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

Percentage Accurate: 100.0% → 100.0%

Time: 7.9s

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 99.9%

   \[\frac{x - y}{z - y} \]
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: 75.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{y - z}\\ t_1 := \frac{x}{z - y}\\ \mathbf{if}\;y \leq -62000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-99}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{-123}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 85 \lor \neg \left(y \leq 1.5 \cdot 10^{+243}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ y (- y z))) (t_1 (/ x (- z y))))
   (if (<= y -62000.0)
     t_0
     (if (<= y -4.8e-99)
       t_1
       (if (<= y -9.2e-123)
         t_0
         (if (<= y 2.1e-77)
           t_1
           (if (or (<= y 85.0) (not (<= y 1.5e+243)))
             t_0
             (- 1.0 (/ x y)))))))))

C

double code(double x, double y, double z) {
	double t_0 = y / (y - z);
	double t_1 = x / (z - y);
	double tmp;
	if (y <= -62000.0) {
		tmp = t_0;
	} else if (y <= -4.8e-99) {
		tmp = t_1;
	} else if (y <= -9.2e-123) {
		tmp = t_0;
	} else if (y <= 2.1e-77) {
		tmp = t_1;
	} else if ((y <= 85.0) || !(y <= 1.5e+243)) {
		tmp = t_0;
	} else {
		tmp = 1.0 - (x / 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) :: t_1
    real(8) :: tmp
    t_0 = y / (y - z)
    t_1 = x / (z - y)
    if (y <= (-62000.0d0)) then
        tmp = t_0
    else if (y <= (-4.8d-99)) then
        tmp = t_1
    else if (y <= (-9.2d-123)) then
        tmp = t_0
    else if (y <= 2.1d-77) then
        tmp = t_1
    else if ((y <= 85.0d0) .or. (.not. (y <= 1.5d+243))) then
        tmp = t_0
    else
        tmp = 1.0d0 - (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y / (y - z);
	double t_1 = x / (z - y);
	double tmp;
	if (y <= -62000.0) {
		tmp = t_0;
	} else if (y <= -4.8e-99) {
		tmp = t_1;
	} else if (y <= -9.2e-123) {
		tmp = t_0;
	} else if (y <= 2.1e-77) {
		tmp = t_1;
	} else if ((y <= 85.0) || !(y <= 1.5e+243)) {
		tmp = t_0;
	} else {
		tmp = 1.0 - (x / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y / (y - z)
	t_1 = x / (z - y)
	tmp = 0
	if y <= -62000.0:
		tmp = t_0
	elif y <= -4.8e-99:
		tmp = t_1
	elif y <= -9.2e-123:
		tmp = t_0
	elif y <= 2.1e-77:
		tmp = t_1
	elif (y <= 85.0) or not (y <= 1.5e+243):
		tmp = t_0
	else:
		tmp = 1.0 - (x / y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y / Float64(y - z))
	t_1 = Float64(x / Float64(z - y))
	tmp = 0.0
	if (y <= -62000.0)
		tmp = t_0;
	elseif (y <= -4.8e-99)
		tmp = t_1;
	elseif (y <= -9.2e-123)
		tmp = t_0;
	elseif (y <= 2.1e-77)
		tmp = t_1;
	elseif ((y <= 85.0) || !(y <= 1.5e+243))
		tmp = t_0;
	else
		tmp = Float64(1.0 - Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y / (y - z);
	t_1 = x / (z - y);
	tmp = 0.0;
	if (y <= -62000.0)
		tmp = t_0;
	elseif (y <= -4.8e-99)
		tmp = t_1;
	elseif (y <= -9.2e-123)
		tmp = t_0;
	elseif (y <= 2.1e-77)
		tmp = t_1;
	elseif ((y <= 85.0) || ~((y <= 1.5e+243)))
		tmp = t_0;
	else
		tmp = 1.0 - (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -62000.0], t$95$0, If[LessEqual[y, -4.8e-99], t$95$1, If[LessEqual[y, -9.2e-123], t$95$0, If[LessEqual[y, 2.1e-77], t$95$1, If[Or[LessEqual[y, 85.0], N[Not[LessEqual[y, 1.5e+243]], $MachinePrecision]], t$95$0, N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -62000 or -4.8000000000000001e-99 < y < -9.19999999999999947e-123 or 2.10000000000000015e-77 < y < 85 or 1.49999999999999992e243 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 86.0%

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

      1. +-commutative 86.0%

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

      2. mul-1-neg 86.0%

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

      3. unsub-neg 86.0%

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

      4. *-commutative 86.0%

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

   5. Simplified 86.0%

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

   6. Taylor expanded in x around 0 80.0%

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

      1. mul-1-neg 80.0%

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

      2. distribute-neg-frac2 80.0%

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

      3. neg-sub0 80.0%

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

      4. associate-+l- 80.0%

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

      5. neg-sub0 80.0%

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

      6. +-commutative 80.0%

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

      7. unsub-neg 80.0%

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

   8. Simplified 80.0%

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

   if -62000 < y < -4.8000000000000001e-99 or -9.19999999999999947e-123 < y < 2.10000000000000015e-77

