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

Percentage Accurate: 100.0% → 100.0%

Time: 6.7s

Alternatives: 10

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

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

FPCore

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

C

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

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 / (y - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

Alternative 2: 75.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{+127}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{+15}:\\ \;\;\;\;\frac{y}{y - z}\\ \mathbf{elif}\;y \leq -8.6 \cdot 10^{-165}:\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{elif}\;y \leq 10^{-42}:\\ \;\;\;\;\frac{x}{z} - \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ x y))))
   (if (<= y -4.5e+127)
     t_0
     (if (<= y -1.8e+15)
       (/ y (- y z))
       (if (<= y -8.6e-165)
         (/ x (- z y))
         (if (<= y 1e-42) (- (/ x z) (/ y z)) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (x / y);
	double tmp;
	if (y <= -4.5e+127) {
		tmp = t_0;
	} else if (y <= -1.8e+15) {
		tmp = y / (y - z);
	} else if (y <= -8.6e-165) {
		tmp = x / (z - y);
	} else if (y <= 1e-42) {
		tmp = (x / z) - (y / z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 - (x / y)
    if (y <= (-4.5d+127)) then
        tmp = t_0
    else if (y <= (-1.8d+15)) then
        tmp = y / (y - z)
    else if (y <= (-8.6d-165)) then
        tmp = x / (z - y)
    else if (y <= 1d-42) then
        tmp = (x / z) - (y / z)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 - (x / y);
	double tmp;
	if (y <= -4.5e+127) {
		tmp = t_0;
	} else if (y <= -1.8e+15) {
		tmp = y / (y - z);
	} else if (y <= -8.6e-165) {
		tmp = x / (z - y);
	} else if (y <= 1e-42) {
		tmp = (x / z) - (y / z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (x / y)
	tmp = 0
	if y <= -4.5e+127:
		tmp = t_0
	elif y <= -1.8e+15:
		tmp = y / (y - z)
	elif y <= -8.6e-165:
		tmp = x / (z - y)
	elif y <= 1e-42:
		tmp = (x / z) - (y / z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(x / y))
	tmp = 0.0
	if (y <= -4.5e+127)
		tmp = t_0;
	elseif (y <= -1.8e+15)
		tmp = Float64(y / Float64(y - z));
	elseif (y <= -8.6e-165)
		tmp = Float64(x / Float64(z - y));
	elseif (y <= 1e-42)
		tmp = Float64(Float64(x / z) - Float64(y / z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (x / y);
	tmp = 0.0;
	if (y <= -4.5e+127)
		tmp = t_0;
	elseif (y <= -1.8e+15)
		tmp = y / (y - z);
	elseif (y <= -8.6e-165)
		tmp = x / (z - y);
	elseif (y <= 1e-42)
		tmp = (x / z) - (y / z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.5e+127], t$95$0, If[LessEqual[y, -1.8e+15], N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8.6e-165], N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e-42], N[(N[(x / z), $MachinePrecision] - N[(y / z), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.50000000000000034e127 or 1.00000000000000004e-42 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 83.1%

