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

Percentage Accurate: 100.0% → 100.0%

Time: 5.9s

Alternatives: 9

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 2: 76.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{z - y}\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{+79}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-154}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{-190}:\\ \;\;\;\;\frac{x - y}{z}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-20}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ x (- z y))))
   (if (<= y -2.7e+79)
     (- 1.0 (/ x y))
     (if (<= y -2e-154)
       t_0
       (if (<= y 1.06e-190)
         (/ (- x y) z)
         (if (<= y 6.5e-20) t_0 (/ y (- y z))))))))

C

double code(double x, double y, double z) {
	double t_0 = x / (z - y);
	double tmp;
	if (y <= -2.7e+79) {
		tmp = 1.0 - (x / y);
	} else if (y <= -2e-154) {
		tmp = t_0;
	} else if (y <= 1.06e-190) {
		tmp = (x - y) / z;
	} else if (y <= 6.5e-20) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = x / (z - y)
    if (y <= (-2.7d+79)) then
        tmp = 1.0d0 - (x / y)
    else if (y <= (-2d-154)) then
        tmp = t_0
    else if (y <= 1.06d-190) then
        tmp = (x - y) / z
    else if (y <= 6.5d-20) then
        tmp = t_0
    else
        tmp = y / (y - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x / (z - y);
	double tmp;
	if (y <= -2.7e+79) {
		tmp = 1.0 - (x / y);
	} else if (y <= -2e-154) {
		tmp = t_0;
	} else if (y <= 1.06e-190) {
		tmp = (x - y) / z;
	} else if (y <= 6.5e-20) {
		tmp = t_0;
	} else {
		tmp = y / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x / (z - y)
	tmp = 0
	if y <= -2.7e+79:
		tmp = 1.0 - (x / y)
	elif y <= -2e-154:
		tmp = t_0
	elif y <= 1.06e-190:
		tmp = (x - y) / z
	elif y <= 6.5e-20:
		tmp = t_0
	else:
		tmp = y / (y - z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x / Float64(z - y))
	tmp = 0.0
	if (y <= -2.7e+79)
		tmp = Float64(1.0 - Float64(x / y));
	elseif (y <= -2e-154)
		tmp = t_0;
	elseif (y <= 1.06e-190)
		tmp = Float64(Float64(x - y) / z);
	elseif (y <= 6.5e-20)
		tmp = t_0;
	else
		tmp = Float64(y / Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x / (z - y);
	tmp = 0.0;
	if (y <= -2.7e+79)
		tmp = 1.0 - (x / y);
	elseif (y <= -2e-154)
		tmp = t_0;
	elseif (y <= 1.06e-190)
		tmp = (x - y) / z;
	elseif (y <= 6.5e-20)
		tmp = t_0;
	else
		tmp = y / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.7e+79], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2e-154], t$95$0, If[LessEqual[y, 1.06e-190], N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 6.5e-20], t$95$0, N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.7e79

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 90.7%

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

      1. div-sub 90.7%

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

      2. sub-neg 90.7%

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

      3. *-inverses 90.7%

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

      4. metadata-eval 90.7%

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

      5. distribute-lft-in 90.7%

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

      6. metadata-eval 90.7%

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

      7. +-commutative 90.7%

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

      8. mul-1-neg 90.7%

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

      9. unsub-neg 90.7%

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

   5. Simplified 90.7%

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

   if -2.7e79 < y < -1.9999999999999999e-154 or 1.05999999999999997e-190 < y < 6.50000000000000032e-20

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 75.1%

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

   if -1.9999999999999999e-154 < y < 1.05999999999999997e-190

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 92.0%

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

   if 6.50000000000000032e-20 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 79.8%

