not (<= z 1.55e+92)))
   (/ (- x y) z)
   (- 1.0 (/ x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.55e-31) || !(z <= 1.55e+92)) {
		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 <= (-1.55d-31)) .or. (.not. (z <= 1.55d+92))) 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 <= -1.55e-31) || !(z <= 1.55e+92)) {
		tmp = (x - y) / z;
	} else {
		tmp = 1.0 - (x / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.55e-31) or not (z <= 1.55e+92):
		tmp = (x - y) / z
	else:
		tmp = 1.0 - (x / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.55e-31) || !(z <= 1.55e+92))
		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 <= -1.55e-31) || ~((z <= 1.55e+92)))
		tmp = (x - y) / z;
	else
		tmp = 1.0 - (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.55e-31], N[Not[LessEqual[z, 1.55e+92]], $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 < -1.55e-31 or 1.5500000000000001e92 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 83.6%

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

   if -1.55e-31 < z < 1.5500000000000001e92

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 80.6%

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

      1. div-sub 80.6%

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

      2. sub-neg 80.6%

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

      3. *-inverses 80.6%

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

      4. metadata-eval 80.6%

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

      5. distribute-lft-in 80.6%

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

      6. metadata-eval 80.6%

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

      7. +-commutative 80.6%

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

      8. mul-1-neg 80.6%

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

      9. unsub-neg 80.6%

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

   5. Simplified 80.6%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-31} \lor \neg \left(z \leq 1.55 \cdot 10^{+92}\right):\\ \;\;\;\;\frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1700 \lor \neg \left(x \leq 7.2 \cdot 10^{+113}\right):\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1700.0) (not (<= x 7.2e+113))) (/ x (- z y)) (/ y (- y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1700.0) || !(x <= 7.2e+113)) {
		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) :: tmp
    if ((x <= (-1700.0d0)) .or. (.not. (x <= 7.2d+113))) 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 tmp;
	if ((x <= -1700.0) || !(x <= 7.2e+113)) {
		tmp = x / (z - y);
	} else {
		tmp = y / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1700.0) or not (x <= 7.2e+113):
		tmp = x / (z - y)
	else:
		tmp = y / (y - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1700.0) || !(x <= 7.2e+113))
		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)
	tmp = 0.0;
	if ((x <= -1700.0) || ~((x <= 7.2e+113)))
		tmp = x / (z - y);
	else
		tmp = y / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1700.0], N[Not[LessEqual[x, 7.2e+113]], $MachinePrecision]], N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision], N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1700 or 7.19999999999999984e113 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 84.7%

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

   if -1700 < x < 7.19999999999999984e113

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 82.5%

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

      1. neg-mul-1 82.5%

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

      2. distribute-neg-frac 82.5%

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

   5. Simplified 82.5%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1700 \lor \neg \left(x \leq 7.2 \cdot 10^{+113}\right):\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -98000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+42}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -98000000000.0) 1.0 (if (<= y 4.5e+42) (/ x z) 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -98000000000.0) {
		tmp = 1.0;
	} else if (y <= 4.5e+42) {
		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 <= (-98000000000.0d0)) then
        tmp = 1.0d0
    else if (y <= 4.5d+42) 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 <= -98000000000.0) {
		tmp = 1.0;
	} else if (y <= 4.5e+42) {
		tmp = x / z;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -98000000000.0:
		tmp = 1.0
	elif y <= 4.5e+42:
		tmp = x / z
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -98000000000.0)
		tmp = 1.0;
	elseif (y <= 4.5e+42)
		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 <= -98000000000.0)
		tmp = 1.0;
	elseif (y <= 4.5e+42)
		tmp = x / z;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -98000000000.0], 1.0, If[LessEqual[y, 4.5e+42], N[(x / z), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -9.8e10 or 4.50000000000000012e42 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 61.2%

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

   if -9.8e10 < y < 4.50000000000000012e42

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 67.5%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -98000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+42}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 35.1% 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 35.0%

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

4. Final simplification 35.0%

   \[\leadsto 1 \]
5. 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 2024059 
(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)))