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

      1. div-sub 83.1%

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

      2. sub-neg 83.1%

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

      3. *-inverses 83.1%

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

      4. metadata-eval 83.1%

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

      5. distribute-lft-in 83.1%

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

      6. metadata-eval 83.1%

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

      7. +-commutative 83.1%

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

      8. mul-1-neg 83.1%

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

      9. unsub-neg 83.1%

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

   5. Simplified 83.1%

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

   if -4.50000000000000034e127 < y < -1.8e15

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 91.9%

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

      1. neg-mul-1 91.9%

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

      2. distribute-neg-frac 91.9%

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

   5. Simplified 91.9%

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

      1. frac-2neg 91.9%

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

      2. div-inv 91.3%

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

      3. remove-double-neg 91.3%

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

      4. sub-neg 91.3%

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

      5. distribute-neg-in 91.3%

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

      6. remove-double-neg 91.3%

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

   7. Applied egg-rr 91.3%

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

      1. associate-*r/ 91.9%

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

      2. *-rgt-identity 91.9%

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

      3. +-commutative 91.9%

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

      4. unsub-neg 91.9%

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

   9. Simplified 91.9%

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

   if -1.8e15 < y < -8.60000000000000013e-165

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 82.4%

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

   if -8.60000000000000013e-165 < y < 1.00000000000000004e-42

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 90.6%

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

      1. div-sub 90.6%

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

   5. Applied egg-rr 90.6%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+127}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{+15}:\\ \;\;\;\;\frac{y}{y - z}\\ \mathbf{elif}\;y \leq -8.6 \cdot 10^{-165}:\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{elif}\;y \leq 10^{-42}:\\ \;\;\;\;\frac{x}{z} - \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 68.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{+124}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -1.26 \cdot 10^{+82}:\\ \;\;\;\;\frac{y}{-z}\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-106} \lor \neg \left(y \leq 1.45 \cdot 10^{-48}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ x y))))
   (if (<= y -2.4e+124)
     t_0
     (if (<= y -1.26e+82)
       (/ y (- z))
       (if (or (<= y -1.4e-106) (not (<= y 1.45e-48))) t_0 (/ x z))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (x / y);
	double tmp;
	if (y <= -2.4e+124) {
		tmp = t_0;
	} else if (y <= -1.26e+82) {
		tmp = y / -z;
	} else if ((y <= -1.4e-106) || !(y <= 1.45e-48)) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 - (x / y)
    if (y <= (-2.4d+124)) then
        tmp = t_0
    else if (y <= (-1.26d+82)) then
        tmp = y / -z
    else if ((y <= (-1.4d-106)) .or. (.not. (y <= 1.45d-48))) then
        tmp = t_0
    else
        tmp = x / 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 <= -2.4e+124) {
		tmp = t_0;
	} else if (y <= -1.26e+82) {
		tmp = y / -z;
	} else if ((y <= -1.4e-106) || !(y <= 1.45e-48)) {
		tmp = t_0;
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (x / y)
	tmp = 0
	if y <= -2.4e+124:
		tmp = t_0
	elif y <= -1.26e+82:
		tmp = y / -z
	elif (y <= -1.4e-106) or not (y <= 1.45e-48):
		tmp = t_0
	else:
		tmp = x / z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(x / y))
	tmp = 0.0
	if (y <= -2.4e+124)
		tmp = t_0;
	elseif (y <= -1.26e+82)
		tmp = Float64(y / Float64(-z));
	elseif ((y <= -1.4e-106) || !(y <= 1.45e-48))
		tmp = t_0;
	else
		tmp = Float64(x / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (x / y);
	tmp = 0.0;
	if (y <= -2.4e+124)
		tmp = t_0;
	elseif (y <= -1.26e+82)
		tmp = y / -z;
	elseif ((y <= -1.4e-106) || ~((y <= 1.45e-48)))
		tmp = t_0;
	else
		tmp = x / 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, -2.4e+124], t$95$0, If[LessEqual[y, -1.26e+82], N[(y / (-z)), $MachinePrecision], If[Or[LessEqual[y, -1.4e-106], N[Not[LessEqual[y, 1.45e-48]], $MachinePrecision]], t$95$0, N[(x / z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.40000000000000006e124 or -1.2600000000000001e82 < y < -1.39999999999999994e-106 or 1.4500000000000001e-48 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 76.5%