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

      1. neg-mul-1 79.8%

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

      2. distribute-neg-frac 79.8%

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

   5. Simplified 79.8%

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

      1. frac-2neg 79.8%

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

      2. div-inv 79.7%

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

      3. remove-double-neg 79.7%

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

      4. sub-neg 79.7%

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

      5. distribute-neg-in 79.7%

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

      6. neg-mul-1 79.7%

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

      7. remove-double-neg 79.7%

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

      8. fma-define 79.7%

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

   7. Applied egg-rr 79.7%

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

      1. associate-*r/ 79.8%

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

      2. *-rgt-identity 79.8%

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

      3. fma-undefine 79.8%

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

      4. neg-mul-1 79.8%

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

      5. +-commutative 79.8%

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

      6. unsub-neg 79.8%

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

   9. Simplified 79.8%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+79}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-154}:\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{-190}:\\ \;\;\;\;\frac{x - y}{z}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-20}:\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{z - y}\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{+79}:\\ \;\;\;\;1 + \frac{z - x}{y}\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-154}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-189}:\\ \;\;\;\;\frac{x - y}{z}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-20}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ x (- z y))))
   (if (<= y -2.7e+79)
     (+ 1.0 (/ (- z x) y))
     (if (<= y -2.05e-154)
       t_0
       (if (<= y 1.25e-189)
         (/ (- x y) z)
         (if (<= y 1.25e-20) t_0 (/ y (- y z))))))))

C

double code(double x, double y, double z) {
	double t_0 = x / (z - y);
	double tmp;
	if (y <= -2.7e+79) {
		tmp = 1.0 + ((z - x) / y);
	} else if (y <= -2.05e-154) {
		tmp = t_0;
	} else if (y <= 1.25e-189) {
		tmp = (x - y) / z;
	} else if (y <= 1.25e-20) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = x / (z - y)
    if (y <= (-2.7d+79)) then
        tmp = 1.0d0 + ((z - x) / y)
    else if (y <= (-2.05d-154)) then
        tmp = t_0
    else if (y <= 1.25d-189) then
        tmp = (x - y) / z
    else if (y <= 1.25d-20) then
        tmp = t_0
    else
        tmp = y / (y - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x / (z - y);
	double tmp;
	if (y <= -2.7e+79) {
		tmp = 1.0 + ((z - x) / y);
	} else if (y <= -2.05e-154) {
		tmp = t_0;
	} else if (y <= 1.25e-189) {
		tmp = (x - y) / z;
	} else if (y <= 1.25e-20) {
		tmp = t_0;
	} else {
		tmp = y / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x / (z - y)
	tmp = 0
	if y <= -2.7e+79:
		tmp = 1.0 + ((z - x) / y)
	elif y <= -2.05e-154:
		tmp = t_0
	elif y <= 1.25e-189:
		tmp = (x - y) / z
	elif y <= 1.25e-20:
		tmp = t_0
	else:
		tmp = y / (y - z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x / Float64(z - y))
	tmp = 0.0
	if (y <= -2.7e+79)
		tmp = Float64(1.0 + Float64(Float64(z - x) / y));
	elseif (y <= -2.05e-154)
		tmp = t_0;
	elseif (y <= 1.25e-189)
		tmp = Float64(Float64(x - y) / z);
	elseif (y <= 1.25e-20)
		tmp = t_0;
	else
		tmp = Float64(y / Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x / (z - y);
	tmp = 0.0;
	if (y <= -2.7e+79)
		tmp = 1.0 + ((z - x) / y);
	elseif (y <= -2.05e-154)
		tmp = t_0;
	elseif (y <= 1.25e-189)
		tmp = (x - y) / z;
	elseif (y <= 1.25e-20)
		tmp = t_0;
	else
		tmp = y / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.7e+79], N[(1.0 + N[(N[(z - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.05e-154], t$95$0, If[LessEqual[y, 1.25e-189], N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 1.25e-20], t$95$0, N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.7e79

