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

Percentage Accurate: 100.0% → 100.0%

Time: 5.3s

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: 59.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+93}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{+32}:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-22}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 10^{-49}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 950000000000 \lor \neg \left(y \leq 3.5 \cdot 10^{+79}\right) \land y \leq 1.55 \cdot 10^{+152}:\\ \;\;\;\;\frac{y}{-z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.4e+93)
   1.0
   (if (<= y -2.5e+32)
     (/ x (- y))
     (if (<= y -3.6e-22)
       1.0
       (if (<= y 1e-49)
         (/ x z)
         (if (or (<= y 950000000000.0)
                 (and (not (<= y 3.5e+79)) (<= y 1.55e+152)))
           (/ y (- z))
           1.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.4e+93) {
		tmp = 1.0;
	} else if (y <= -2.5e+32) {
		tmp = x / -y;
	} else if (y <= -3.6e-22) {
		tmp = 1.0;
	} else if (y <= 1e-49) {
		tmp = x / z;
	} else if ((y <= 950000000000.0) || (!(y <= 3.5e+79) && (y <= 1.55e+152))) {
		tmp = y / -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 <= (-3.4d+93)) then
        tmp = 1.0d0
    else if (y <= (-2.5d+32)) then
        tmp = x / -y
    else if (y <= (-3.6d-22)) then
        tmp = 1.0d0
    else if (y <= 1d-49) then
        tmp = x / z
    else if ((y <= 950000000000.0d0) .or. (.not. (y <= 3.5d+79)) .and. (y <= 1.55d+152)) then
        tmp = y / -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 <= -3.4e+93) {
		tmp = 1.0;
	} else if (y <= -2.5e+32) {
		tmp = x / -y;
	} else if (y <= -3.6e-22) {
		tmp = 1.0;
	} else if (y <= 1e-49) {
		tmp = x / z;
	} else if ((y <= 950000000000.0) || (!(y <= 3.5e+79) && (y <= 1.55e+152))) {
		tmp = y / -z;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.4e+93:
		tmp = 1.0
	elif y <= -2.5e+32:
		tmp = x / -y
	elif y <= -3.6e-22:
		tmp = 1.0
	elif y <= 1e-49:
		tmp = x / z
	elif (y <= 950000000000.0) or (not (y <= 3.5e+79) and (y <= 1.55e+152)):
		tmp = y / -z
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.4e+93)
		tmp = 1.0;
	elseif (y <= -2.5e+32)
		tmp = Float64(x / Float64(-y));
	elseif (y <= -3.6e-22)
		tmp = 1.0;
	elseif (y <= 1e-49)
		tmp = Float64(x / z);
	elseif ((y <= 950000000000.0) || (!(y <= 3.5e+79) && (y <= 1.55e+152)))
		tmp = Float64(y / Float64(-z));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.4e+93)
		tmp = 1.0;
	elseif (y <= -2.5e+32)
		tmp = x / -y;
	elseif (y <= -3.6e-22)
		tmp = 1.0;
	elseif (y <= 1e-49)
		tmp = x / z;
	elseif ((y <= 950000000000.0) || (~((y <= 3.5e+79)) && (y <= 1.55e+152)))
		tmp = y / -z;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.4e+93], 1.0, If[LessEqual[y, -2.5e+32], N[(x / (-y)), $MachinePrecision], If[LessEqual[y, -3.6e-22], 1.0, If[LessEqual[y, 1e-49], N[(x / z), $MachinePrecision], If[Or[LessEqual[y, 950000000000.0], And[N[Not[LessEqual[y, 3.5e+79]], $MachinePrecision], LessEqual[y, 1.55e+152]]], N[(y / (-z)), $MachinePrecision], 1.0]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.4e93 or -2.4999999999999999e32 < y < -3.5999999999999998e-22 or 9.5e11 < y < 3.4999999999999998e79 or 1.55e152 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 73.3%

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

   if -3.4e93 < y < -2.4999999999999999e32

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 87.7%

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

   4. Taylor expanded in z around 0 72.9%

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

      1. associate-*r/ 72.9%

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

      2. neg-mul-1 72.9%

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

   6. Simplified 72.9%

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

   if -3.5999999999999998e-22 < y < 9.99999999999999936e-50

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 76.7%

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

   if 9.99999999999999936e-50 < y < 9.5e11 or 3.4999999999999998e79 < y < 1.55e152

   1. Initial program 100.0%

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

      1. clear-num 99.7%

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

      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. Taylor expanded in z around inf 63.0%