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 89.1%

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

   if 85 < y < 1.49999999999999992e243

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 82.3%

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

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -62000:\\ \;\;\;\;\frac{y}{y - z}\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-99}:\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{-123}:\\ \;\;\;\;\frac{y}{y - z}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-77}:\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{elif}\;y \leq 85 \lor \neg \left(y \leq 1.5 \cdot 10^{+243}\right):\\ \;\;\;\;\frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 60.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{-z}\\ \mathbf{if}\;y \leq -3.7 \cdot 10^{+56}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-74}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-51}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-15}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+22}:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+51}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ y (- z))))
   (if (<= y -3.7e+56)
     1.0
     (if (<= y 3.1e-74)
       (/ x z)
       (if (<= y 3.9e-51)
         t_0
         (if (<= y 1.4e-15)
           (/ x z)
           (if (<= y 2.9e+22) (/ x (- y)) (if (<= y 1.45e+51) t_0 1.0))))))))

C

double code(double x, double y, double z) {
	double t_0 = y / -z;
	double tmp;
	if (y <= -3.7e+56) {
		tmp = 1.0;
	} else if (y <= 3.1e-74) {
		tmp = x / z;
	} else if (y <= 3.9e-51) {
		tmp = t_0;
	} else if (y <= 1.4e-15) {
		tmp = x / z;
	} else if (y <= 2.9e+22) {
		tmp = x / -y;
	} else if (y <= 1.45e+51) {
		tmp = t_0;
	} 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 = y / -z
    if (y <= (-3.7d+56)) then
        tmp = 1.0d0
    else if (y <= 3.1d-74) then
        tmp = x / z
    else if (y <= 3.9d-51) then
        tmp = t_0
    else if (y <= 1.4d-15) then
        tmp = x / z
    else if (y <= 2.9d+22) then
        tmp = x / -y
    else if (y <= 1.45d+51) then
        tmp = t_0
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y / -z;
	double tmp;
	if (y <= -3.7e+56) {
		tmp = 1.0;
	} else if (y <= 3.1e-74) {
		tmp = x / z;
	} else if (y <= 3.9e-51) {
		tmp = t_0;
	} else if (y <= 1.4e-15) {
		tmp = x / z;
	} else if (y <= 2.9e+22) {
		tmp = x / -y;
	} else if (y <= 1.45e+51) {
		tmp = t_0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y / -z
	tmp = 0
	if y <= -3.7e+56:
		tmp = 1.0
	elif y <= 3.1e-74:
		tmp = x / z
	elif y <= 3.9e-51:
		tmp = t_0
	elif y <= 1.4e-15:
		tmp = x / z
	elif y <= 2.9e+22:
		tmp = x / -y
	elif y <= 1.45e+51:
		tmp = t_0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y / Float64(-z))
	tmp = 0.0
	if (y <= -3.7e+56)
		tmp = 1.0;
	elseif (y <= 3.1e-74)
		tmp = Float64(x / z);
	elseif (y <= 3.9e-51)
		tmp = t_0;
	elseif (y <= 1.4e-15)
		tmp = Float64(x / z);
	elseif (y <= 2.9e+22)
		tmp = Float64(x / Float64(-y));
	elseif (y <= 1.45e+51)
		tmp = t_0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y / -z;
	tmp = 0.0;
	if (y <= -3.7e+56)
		tmp = 1.0;
	elseif (y <= 3.1e-74)
		tmp = x / z;
	elseif (y <= 3.9e-51)
		tmp = t_0;
	elseif (y <= 1.4e-15)
		tmp = x / z;
	elseif (y <= 2.9e+22)
		tmp = x / -y;
	elseif (y <= 1.45e+51)
		tmp = t_0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y / (-z)), $MachinePrecision]}, If[LessEqual[y, -3.7e+56], 1.0, If[LessEqual[y, 3.1e-74], N[(x / z), $MachinePrecision], If[LessEqual[y, 3.9e-51], t$95$0, If[LessEqual[y, 1.4e-15], N[(x / z), $MachinePrecision], If[LessEqual[y, 2.9e+22], N[(x / (-y)), $MachinePrecision], If[LessEqual[y, 1.45e+51], t$95$0, 1.0]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.69999999999999997e56 or 1.4499999999999999e51 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 68.0%

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

   if -3.69999999999999997e56 < y < 3.1000000000000002e-74 or 3.8999999999999997e-51 < y < 1.40000000000000007e-15

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 68.6%

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

   if 3.1000000000000002e-74 < y < 3.8999999999999997e-51 or 2.9e22 < y < 1.4499999999999999e51