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

      1. div-sub 76.5%

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

      2. sub-neg 76.5%

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

      3. *-inverses 76.5%

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

      4. metadata-eval 76.5%

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

      5. distribute-lft-in 76.5%

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

      6. metadata-eval 76.5%

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

      7. +-commutative 76.5%

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

      8. mul-1-neg 76.5%

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

      9. unsub-neg 76.5%

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

   5. Simplified 76.5%

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

   if -2.40000000000000006e124 < y < -1.2600000000000001e82

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 77.9%

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

   4. Taylor expanded in x around 0 77.9%

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

      1. neg-mul-1 77.9%

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

      2. distribute-neg-frac2 77.9%

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

   6. Simplified 77.9%

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

   if -1.39999999999999994e-106 < y < 1.4500000000000001e-48

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 79.2%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+124}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq -1.26 \cdot 10^{+82}:\\ \;\;\;\;\frac{y}{-z}\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-106} \lor \neg \left(y \leq 1.45 \cdot 10^{-48}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -3.75 \cdot 10^{+124}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -1.26 \cdot 10^{+82}:\\ \;\;\;\;\frac{y}{-z}\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-7} \lor \neg \left(y \leq 7 \cdot 10^{-46}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ x y))))
   (if (<= y -3.75e+124)
     t_0
     (if (<= y -1.26e+82)
       (/ y (- z))
       (if (or (<= y -4.4e-7) (not (<= y 7e-46))) t_0 (/ x (- z y)))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (x / y);
	double tmp;
	if (y <= -3.75e+124) {
		tmp = t_0;
	} else if (y <= -1.26e+82) {
		tmp = y / -z;
	} else if ((y <= -4.4e-7) || !(y <= 7e-46)) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 - (x / y)
    if (y <= (-3.75d+124)) then
        tmp = t_0
    else if (y <= (-1.26d+82)) then
        tmp = y / -z
    else if ((y <= (-4.4d-7)) .or. (.not. (y <= 7d-46))) then
        tmp = t_0
    else
        tmp = x / (z - y)
    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 <= -3.75e+124) {
		tmp = t_0;
	} else if (y <= -1.26e+82) {
		tmp = y / -z;
	} else if ((y <= -4.4e-7) || !(y <= 7e-46)) {
		tmp = t_0;
	} else {
		tmp = x / (z - y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (x / y)
	tmp = 0
	if y <= -3.75e+124:
		tmp = t_0
	elif y <= -1.26e+82:
		tmp = y / -z
	elif (y <= -4.4e-7) or not (y <= 7e-46):
		tmp = t_0
	else:
		tmp = x / (z - y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(x / y))
	tmp = 0.0
	if (y <= -3.75e+124)
		tmp = t_0;
	elseif (y <= -1.26e+82)
		tmp = Float64(y / Float64(-z));
	elseif ((y <= -4.4e-7) || !(y <= 7e-46))
		tmp = t_0;
	else
		tmp = Float64(x / Float64(z - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (x / y);
	tmp = 0.0;
	if (y <= -3.75e+124)
		tmp = t_0;
	elseif (y <= -1.26e+82)
		tmp = y / -z;
	elseif ((y <= -4.4e-7) || ~((y <= 7e-46)))
		tmp = t_0;
	else
		tmp = x / (z - y);
	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, -3.75e+124], t$95$0, If[LessEqual[y, -1.26e+82], N[(y / (-z)), $MachinePrecision], If[Or[LessEqual[y, -4.4e-7], N[Not[LessEqual[y, 7e-46]], $MachinePrecision]], t$95$0, N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.75000000000000019e124 or -1.2600000000000001e82 < y < -4.4000000000000002e-7 or 7.0000000000000004e-46 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 79.6%