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

   6. Taylor expanded in x around 0 55.1%

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

      1. neg-mul-1 55.1%

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

      2. distribute-neg-frac 55.1%

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

   8. Simplified 55.1%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+93}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{+32}:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-22}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 10^{-49}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 950000000000 \lor \neg \left(y \leq 3.5 \cdot 10^{+79}\right) \land y \leq 1.55 \cdot 10^{+152}:\\ \;\;\;\;\frac{y}{-z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 61.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{-y}\\ \mathbf{if}\;y \leq -3.4 \cdot 10^{+93}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{+33}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -2.55 \cdot 10^{-22}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-49}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 44000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+26}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ x (- y))))
   (if (<= y -3.4e+93)
     1.0
     (if (<= y -1.25e+33)
       t_0
       (if (<= y -2.55e-22)
         1.0
         (if (<= y 1.65e-49)
           (/ x z)
           (if (<= y 44000.0) t_0 (if (<= y 1.2e+26) (/ x z) 1.0))))))))

C

double code(double x, double y, double z) {
	double t_0 = x / -y;
	double tmp;
	if (y <= -3.4e+93) {
		tmp = 1.0;
	} else if (y <= -1.25e+33) {
		tmp = t_0;
	} else if (y <= -2.55e-22) {
		tmp = 1.0;
	} else if (y <= 1.65e-49) {
		tmp = x / z;
	} else if (y <= 44000.0) {
		tmp = t_0;
	} else if (y <= 1.2e+26) {
		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) :: t_0
    real(8) :: tmp
    t_0 = x / -y
    if (y <= (-3.4d+93)) then
        tmp = 1.0d0
    else if (y <= (-1.25d+33)) then
        tmp = t_0
    else if (y <= (-2.55d-22)) then
        tmp = 1.0d0
    else if (y <= 1.65d-49) then
        tmp = x / z
    else if (y <= 44000.0d0) then
        tmp = t_0
    else if (y <= 1.2d+26) 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 t_0 = x / -y;
	double tmp;
	if (y <= -3.4e+93) {
		tmp = 1.0;
	} else if (y <= -1.25e+33) {
		tmp = t_0;
	} else if (y <= -2.55e-22) {
		tmp = 1.0;
	} else if (y <= 1.65e-49) {
		tmp = x / z;
	} else if (y <= 44000.0) {
		tmp = t_0;
	} else if (y <= 1.2e+26) {
		tmp = x / z;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x / -y
	tmp = 0
	if y <= -3.4e+93:
		tmp = 1.0
	elif y <= -1.25e+33:
		tmp = t_0
	elif y <= -2.55e-22:
		tmp = 1.0
	elif y <= 1.65e-49:
		tmp = x / z
	elif y <= 44000.0:
		tmp = t_0
	elif y <= 1.2e+26:
		tmp = x / z
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x / Float64(-y))
	tmp = 0.0
	if (y <= -3.4e+93)
		tmp = 1.0;
	elseif (y <= -1.25e+33)
		tmp = t_0;
	elseif (y <= -2.55e-22)
		tmp = 1.0;
	elseif (y <= 1.65e-49)
		tmp = Float64(x / z);
	elseif (y <= 44000.0)
		tmp = t_0;
	elseif (y <= 1.2e+26)
		tmp = Float64(x / z);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x / -y;
	tmp = 0.0;
	if (y <= -3.4e+93)
		tmp = 1.0;
	elseif (y <= -1.25e+33)
		tmp = t_0;
	elseif (y <= -2.55e-22)
		tmp = 1.0;
	elseif (y <= 1.65e-49)
		tmp = x / z;
	elseif (y <= 44000.0)
		tmp = t_0;
	elseif (y <= 1.2e+26)
		tmp = x / z;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x / (-y)), $MachinePrecision]}, If[LessEqual[y, -3.4e+93], 1.0, If[LessEqual[y, -1.25e+33], t$95$0, If[LessEqual[y, -2.55e-22], 1.0, If[LessEqual[y, 1.65e-49], N[(x / z), $MachinePrecision], If[LessEqual[y, 44000.0], t$95$0, If[LessEqual[y, 1.2e+26], N[(x / z), $MachinePrecision], 1.0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.4e93 or -1.24999999999999993e33 < y < -2.55000000000000011e-22 or 1.20000000000000002e26 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 66.6%