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 90.8%

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

      1. associate-+r- 90.8%

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

      2. distribute-lft-out-- 90.8%

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

      3. div-sub 90.8%

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

      4. mul-1-neg 90.8%

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

      5. unsub-neg 90.8%

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

   5. Simplified 90.8%

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

   if -2.7e79 < y < -2.05e-154 or 1.2499999999999999e-189 < y < 1.25e-20

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 75.1%

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

   if -2.05e-154 < y < 1.2499999999999999e-189

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 92.0%

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

   if 1.25e-20 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 79.8%

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

      1. neg-mul-1 79.8%

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

      2. distribute-neg-frac 79.8%

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

   5. Simplified 79.8%

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

      1. frac-2neg 79.8%

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

      2. div-inv 79.7%

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

      3. remove-double-neg 79.7%

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

      4. sub-neg 79.7%

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

      5. distribute-neg-in 79.7%

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

      6. neg-mul-1 79.7%

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

      7. remove-double-neg 79.7%

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

      8. fma-define 79.7%

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

   7. Applied egg-rr 79.7%

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

      1. associate-*r/ 79.8%

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

      2. *-rgt-identity 79.8%

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

      3. fma-undefine 79.8%

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

      4. neg-mul-1 79.8%

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

      5. +-commutative 79.8%

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

      6. unsub-neg 79.8%

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

   9. Simplified 79.8%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+79}:\\ \;\;\;\;1 + \frac{z - x}{y}\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-154}:\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-189}:\\ \;\;\;\;\frac{x - y}{z}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-20}:\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 70.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-14} \lor \neg \left(y \leq 1.28 \cdot 10^{-43}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.4e-14) (not (<= y 1.28e-43))) (- 1.0 (/ x y)) (/ x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.4e-14) || !(y <= 1.28e-43)) {
		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 <= (-1.4d-14)) .or. (.not. (y <= 1.28d-43))) 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 <= -1.4e-14) || !(y <= 1.28e-43)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.4e-14) or not (y <= 1.28e-43):
		tmp = 1.0 - (x / y)
	else:
		tmp = x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.4e-14) || !(y <= 1.28e-43))
		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 <= -1.4e-14) || ~((y <= 1.28e-43)))
		tmp = 1.0 - (x / y);
	else
		tmp = x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.4e-14], N[Not[LessEqual[y, 1.28e-43]], $MachinePrecision]], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4e-14 or 1.27999999999999998e-43 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 80.2%

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

      1. div-sub 80.2%

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

      2. sub-neg 80.2%

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

      3. *-inverses 80.2%

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

      4. metadata-eval 80.2%

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

      5. distribute-lft-in 80.2%

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

      6. metadata-eval 80.2%

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

      7. +-commutative 80.2%

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

      8. mul-1-neg 80.2%

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

      9. unsub-neg 80.2%

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

   5. Simplified 80.2%

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

   if -1.4e-14 < y < 1.27999999999999998e-43

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 69.7%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-14} \lor \neg \left(y \leq 1.28 \cdot 10^{-43}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+79} \lor \neg \left(y \leq 7.5 \cdot 10^{-11}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.7e+79) (not (<= y 7.5e-11))) (- 1.0 (/ x y)) (/ x (- z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.7e+79) || !(y <= 7.5e-11)) {
		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 <= (-2.7d+79)) .or. (.not. (y <= 7.5d-11))) 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 <= -2.7e+79) || !(y <= 7.5e-11)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x / (z - y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.7e+79) or not (y <= 7.5e-11):
		tmp = 1.0 - (x / y)
	else:
		tmp = x / (z - y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.7e+79) || !(y <= 7.5e-11))
		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 <= -2.7e+79) || ~((y <= 7.5e-11)))
		tmp = 1.0 - (x / y);
	else
		tmp = x / (z - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.7e+79], N[Not[LessEqual[y, 7.5e-11]], $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 < -2.7e79 or 7.5e-11 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 84.8%

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

      1. div-sub 84.8%

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

      2. sub-neg 84.8%

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

      3. *-inverses 84.8%

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

      4. metadata-eval 84.8%

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

      5. distribute-lft-in 84.8%

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

      6. metadata-eval 84.8%

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

      7. +-commutative 84.8%

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

      8. mul-1-neg 84.8%

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

      9. unsub-neg 84.8%

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

   5. Simplified 84.8%

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

   if -2.7e79 < y < 7.5e-11

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 78.4%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+79} \lor \neg \left(y \leq 7.5 \cdot 10^{-11}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+79}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-13}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.7e+79) 1.0 (if (<= y 1.4e-13) (/ x z) (+ 1.0 (/ z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.7e+79) {
		tmp = 1.0;
	} else if (y <= 1.4e-13) {
		tmp = x / z;
	} else {
		tmp = 1.0 + (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 <= (-2.7d+79)) then
        tmp = 1.0d0
    else if (y <= 1.4d-13) then
        tmp = x / z
    else
        tmp = 1.0d0 + (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.7e+79) {
		tmp = 1.0;
	} else if (y <= 1.4e-13) {
		tmp = x / z;
	} else {
		tmp = 1.0 + (z / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.7e+79:
		tmp = 1.0
	elif y <= 1.4e-13:
		tmp = x / z
	else:
		tmp = 1.0 + (z / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.7e+79)
		tmp = 1.0;
	elseif (y <= 1.4e-13)
		tmp = Float64(x / z);
	else
		tmp = Float64(1.0 + Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.7e+79)
		tmp = 1.0;
	elseif (y <= 1.4e-13)
		tmp = x / z;
	else
		tmp = 1.0 + (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.7e+79], 1.0, If[LessEqual[y, 1.4e-13], N[(x / z), $MachinePrecision], N[(1.0 + N[(z / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.7e79

