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

Percentage Accurate: 100.0% → 100.0%

Time: 5.6s

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: 75.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+68} \lor \neg \left(x \leq -1.53 \cdot 10^{+41}\right) \land \left(x \leq -9.6 \cdot 10^{-45} \lor \neg \left(x \leq 0.01\right)\right):\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.3e+68)
         (and (not (<= x -1.53e+41)) (or (<= x -9.6e-45) (not (<= x 0.01)))))
   (/ x (- z y))
   (/ y (- y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.3e+68) || (!(x <= -1.53e+41) && ((x <= -9.6e-45) || !(x <= 0.01)))) {
		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 <= (-1.3d+68)) .or. (.not. (x <= (-1.53d+41))) .and. (x <= (-9.6d-45)) .or. (.not. (x <= 0.01d0))) 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 <= -1.3e+68) || (!(x <= -1.53e+41) && ((x <= -9.6e-45) || !(x <= 0.01)))) {
		tmp = x / (z - y);
	} else {
		tmp = y / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.3e+68) or (not (x <= -1.53e+41) and ((x <= -9.6e-45) or not (x <= 0.01))):
		tmp = x / (z - y)
	else:
		tmp = y / (y - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.3e+68) || (!(x <= -1.53e+41) && ((x <= -9.6e-45) || !(x <= 0.01))))
		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 <= -1.3e+68) || (~((x <= -1.53e+41)) && ((x <= -9.6e-45) || ~((x <= 0.01)))))
		tmp = x / (z - y);
	else
		tmp = y / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.3e+68], And[N[Not[LessEqual[x, -1.53e+41]], $MachinePrecision], Or[LessEqual[x, -9.6e-45], N[Not[LessEqual[x, 0.01]], $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 < -1.2999999999999999e68 or -1.52999999999999997e41 < x < -9.5999999999999996e-45 or 0.0100000000000000002 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 81.4%

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

   if -1.2999999999999999e68 < x < -1.52999999999999997e41 or -9.5999999999999996e-45 < x < 0.0100000000000000002

   1. Initial program 100.0%

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

      1. clear-num 99.3%

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

      2. associate-/r/ 99.6%

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

   4. Applied egg-rr 99.6%

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

      1. associate-*l/ 100.0%

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

      2. *-un-lft-identity 100.0%

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

      3. clear-num 99.3%

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

   6. Applied egg-rr 99.3%

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

   7. Taylor expanded in x around 0 85.6%

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

      1. mul-1-neg 85.6%

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

      2. distribute-neg-frac2 85.6%

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

      3. neg-sub0 85.6%

         \[\leadsto \frac{y}{\color{blue}{0 - \left(z - y\right)}} \]

      4. associate-+l- 85.6%

         \[\leadsto \frac{y}{\color{blue}{\left(0 - z\right) + y}} \]

      5. neg-sub0 85.6%

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

      6. +-commutative 85.6%

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

      7. unsub-neg 85.6%

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

   9. Simplified 85.6%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+68} \lor \neg \left(x \leq -1.53 \cdot 10^{+41}\right) \land \left(x \leq -9.6 \cdot 10^{-45} \lor \neg \left(x \leq 0.01\right)\right):\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 68.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -4.1 \cdot 10^{-11}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-130}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+18} \lor \neg \left(y \leq 8.8 \cdot 10^{+61}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{-z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ x y))))
   (if (<= y -4.1e-11)
     t_0
     (if (<= y 1.1e-130)
       (/ x z)
       (if (or (<= y 2.6e+18) (not (<= y 8.8e+61))) t_0 (/ y (- z)))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (x / y);
	double tmp;
	if (y <= -4.1e-11) {
		tmp = t_0;
	} else if (y <= 1.1e-130) {
		tmp = x / z;
	} else if ((y <= 2.6e+18) || !(y <= 8.8e+61)) {
		tmp = t_0;
	} else {
		tmp = y / -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 - (x / y)
    if (y <= (-4.1d-11)) then
        tmp = t_0
    else if (y <= 1.1d-130) then
        tmp = x / z
    else if ((y <= 2.6d+18) .or. (.not. (y <= 8.8d+61))) then
        tmp = t_0
    else
        tmp = y / -z
    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 <= -4.1e-11) {
		tmp = t_0;
	} else if (y <= 1.1e-130) {
		tmp = x / z;
	} else if ((y <= 2.6e+18) || !(y <= 8.8e+61)) {
		tmp = t_0;
	} else {
		tmp = y / -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (x / y)
	tmp = 0
	if y <= -4.1e-11:
		tmp = t_0
	elif y <= 1.1e-130:
		tmp = x / z
	elif (y <= 2.6e+18) or not (y <= 8.8e+61):
		tmp = t_0
	else:
		tmp = y / -z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(x / y))
	tmp = 0.0
	if (y <= -4.1e-11)
		tmp = t_0;
	elseif (y <= 1.1e-130)
		tmp = Float64(x / z);
	elseif ((y <= 2.6e+18) || !(y <= 8.8e+61))
		tmp = t_0;
	else
		tmp = Float64(y / Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (x / y);
	tmp = 0.0;
	if (y <= -4.1e-11)
		tmp = t_0;
	elseif (y <= 1.1e-130)
		tmp = x / z;
	elseif ((y <= 2.6e+18) || ~((y <= 8.8e+61)))
		tmp = t_0;
	else
		tmp = y / -z;
	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, -4.1e-11], t$95$0, If[LessEqual[y, 1.1e-130], N[(x / z), $MachinePrecision], If[Or[LessEqual[y, 2.6e+18], N[Not[LessEqual[y, 8.8e+61]], $MachinePrecision]], t$95$0, N[(y / (-z)), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.1000000000000001e-11 or 1.0999999999999999e-130 < y < 2.6e18 or 8.8000000000000001e61 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 73.0%