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

   if -3.4e93 < y < -1.24999999999999993e33 or 1.65e-49 < y < 44000

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 60.3%

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

   4. Taylor expanded in z around 0 52.6%

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

      1. associate-*r/ 52.6%

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

      2. neg-mul-1 52.6%

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

   6. Simplified 52.6%

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

   if -2.55000000000000011e-22 < y < 1.65e-49 or 44000 < y < 1.20000000000000002e26

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 75.1%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+93}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{+33}:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{elif}\;y \leq -2.55 \cdot 10^{-22}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-49}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 44000:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+26}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 68.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -1.12 \cdot 10^{-23}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-56}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+79} \lor \neg \left(y \leq 1.35 \cdot 10^{+152}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{-z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ x y))))
   (if (<= y -1.12e-23)
     t_0
     (if (<= y 3.5e-56)
       (/ x z)
       (if (or (<= y 6e+79) (not (<= y 1.35e+152))) t_0 (/ y (- z)))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (x / y);
	double tmp;
	if (y <= -1.12e-23) {
		tmp = t_0;
	} else if (y <= 3.5e-56) {
		tmp = x / z;
	} else if ((y <= 6e+79) || !(y <= 1.35e+152)) {
		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 <= (-1.12d-23)) then
        tmp = t_0
    else if (y <= 3.5d-56) then
        tmp = x / z
    else if ((y <= 6d+79) .or. (.not. (y <= 1.35d+152))) 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 <= -1.12e-23) {
		tmp = t_0;
	} else if (y <= 3.5e-56) {
		tmp = x / z;
	} else if ((y <= 6e+79) || !(y <= 1.35e+152)) {
		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 <= -1.12e-23:
		tmp = t_0
	elif y <= 3.5e-56:
		tmp = x / z
	elif (y <= 6e+79) or not (y <= 1.35e+152):
		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 <= -1.12e-23)
		tmp = t_0;
	elseif (y <= 3.5e-56)
		tmp = Float64(x / z);
	elseif ((y <= 6e+79) || !(y <= 1.35e+152))
		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 <= -1.12e-23)
		tmp = t_0;
	elseif (y <= 3.5e-56)
		tmp = x / z;
	elseif ((y <= 6e+79) || ~((y <= 1.35e+152)))
		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, -1.12e-23], t$95$0, If[LessEqual[y, 3.5e-56], N[(x / z), $MachinePrecision], If[Or[LessEqual[y, 6e+79], N[Not[LessEqual[y, 1.35e+152]], $MachinePrecision]], t$95$0, N[(y / (-z)), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.1200000000000001e-23 or 3.4999999999999998e-56 < y < 5.99999999999999948e79 or 1.35000000000000007e152 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 82.2%

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

      1. div-sub 82.2%

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

      2. sub-neg 82.2%

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

      3. *-inverses 82.2%

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

      4. metadata-eval 82.2%

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

      5. distribute-lft-in 82.2%

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

      6. metadata-eval 82.2%

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

      7. +-commutative 82.2%

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

      8. mul-1-neg 82.2%

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

      9. unsub-neg 82.2%

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

   5. Simplified 82.2%

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

   if -1.1200000000000001e-23 < y < 3.4999999999999998e-56

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 77.3%

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

   if 5.99999999999999948e79 < y < 1.35000000000000007e152

   1. Initial program 100.0%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in z around inf 71.1%

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

   6. Taylor expanded in x around 0 65.2%

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

      1. neg-mul-1 65.2%

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

      2. distribute-neg-frac 65.2%

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

   8. Simplified 65.2%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{-23}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-56}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+79} \lor \neg \left(y \leq 1.35 \cdot 10^{+152}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{-z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -8 \cdot 10^{-19}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{-51}:\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+79} \lor \neg \left(y \leq 1.35 \cdot 10^{+152}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{-z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ x y))))
   (if (<= y -8e-19)
     t_0
     (if (<= y 2.45e-51)
       (/ x (- z y))
       (if (or (<= y 6e+79) (not (<= y 1.35e+152))) t_0 (/ y (- z)))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (x / y);
	double tmp;
	if (y <= -8e-19) {
		tmp = t_0;
	} else if (y <= 2.45e-51) {
		tmp = x / (z - y);
	} else if ((y <= 6e+79) || !(y <= 1.35e+152)) {
		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 <= (-8d-19)) then
        tmp = t_0
    else if (y <= 2.45d-51) then
        tmp = x / (z - y)
    else if ((y <= 6d+79) .or. (.not. (y <= 1.35d+152))) 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 <= -8e-19) {
		tmp = t_0;
	} else if (y <= 2.45e-51) {
		tmp = x / (z - y);
	} else if ((y <= 6e+79) || !(y <= 1.35e+152)) {
		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 <= -8e-19:
		tmp = t_0
	elif y <= 2.45e-51:
		tmp = x / (z - y)
	elif (y <= 6e+79) or not (y <= 1.35e+152):
		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 <= -8e-19)
		tmp = t_0;
	elseif (y <= 2.45e-51)
		tmp = Float64(x / Float64(z - y));
	elseif ((y <= 6e+79) || !(y <= 1.35e+152))
		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 <= -8e-19)
		tmp = t_0;
	elseif (y <= 2.45e-51)
		tmp = x / (z - y);
	elseif ((y <= 6e+79) || ~((y <= 1.35e+152)))
		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, -8e-19], t$95$0, If[LessEqual[y, 2.45e-51], N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 6e+79], N[Not[LessEqual[y, 1.35e+152]], $MachinePrecision]], t$95$0, N[(y / (-z)), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.9999999999999998e-19 or 2.44999999999999987e-51 < y < 5.99999999999999948e79 or 1.35000000000000007e152 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 82.0%