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 75.3%

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

   if -2.7e79 < y < 1.4000000000000001e-13

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 61.6%

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

   if 1.4000000000000001e-13 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 80.8%

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

      1. associate-+r- 80.8%

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

      2. distribute-lft-out-- 80.8%

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

      3. div-sub 80.8%

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

      4. mul-1-neg 80.8%

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

      5. unsub-neg 80.8%

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

   5. Simplified 80.8%

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

   6. Taylor expanded in x around 0 68.6%

      \[\leadsto \color{blue}{1 + \frac{z}{y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+79}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-13}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+79}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-21}:\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.7e+79)
   (- 1.0 (/ x y))
   (if (<= y 3e-21) (/ x (- z y)) (/ y (- y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.7e+79) {
		tmp = 1.0 - (x / y);
	} else if (y <= 3e-21) {
		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 (y <= (-2.7d+79)) then
        tmp = 1.0d0 - (x / y)
    else if (y <= 3d-21) 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 (y <= -2.7e+79) {
		tmp = 1.0 - (x / y);
	} else if (y <= 3e-21) {
		tmp = x / (z - y);
	} else {
		tmp = y / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.7e+79:
		tmp = 1.0 - (x / y)
	elif y <= 3e-21:
		tmp = x / (z - y)
	else:
		tmp = y / (y - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.7e+79)
		tmp = Float64(1.0 - Float64(x / y));
	elseif (y <= 3e-21)
		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 (y <= -2.7e+79)
		tmp = 1.0 - (x / y);
	elseif (y <= 3e-21)
		tmp = x / (z - y);
	else
		tmp = y / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.7e+79], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3e-21], N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision], N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.7e79

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 90.7%

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

      1. div-sub 90.7%

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

      2. sub-neg 90.7%

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

      3. *-inverses 90.7%

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

      4. metadata-eval 90.7%

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

      5. distribute-lft-in 90.7%

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

      6. metadata-eval 90.7%

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

      7. +-commutative 90.7%

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

      8. mul-1-neg 90.7%

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

      9. unsub-neg 90.7%

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

   5. Simplified 90.7%

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

   if -2.7e79 < y < 2.99999999999999991e-21

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 78.9%

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

   if 2.99999999999999991e-21 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 79.8%

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

      1. neg-mul-1 79.8%

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

      2. distribute-neg-frac 79.8%

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

   5. Simplified 79.8%

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

      1. frac-2neg 79.8%

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

      2. div-inv 79.7%

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

      3. remove-double-neg 79.7%

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

      4. sub-neg 79.7%

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

      5. distribute-neg-in 79.7%

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

      6. neg-mul-1 79.7%

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

      7. remove-double-neg 79.7%

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

      8. fma-define 79.7%

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

   7. Applied egg-rr 79.7%

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

      1. associate-*r/ 79.8%

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

      2. *-rgt-identity 79.8%

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

      3. fma-undefine 79.8%

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

      4. neg-mul-1 79.8%

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

      5. +-commutative 79.8%

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

      6. unsub-neg 79.8%

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

   9. Simplified 79.8%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+79}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-21}:\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 60.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+79}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{-18}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.7e+79) 1.0 (if (<= y 1.18e-18) (/ x z) 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.7e+79) {
		tmp = 1.0;
	} else if (y <= 1.18e-18) {
		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 <= (-2.7d+79)) then
        tmp = 1.0d0
    else if (y <= 1.18d-18) 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 <= -2.7e+79) {
		tmp = 1.0;
	} else if (y <= 1.18e-18) {
		tmp = x / z;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.7e+79:
		tmp = 1.0
	elif y <= 1.18e-18:
		tmp = x / z
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.7e+79)
		tmp = 1.0;
	elseif (y <= 1.18e-18)
		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 <= -2.7e+79)
		tmp = 1.0;
	elseif (y <= 1.18e-18)
		tmp = x / z;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.7e+79], 1.0, If[LessEqual[y, 1.18e-18], N[(x / z), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -2.7e79 or 1.18000000000000008e-18 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 71.2%

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

   if -2.7e79 < y < 1.18000000000000008e-18

   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 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+79}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{-18}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 34.4% 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 39.2%

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

4. Final simplification 39.2%

   \[\leadsto 1 \]
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 2024130 
(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)))