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

      1. div-sub 79.6%

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

      2. sub-neg 79.6%

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

      3. *-inverses 79.6%

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

      4. metadata-eval 79.6%

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

      5. distribute-lft-in 79.6%

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

      6. metadata-eval 79.6%

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

      7. +-commutative 79.6%

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

      8. mul-1-neg 79.6%

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

      9. unsub-neg 79.6%

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

   5. Simplified 79.6%

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

   if -3.75000000000000019e124 < y < -1.2600000000000001e82

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 77.9%

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

   4. Taylor expanded in x around 0 77.9%

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

      1. neg-mul-1 77.9%

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

      2. distribute-neg-frac2 77.9%

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

   6. Simplified 77.9%

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

   if -4.4000000000000002e-7 < y < 7.0000000000000004e-46

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 84.9%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.75 \cdot 10^{+124}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq -1.26 \cdot 10^{+82}:\\ \;\;\;\;\frac{y}{-z}\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-7} \lor \neg \left(y \leq 7 \cdot 10^{-46}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -1.65 \cdot 10^{+128}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -900000000000:\\ \;\;\;\;\frac{y}{y - z}\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-165}:\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-42}:\\ \;\;\;\;\frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ x y))))
   (if (<= y -1.65e+128)
     t_0
     (if (<= y -900000000000.0)
       (/ y (- y z))
       (if (<= y -2.4e-165)
         (/ x (- z y))
         (if (<= y 1.25e-42) (/ (- x y) z) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (x / y);
	double tmp;
	if (y <= -1.65e+128) {
		tmp = t_0;
	} else if (y <= -900000000000.0) {
		tmp = y / (y - z);
	} else if (y <= -2.4e-165) {
		tmp = x / (z - y);
	} else if (y <= 1.25e-42) {
		tmp = (x - y) / z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 - (x / y)
    if (y <= (-1.65d+128)) then
        tmp = t_0
    else if (y <= (-900000000000.0d0)) then
        tmp = y / (y - z)
    else if (y <= (-2.4d-165)) then
        tmp = x / (z - y)
    else if (y <= 1.25d-42) then
        tmp = (x - y) / z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 - (x / y);
	double tmp;
	if (y <= -1.65e+128) {
		tmp = t_0;
	} else if (y <= -900000000000.0) {
		tmp = y / (y - z);
	} else if (y <= -2.4e-165) {
		tmp = x / (z - y);
	} else if (y <= 1.25e-42) {
		tmp = (x - y) / z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (x / y)
	tmp = 0
	if y <= -1.65e+128:
		tmp = t_0
	elif y <= -900000000000.0:
		tmp = y / (y - z)
	elif y <= -2.4e-165:
		tmp = x / (z - y)
	elif y <= 1.25e-42:
		tmp = (x - y) / z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(x / y))
	tmp = 0.0
	if (y <= -1.65e+128)
		tmp = t_0;
	elseif (y <= -900000000000.0)
		tmp = Float64(y / Float64(y - z));
	elseif (y <= -2.4e-165)
		tmp = Float64(x / Float64(z - y));
	elseif (y <= 1.25e-42)
		tmp = Float64(Float64(x - y) / z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (x / y);
	tmp = 0.0;
	if (y <= -1.65e+128)
		tmp = t_0;
	elseif (y <= -900000000000.0)
		tmp = y / (y - z);
	elseif (y <= -2.4e-165)
		tmp = x / (z - y);
	elseif (y <= 1.25e-42)
		tmp = (x - y) / z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.65e+128], t$95$0, If[LessEqual[y, -900000000000.0], N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.4e-165], N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.25e-42], N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.65e128 or 1.25000000000000001e-42 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 83.1%