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

      1. div-sub 82.1%

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

      2. sub-neg 82.1%

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

      3. *-inverses 82.1%

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

      4. metadata-eval 82.1%

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

      5. distribute-lft-in 82.1%

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

      6. metadata-eval 82.1%

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

      7. +-commutative 82.1%

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

      8. mul-1-neg 82.1%

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

      9. unsub-neg 82.1%

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

   5. Simplified 82.1%

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

   if -7.9999999999999998e-19 < y < 2.44999999999999987e-51

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 84.6%

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

   if 5.99999999999999948e79 < y < 1.35000000000000007e152

   1. Initial program 100.0%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in z around inf 71.1%

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

   6. Taylor expanded in x around 0 65.2%

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

      1. neg-mul-1 65.2%

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

      2. distribute-neg-frac 65.2%

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

   8. Simplified 65.2%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-19}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{-51}:\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+79} \lor \neg \left(y \leq 1.35 \cdot 10^{+152}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{-z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -3 \cdot 10^{-19}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-99}:\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+152}:\\ \;\;\;\;\frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ x y))))
   (if (<= y -3e-19)
     t_0
     (if (<= y 5.6e-99)
       (/ x (- z y))
       (if (<= y 2.5e+152) (/ y (- y z)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (x / y);
	double tmp;
	if (y <= -3e-19) {
		tmp = t_0;
	} else if (y <= 5.6e-99) {
		tmp = x / (z - y);
	} else if (y <= 2.5e+152) {
		tmp = y / (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 <= (-3d-19)) then
        tmp = t_0
    else if (y <= 5.6d-99) then
        tmp = x / (z - y)
    else if (y <= 2.5d+152) then
        tmp = y / (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 <= -3e-19) {
		tmp = t_0;
	} else if (y <= 5.6e-99) {
		tmp = x / (z - y);
	} else if (y <= 2.5e+152) {
		tmp = y / (y - z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (x / y)
	tmp = 0
	if y <= -3e-19:
		tmp = t_0
	elif y <= 5.6e-99:
		tmp = x / (z - y)
	elif y <= 2.5e+152:
		tmp = y / (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 <= -3e-19)
		tmp = t_0;
	elseif (y <= 5.6e-99)
		tmp = Float64(x / Float64(z - y));
	elseif (y <= 2.5e+152)
		tmp = Float64(y / 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 <= -3e-19)
		tmp = t_0;
	elseif (y <= 5.6e-99)
		tmp = x / (z - y);
	elseif (y <= 2.5e+152)
		tmp = y / (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, -3e-19], t$95$0, If[LessEqual[y, 5.6e-99], N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e+152], N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.99999999999999993e-19 or 2.5e152 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 87.8%