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

      1. div-sub 73.0%

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

      2. sub-neg 73.0%

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

      3. *-inverses 73.0%

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

      4. metadata-eval 73.0%

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

      5. distribute-lft-in 73.0%

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

      6. metadata-eval 73.0%

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

      7. +-commutative 73.0%

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

      8. mul-1-neg 73.0%

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

      9. unsub-neg 73.0%

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

   5. Simplified 73.0%

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

   if -4.1000000000000001e-11 < y < 1.0999999999999999e-130

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 73.4%

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

   if 2.6e18 < y < 8.8000000000000001e61

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 85.9%

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

   4. Taylor expanded in x around 0 71.8%

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

      1. neg-mul-1 71.8%

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

      2. distribute-neg-frac2 71.8%

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

   6. Simplified 71.8%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{-11}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-130}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+18} \lor \neg \left(y \leq 8.8 \cdot 10^{+61}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{-z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+113}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-13}:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-10}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.3e+113)
   1.0
   (if (<= y -1.6e-13) (/ x (- y)) (if (<= y 2e-10) (/ x z) 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.3e+113) {
		tmp = 1.0;
	} else if (y <= -1.6e-13) {
		tmp = x / -y;
	} else if (y <= 2e-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 <= (-2.3d+113)) then
        tmp = 1.0d0
    else if (y <= (-1.6d-13)) then
        tmp = x / -y
    else if (y <= 2d-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 <= -2.3e+113) {
		tmp = 1.0;
	} else if (y <= -1.6e-13) {
		tmp = x / -y;
	} else if (y <= 2e-10) {
		tmp = x / z;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.3e+113:
		tmp = 1.0
	elif y <= -1.6e-13:
		tmp = x / -y
	elif y <= 2e-10:
		tmp = x / z
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.3e+113)
		tmp = 1.0;
	elseif (y <= -1.6e-13)
		tmp = Float64(x / Float64(-y));
	elseif (y <= 2e-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 <= -2.3e+113)
		tmp = 1.0;
	elseif (y <= -1.6e-13)
		tmp = x / -y;
	elseif (y <= 2e-10)
		tmp = x / z;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.3e+113], 1.0, If[LessEqual[y, -1.6e-13], N[(x / (-y)), $MachinePrecision], If[LessEqual[y, 2e-10], N[(x / z), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.29999999999999997e113 or 2.00000000000000007e-10 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 61.7%

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

   if -2.29999999999999997e113 < y < -1.6e-13

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 53.4%

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

   4. Taylor expanded in z around 0 45.7%

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

      1. associate-*r/ 45.7%

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

      2. neg-mul-1 45.7%

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

   6. Simplified 45.7%

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

   if -1.6e-13 < y < 2.00000000000000007e-10

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 67.2%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+113}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-13}:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-10}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{-6} \lor \neg \left(y \leq 6.2 \cdot 10^{-9}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.3e-6) (not (<= y 6.2e-9))) (- 1.0 (/ x y)) (/ x (- z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.3e-6) || !(y <= 6.2e-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 <= (-5.3d-6)) .or. (.not. (y <= 6.2d-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 <= -5.3e-6) || !(y <= 6.2e-9)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x / (z - y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5.3e-6) or not (y <= 6.2e-9):
		tmp = 1.0 - (x / y)
	else:
		tmp = x / (z - y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.3e-6) || !(y <= 6.2e-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 <= -5.3e-6) || ~((y <= 6.2e-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, -5.3e-6], N[Not[LessEqual[y, 6.2e-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 < -5.3000000000000001e-6 or 6.2000000000000001e-9 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 72.9%

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

      1. div-sub 72.9%

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

      2. sub-neg 72.9%

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

      3. *-inverses 72.9%

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

      4. metadata-eval 72.9%

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

      5. distribute-lft-in 72.9%

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

      6. metadata-eval 72.9%

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

      7. +-commutative 72.9%

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

      8. mul-1-neg 72.9%

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

      9. unsub-neg 72.9%

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

   5. Simplified 72.9%

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

   if -5.3000000000000001e-6 < y < 6.2000000000000001e-9

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 82.1%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{-6} \lor \neg \left(y \leq 6.2 \cdot 10^{-9}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{-6}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-9}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.6e-6) 1.0 (if (<= y 1.3e-9) (/ x z) 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.6e-6) {
		tmp = 1.0;
	} else if (y <= 1.3e-9) {
		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 <= (-3.6d-6)) then
        tmp = 1.0d0
    else if (y <= 1.3d-9) 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 <= -3.6e-6) {
		tmp = 1.0;
	} else if (y <= 1.3e-9) {
		tmp = x / z;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.6e-6:
		tmp = 1.0
	elif y <= 1.3e-9:
		tmp = x / z
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.6e-6)
		tmp = 1.0;
	elseif (y <= 1.3e-9)
		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 <= -3.6e-6)
		tmp = 1.0;
	elseif (y <= 1.3e-9)
		tmp = x / z;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.6e-6], 1.0, If[LessEqual[y, 1.3e-9], N[(x / z), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -3.59999999999999984e-6 or 1.3000000000000001e-9 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 54.9%

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

   if -3.59999999999999984e-6 < y < 1.3000000000000001e-9

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 66.3%

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

Alternative 7: 34.8% 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 31.9%

   \[\leadsto \color{blue}{1} \]
4. 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 2024091 
(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)))