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

      1. div-sub 83.1%

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

      2. sub-neg 83.1%

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

      3. *-inverses 83.1%

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

      4. metadata-eval 83.1%

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

      5. distribute-lft-in 83.1%

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

      6. metadata-eval 83.1%

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

      7. +-commutative 83.1%

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

      8. mul-1-neg 83.1%

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

      9. unsub-neg 83.1%

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

   5. Simplified 83.1%

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

   if -1.65e128 < y < -9e11

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 91.9%

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

      1. neg-mul-1 91.9%

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

      2. distribute-neg-frac 91.9%

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

   5. Simplified 91.9%

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

      1. frac-2neg 91.9%

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

      2. div-inv 91.3%

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

      3. remove-double-neg 91.3%

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

      4. sub-neg 91.3%

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

      5. distribute-neg-in 91.3%

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

      6. remove-double-neg 91.3%

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

   7. Applied egg-rr 91.3%

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

      1. associate-*r/ 91.9%

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

      2. *-rgt-identity 91.9%

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

      3. +-commutative 91.9%

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

      4. unsub-neg 91.9%

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

   9. Simplified 91.9%

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

   if -9e11 < y < -2.4000000000000002e-165

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 82.4%

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

   if -2.4000000000000002e-165 < y < 1.25000000000000001e-42

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 90.6%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+128}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq -900000000000:\\ \;\;\;\;\frac{y}{y - z}\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-165}:\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-42}:\\ \;\;\;\;\frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+124}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.26 \cdot 10^{+82}:\\ \;\;\;\;\frac{y}{-z}\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-7}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-48}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.4e+124)
   1.0
   (if (<= y -1.26e+82)
     (/ y (- z))
     (if (<= y -3.6e-7) 1.0 (if (<= y 4e-48) (/ x z) 1.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.4e+124) {
		tmp = 1.0;
	} else if (y <= -1.26e+82) {
		tmp = y / -z;
	} else if (y <= -3.6e-7) {
		tmp = 1.0;
	} else if (y <= 4e-48) {
		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 <= (-2.4d+124)) then
        tmp = 1.0d0
    else if (y <= (-1.26d+82)) then
        tmp = y / -z
    else if (y <= (-3.6d-7)) then
        tmp = 1.0d0
    else if (y <= 4d-48) 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 <= -2.4e+124) {
		tmp = 1.0;
	} else if (y <= -1.26e+82) {
		tmp = y / -z;
	} else if (y <= -3.6e-7) {
		tmp = 1.0;
	} else if (y <= 4e-48) {
		tmp = x / z;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.4e+124:
		tmp = 1.0
	elif y <= -1.26e+82:
		tmp = y / -z
	elif y <= -3.6e-7:
		tmp = 1.0
	elif y <= 4e-48:
		tmp = x / z
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.4e+124)
		tmp = 1.0;
	elseif (y <= -1.26e+82)
		tmp = Float64(y / Float64(-z));
	elseif (y <= -3.6e-7)
		tmp = 1.0;
	elseif (y <= 4e-48)
		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 <= -2.4e+124)
		tmp = 1.0;
	elseif (y <= -1.26e+82)
		tmp = y / -z;
	elseif (y <= -3.6e-7)
		tmp = 1.0;
	elseif (y <= 4e-48)
		tmp = x / z;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.4e+124], 1.0, If[LessEqual[y, -1.26e+82], N[(y / (-z)), $MachinePrecision], If[LessEqual[y, -3.6e-7], 1.0, If[LessEqual[y, 4e-48], N[(x / z), $MachinePrecision], 1.0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.40000000000000006e124 or -1.2600000000000001e82 < y < -3.59999999999999994e-7 or 3.9999999999999999e-48 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 62.1%