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

      1. div-sub 87.8%

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

      2. sub-neg 87.8%

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

      3. *-inverses 87.8%

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

      4. metadata-eval 87.8%

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

      5. distribute-lft-in 87.8%

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

      6. metadata-eval 87.8%

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

      7. +-commutative 87.8%

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

      8. mul-1-neg 87.8%

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

      9. unsub-neg 87.8%

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

   5. Simplified 87.8%

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

   if -2.99999999999999993e-19 < y < 5.6000000000000001e-99

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 87.0%

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

   if 5.6000000000000001e-99 < y < 2.5e152

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 70.2%

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

      1. neg-mul-1 70.2%

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

      2. distribute-neg-frac 70.2%

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

   5. Simplified 70.2%

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

      1. frac-2neg 70.2%

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

      2. div-inv 69.9%

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

      3. remove-double-neg 69.9%

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

      4. sub-neg 69.9%

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

      5. distribute-neg-in 69.9%

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

      6. remove-double-neg 69.9%

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

   7. Applied egg-rr 69.9%

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

      1. associate-*r/ 70.2%

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

      2. *-rgt-identity 70.2%

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

      3. +-commutative 70.2%

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

      4. unsub-neg 70.2%

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

   9. Simplified 70.2%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-19}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-99}:\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+152}:\\ \;\;\;\;\frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -2.35 \cdot 10^{-23}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-51}:\\ \;\;\;\;\frac{x - y}{z}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+152}:\\ \;\;\;\;\frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ x y))))
   (if (<= y -2.35e-23)
     t_0
     (if (<= y 1.22e-51)
       (/ (- x y) z)
       (if (<= y 2.4e+152) (/ y (- y z)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (x / y);
	double tmp;
	if (y <= -2.35e-23) {
		tmp = t_0;
	} else if (y <= 1.22e-51) {
		tmp = (x - y) / z;
	} else if (y <= 2.4e+152) {
		tmp = y / (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 <= (-2.35d-23)) then
        tmp = t_0
    else if (y <= 1.22d-51) then
        tmp = (x - y) / z
    else if (y <= 2.4d+152) then
        tmp = y / (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 <= -2.35e-23) {
		tmp = t_0;
	} else if (y <= 1.22e-51) {
		tmp = (x - y) / z;
	} else if (y <= 2.4e+152) {
		tmp = y / (y - z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (x / y)
	tmp = 0
	if y <= -2.35e-23:
		tmp = t_0
	elif y <= 1.22e-51:
		tmp = (x - y) / z
	elif y <= 2.4e+152:
		tmp = y / (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 <= -2.35e-23)
		tmp = t_0;
	elseif (y <= 1.22e-51)
		tmp = Float64(Float64(x - y) / z);
	elseif (y <= 2.4e+152)
		tmp = Float64(y / 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 <= -2.35e-23)
		tmp = t_0;
	elseif (y <= 1.22e-51)
		tmp = (x - y) / z;
	elseif (y <= 2.4e+152)
		tmp = y / (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, -2.35e-23], t$95$0, If[LessEqual[y, 1.22e-51], N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 2.4e+152], N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.35e-23 or 2.3999999999999999e152 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 87.9%

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

      1. div-sub 87.9%

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

      2. sub-neg 87.9%

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

      3. *-inverses 87.9%

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

      4. metadata-eval 87.9%

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

      5. distribute-lft-in 87.9%

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

      6. metadata-eval 87.9%

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

      7. +-commutative 87.9%

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

      8. mul-1-neg 87.9%

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

      9. unsub-neg 87.9%

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

   5. Simplified 87.9%

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

   if -2.35e-23 < y < 1.21999999999999998e-51

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 87.5%

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

   if 1.21999999999999998e-51 < y < 2.3999999999999999e152

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 71.2%

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

      1. neg-mul-1 71.2%

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

      2. distribute-neg-frac 71.2%

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

   5. Simplified 71.2%

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

      1. frac-2neg 71.2%

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

      2. div-inv 70.9%

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

      3. remove-double-neg 70.9%

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

      4. sub-neg 70.9%

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

      5. distribute-neg-in 70.9%

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

      6. remove-double-neg 70.9%

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

   7. Applied egg-rr 70.9%

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

      1. associate-*r/ 71.2%

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

      2. *-rgt-identity 71.2%

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

      3. +-commutative 71.2%

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

      4. unsub-neg 71.2%

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

   9. Simplified 71.2%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{-23}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-51}:\\ \;\;\;\;\frac{x - y}{z}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+152}:\\ \;\;\;\;\frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.95 \cdot 10^{-22}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-51}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.95e-22) 1.0 (if (<= y 2.1e-51) (/ x z) 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.95e-22) {
		tmp = 1.0;
	} else if (y <= 2.1e-51) {
		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 <= (-3.95d-22)) then
        tmp = 1.0d0
    else if (y <= 2.1d-51) 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 <= -3.95e-22) {
		tmp = 1.0;
	} else if (y <= 2.1e-51) {
		tmp = x / z;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.95e-22:
		tmp = 1.0
	elif y <= 2.1e-51:
		tmp = x / z
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.95e-22)
		tmp = 1.0;
	elseif (y <= 2.1e-51)
		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 <= -3.95e-22)
		tmp = 1.0;
	elseif (y <= 2.1e-51)
		tmp = x / z;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.95e-22], 1.0, If[LessEqual[y, 2.1e-51], N[(x / z), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -3.9499999999999999e-22 or 2.10000000000000002e-51 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 56.3%

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

   if -3.9499999999999999e-22 < y < 2.10000000000000002e-51

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 77.3%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.95 \cdot 10^{-22}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-51}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 34.6% 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 35.6%

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

4. Final simplification 35.6%

   \[\leadsto 1 \]
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 2024078 
(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)))