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

Percentage Accurate: 100.0% → 100.0%

Time: 7.1s

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, 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]

Derivation

1. Initial program 100.0%

   \[\frac{x - y}{z - y} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. div-sub 100.0%

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

4. Applied egg-rr 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 59.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.58 \cdot 10^{+69}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-125}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 2.02 \cdot 10^{+18}:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.58e+69)
   1.0
   (if (<= y 1.05e-125) (/ x z) (if (<= y 2.02e+18) (/ x (- y)) 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.58e+69) {
		tmp = 1.0;
	} else if (y <= 1.05e-125) {
		tmp = x / z;
	} else if (y <= 2.02e+18) {
		tmp = x / -y;
	} 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 <= (-1.58d+69)) then
        tmp = 1.0d0
    else if (y <= 1.05d-125) then
        tmp = x / z
    else if (y <= 2.02d+18) then
        tmp = x / -y
    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 <= -1.58e+69) {
		tmp = 1.0;
	} else if (y <= 1.05e-125) {
		tmp = x / z;
	} else if (y <= 2.02e+18) {
		tmp = x / -y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.58e+69:
		tmp = 1.0
	elif y <= 1.05e-125:
		tmp = x / z
	elif y <= 2.02e+18:
		tmp = x / -y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.58e+69)
		tmp = 1.0;
	elseif (y <= 1.05e-125)
		tmp = Float64(x / z);
	elseif (y <= 2.02e+18)
		tmp = Float64(x / Float64(-y));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.58e+69)
		tmp = 1.0;
	elseif (y <= 1.05e-125)
		tmp = x / z;
	elseif (y <= 2.02e+18)
		tmp = x / -y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.58e+69], 1.0, If[LessEqual[y, 1.05e-125], N[(x / z), $MachinePrecision], If[LessEqual[y, 2.02e+18], N[(x / (-y)), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.58e69 or 2.02e18 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 57.9%

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

   if -1.58e69 < y < 1.05e-125

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 68.1%

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

   if 1.05e-125 < y < 2.02e18

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 69.7%

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

   4. Taylor expanded in z around 0 50.7%

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

      1. mul-1-neg 50.7%

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

      2. distribute-neg-frac2 50.7%

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

   6. Simplified 50.7%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.58 \cdot 10^{+69}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-125}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 2.02 \cdot 10^{+18}:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 69.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{-50} \lor \neg \left(y \leq 7.2 \cdot 10^{-158}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.35e-50) (not (<= y 7.2e-158))) (- 1.0 (/ x y)) (/ x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.35e-50) || !(y <= 7.2e-158)) {
		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 <= (-2.35d-50)) .or. (.not. (y <= 7.2d-158))) 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 <= -2.35e-50) || !(y <= 7.2e-158)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.35e-50) or not (y <= 7.2e-158):
		tmp = 1.0 - (x / y)
	else:
		tmp = x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.35e-50) || !(y <= 7.2e-158))
		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 <= -2.35e-50) || ~((y <= 7.2e-158)))
		tmp = 1.0 - (x / y);
	else
		tmp = x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.35e-50], N[Not[LessEqual[y, 7.2e-158]], $MachinePrecision]], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.3500000000000001e-50 or 7.19999999999999982e-158 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 67.7%

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

      1. div-sub 67.7%

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

      2. sub-neg 67.7%

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

      3. *-inverses 67.7%

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

      4. metadata-eval 67.7%

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

      5. distribute-lft-in 67.7%

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

      6. metadata-eval 67.7%

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

      7. +-commutative 67.7%

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

      8. mul-1-neg 67.7%

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

      9. unsub-neg 67.7%

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

   5. Simplified 67.7%

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

   if -2.3500000000000001e-50 < y < 7.19999999999999982e-158

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 79.8%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{-50} \lor \neg \left(y \leq 7.2 \cdot 10^{-158}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9800000000 \lor \neg \left(y \leq 8 \cdot 10^{-8}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -9800000000.0) (not (<= y 8e-8)))
   (- 1.0 (/ x y))
   (/ x (- z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -9800000000.0) || !(y <= 8e-8)) {
		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 <= (-9800000000.0d0)) .or. (.not. (y <= 8d-8))) 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 <= -9800000000.0) || !(y <= 8e-8)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x / (z - y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -9800000000.0) or not (y <= 8e-8):
		tmp = 1.0 - (x / y)
	else:
		tmp = x / (z - y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -9800000000.0) || !(y <= 8e-8))
		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 <= -9800000000.0) || ~((y <= 8e-8)))
		tmp = 1.0 - (x / y);
	else
		tmp = x / (z - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -9800000000.0], N[Not[LessEqual[y, 8e-8]], $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 < -9.8e9 or 8.0000000000000002e-8 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 70.9%