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

   if -2.40000000000000006e124 < y < -1.2600000000000001e82

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 77.9%

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

   4. Taylor expanded in x around 0 77.9%

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

      1. neg-mul-1 77.9%

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

      2. distribute-neg-frac2 77.9%

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

   6. Simplified 77.9%

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

   if -3.59999999999999994e-7 < y < 3.9999999999999999e-48

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 71.5%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+124}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.26 \cdot 10^{+82}:\\ \;\;\;\;\frac{y}{-z}\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-7}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-48}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -3.1 \cdot 10^{+127}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -21000000000000:\\ \;\;\;\;\frac{y}{y - z}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-50}:\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ x y))))
   (if (<= y -3.1e+127)
     t_0
     (if (<= y -21000000000000.0)
       (/ y (- y z))
       (if (<= y 2.1e-50) (/ x (- z y)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (x / y);
	double tmp;
	if (y <= -3.1e+127) {
		tmp = t_0;
	} else if (y <= -21000000000000.0) {
		tmp = y / (y - z);
	} else if (y <= 2.1e-50) {
		tmp = x / (z - y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 - (x / y)
    if (y <= (-3.1d+127)) then
        tmp = t_0
    else if (y <= (-21000000000000.0d0)) then
        tmp = y / (y - z)
    else if (y <= 2.1d-50) then
        tmp = x / (z - y)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 - (x / y);
	double tmp;
	if (y <= -3.1e+127) {
		tmp = t_0;
	} else if (y <= -21000000000000.0) {
		tmp = y / (y - z);
	} else if (y <= 2.1e-50) {
		tmp = x / (z - y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (x / y)
	tmp = 0
	if y <= -3.1e+127:
		tmp = t_0
	elif y <= -21000000000000.0:
		tmp = y / (y - z)
	elif y <= 2.1e-50:
		tmp = x / (z - y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(x / y))
	tmp = 0.0
	if (y <= -3.1e+127)
		tmp = t_0;
	elseif (y <= -21000000000000.0)
		tmp = Float64(y / Float64(y - z));
	elseif (y <= 2.1e-50)
		tmp = Float64(x / Float64(z - y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (x / y);
	tmp = 0.0;
	if (y <= -3.1e+127)
		tmp = t_0;
	elseif (y <= -21000000000000.0)
		tmp = y / (y - z);
	elseif (y <= 2.1e-50)
		tmp = x / (z - y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.1e+127], t$95$0, If[LessEqual[y, -21000000000000.0], N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.1e-50], N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.1000000000000002e127 or 2.1000000000000001e-50 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 82.4%

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

      1. div-sub 82.4%

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

      2. sub-neg 82.4%

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

      3. *-inverses 82.4%

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

      4. metadata-eval 82.4%

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

      5. distribute-lft-in 82.4%

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

      6. metadata-eval 82.4%

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

      7. +-commutative 82.4%

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

      8. mul-1-neg 82.4%

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

      9. unsub-neg 82.4%

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

   5. Simplified 82.4%

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

   if -3.1000000000000002e127 < y < -2.1e13

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 91.9%

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

      1. neg-mul-1 91.9%

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

      2. distribute-neg-frac 91.9%

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

   5. Simplified 91.9%

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

      1. frac-2neg 91.9%

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

      2. div-inv 91.3%

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

      3. remove-double-neg 91.3%

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

      4. sub-neg 91.3%

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

      5. distribute-neg-in 91.3%

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

      6. remove-double-neg 91.3%

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

   7. Applied egg-rr 91.3%

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

      1. associate-*r/ 91.9%

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

      2. *-rgt-identity 91.9%

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

      3. +-commutative 91.9%

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

      4. unsub-neg 91.9%

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

   9. Simplified 91.9%

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

   if -2.1e13 < y < 2.1000000000000001e-50

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 83.3%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+127}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq -21000000000000:\\ \;\;\;\;\frac{y}{y - z}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-50}:\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 60.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-7}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-46}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6.5e-7) 1.0 (if (<= y 1.9e-46) (/ x z) 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.5e-7) {
		tmp = 1.0;
	} else if (y <= 1.9e-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 <= (-6.5d-7)) then
        tmp = 1.0d0
    else if (y <= 1.9d-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 <= -6.5e-7) {
		tmp = 1.0;
	} else if (y <= 1.9e-46) {
		tmp = x / z;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -6.5e-7:
		tmp = 1.0
	elif y <= 1.9e-46:
		tmp = x / z
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6.5e-7)
		tmp = 1.0;
	elseif (y <= 1.9e-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 <= -6.5e-7)
		tmp = 1.0;
	elseif (y <= 1.9e-46)
		tmp = x / z;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6.5e-7], 1.0, If[LessEqual[y, 1.9e-46], N[(x / z), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -6.50000000000000024e-7 or 1.8999999999999998e-46 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 59.0%

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

   if -6.50000000000000024e-7 < y < 1.8999999999999998e-46

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 71.5%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-7}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-46}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 10: 33.8% 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 35.7%

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

4. Final simplification 35.7%

   \[\leadsto 1 \]
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 2024115 
(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)))