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

      1. div-sub 70.9%

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

      2. sub-neg 70.9%

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

      3. *-inverses 70.9%

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

      4. metadata-eval 70.9%

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

      5. distribute-lft-in 70.9%

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

      6. metadata-eval 70.9%

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

      7. +-commutative 70.9%

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

      8. mul-1-neg 70.9%

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

      9. unsub-neg 70.9%

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

   5. Simplified 70.9%

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

   if -9.8e9 < y < 8.0000000000000002e-8

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 83.7%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9800000000 \lor \neg \left(y \leq 8 \cdot 10^{-8}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{+14} \lor \neg \left(x \leq 1.4 \cdot 10^{-74}\right):\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.7e+14) (not (<= x 1.4e-74))) (/ x (- z y)) (/ y (- y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.7e+14) || !(x <= 1.4e-74)) {
		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 <= (-3.7d+14)) .or. (.not. (x <= 1.4d-74))) 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 <= -3.7e+14) || !(x <= 1.4e-74)) {
		tmp = x / (z - y);
	} else {
		tmp = y / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.7e+14) or not (x <= 1.4e-74):
		tmp = x / (z - y)
	else:
		tmp = y / (y - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.7e+14) || !(x <= 1.4e-74))
		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 <= -3.7e+14) || ~((x <= 1.4e-74)))
		tmp = x / (z - y);
	else
		tmp = y / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.7e+14], N[Not[LessEqual[x, 1.4e-74]], $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 < -3.7e14 or 1.39999999999999994e-74 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 77.3%

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

   if -3.7e14 < x < 1.39999999999999994e-74

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 83.2%

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

      1. neg-mul-1 83.2%

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

      2. distribute-neg-frac 83.2%

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

   5. Simplified 83.2%

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

      1. frac-2neg 83.2%

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

      2. div-inv 83.1%

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

      3. remove-double-neg 83.1%

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

      4. sub-neg 83.1%

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

      5. distribute-neg-in 83.1%

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

      6. remove-double-neg 83.1%

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

   7. Applied egg-rr 83.1%

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

      1. associate-*r/ 83.2%

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

      2. *-rgt-identity 83.2%

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

      3. +-commutative 83.2%

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

      4. unsub-neg 83.2%

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

   9. Simplified 83.2%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{+14} \lor \neg \left(x \leq 1.4 \cdot 10^{-74}\right):\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+69}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 7800000000000:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.5e+69) 1.0 (if (<= y 7800000000000.0) (/ x z) 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.5e+69) {
		tmp = 1.0;
	} else if (y <= 7800000000000.0) {
		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) :: tmp
    if (y <= (-2.5d+69)) then
        tmp = 1.0d0
    else if (y <= 7800000000000.0d0) 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 tmp;
	if (y <= -2.5e+69) {
		tmp = 1.0;
	} else if (y <= 7800000000000.0) {
		tmp = x / z;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.5e+69:
		tmp = 1.0
	elif y <= 7800000000000.0:
		tmp = x / z
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.5e+69)
		tmp = 1.0;
	elseif (y <= 7800000000000.0)
		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 <= -2.5e+69)
		tmp = 1.0;
	elseif (y <= 7800000000000.0)
		tmp = x / z;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.5e+69], 1.0, If[LessEqual[y, 7800000000000.0], N[(x / z), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -2.50000000000000018e69 or 7.8e12 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 56.7%

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

   if -2.50000000000000018e69 < y < 7.8e12

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 61.6%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+69}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 7800000000000:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 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 8: 34.7% 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 34.0%

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

4. Final simplification 34.0%

   \[\leadsto 1 \]
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 2024077 
(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)))