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 86.4%

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

   4. Taylor expanded in x around 0 86.4%

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

      1. neg-mul-1 86.4%

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

      2. distribute-neg-frac2 86.4%

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

   6. Simplified 86.4%

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

   if 1.40000000000000007e-15 < y < 2.9e22

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 57.0%

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

   4. Taylor expanded in z around 0 49.4%

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

      1. associate-*r/ 49.4%

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

      2. neg-mul-1 49.4%

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

   6. Simplified 49.4%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+56}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-74}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-51}:\\ \;\;\;\;\frac{y}{-z}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-15}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+22}:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+51}:\\ \;\;\;\;\frac{y}{-z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{x}{y}\\ t_1 := \frac{x}{z - y}\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{+56}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-55}:\\ \;\;\;\;\frac{y}{-z}\\ \mathbf{elif}\;y \leq 760000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ x y))) (t_1 (/ x (- z y))))
   (if (<= y -4.8e+56)
     t_0
     (if (<= y 3.1e-74)
       t_1
       (if (<= y 5.4e-55) (/ y (- z)) (if (<= y 760000.0) t_1 t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (x / y);
	double t_1 = x / (z - y);
	double tmp;
	if (y <= -4.8e+56) {
		tmp = t_0;
	} else if (y <= 3.1e-74) {
		tmp = t_1;
	} else if (y <= 5.4e-55) {
		tmp = y / -z;
	} else if (y <= 760000.0) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = 1.0d0 - (x / y)
    t_1 = x / (z - y)
    if (y <= (-4.8d+56)) then
        tmp = t_0
    else if (y <= 3.1d-74) then
        tmp = t_1
    else if (y <= 5.4d-55) then
        tmp = y / -z
    else if (y <= 760000.0d0) then
        tmp = t_1
    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 t_1 = x / (z - y);
	double tmp;
	if (y <= -4.8e+56) {
		tmp = t_0;
	} else if (y <= 3.1e-74) {
		tmp = t_1;
	} else if (y <= 5.4e-55) {
		tmp = y / -z;
	} else if (y <= 760000.0) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (x / y)
	t_1 = x / (z - y)
	tmp = 0
	if y <= -4.8e+56:
		tmp = t_0
	elif y <= 3.1e-74:
		tmp = t_1
	elif y <= 5.4e-55:
		tmp = y / -z
	elif y <= 760000.0:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(x / y))
	t_1 = Float64(x / Float64(z - y))
	tmp = 0.0
	if (y <= -4.8e+56)
		tmp = t_0;
	elseif (y <= 3.1e-74)
		tmp = t_1;
	elseif (y <= 5.4e-55)
		tmp = Float64(y / Float64(-z));
	elseif (y <= 760000.0)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (x / y);
	t_1 = x / (z - y);
	tmp = 0.0;
	if (y <= -4.8e+56)
		tmp = t_0;
	elseif (y <= 3.1e-74)
		tmp = t_1;
	elseif (y <= 5.4e-55)
		tmp = y / -z;
	elseif (y <= 760000.0)
		tmp = t_1;
	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]}, Block[{t$95$1 = N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.8e+56], t$95$0, If[LessEqual[y, 3.1e-74], t$95$1, If[LessEqual[y, 5.4e-55], N[(y / (-z)), $MachinePrecision], If[LessEqual[y, 760000.0], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.80000000000000027e56 or 7.6e5 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 80.0%

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

      1. div-sub 80.1%

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

      2. sub-neg 80.1%

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

      3. *-inverses 80.1%

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

      4. metadata-eval 80.1%

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

      5. distribute-lft-in 80.1%

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

      6. metadata-eval 80.1%

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

      7. +-commutative 80.1%

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

      8. mul-1-neg 80.1%

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

      9. unsub-neg 80.1%

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

   5. Simplified 80.1%

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

   if -4.80000000000000027e56 < y < 3.1000000000000002e-74 or 5.40000000000000008e-55 < y < 7.6e5

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 78.1%

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

   if 3.1000000000000002e-74 < y < 5.40000000000000008e-55

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 84.2%

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

   4. Taylor expanded in x around 0 84.2%

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

      1. neg-mul-1 84.2%

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

      2. distribute-neg-frac2 84.2%

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

   6. Simplified 84.2%

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

Alternative 5: 75.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{y - z}\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{+56}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -9.8 \cdot 10^{-126}:\\ \;\;\;\;\frac{x - y}{z}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-77}:\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ y (- y z))))
   (if (<= y -9.5e+56)
     t_0
     (if (<= y -9.8e-126)
       (/ (- x y) z)
       (if (<= y 1.95e-77) (/ x (- z y)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = y / (y - z);
	double tmp;
	if (y <= -9.5e+56) {
		tmp = t_0;
	} else if (y <= -9.8e-126) {
		tmp = (x - y) / z;
	} else if (y <= 1.95e-77) {
		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 = y / (y - z)
    if (y <= (-9.5d+56)) then
        tmp = t_0
    else if (y <= (-9.8d-126)) then
        tmp = (x - y) / z
    else if (y <= 1.95d-77) 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 = y / (y - z);
	double tmp;
	if (y <= -9.5e+56) {
		tmp = t_0;
	} else if (y <= -9.8e-126) {
		tmp = (x - y) / z;
	} else if (y <= 1.95e-77) {
		tmp = x / (z - y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y / (y - z)
	tmp = 0
	if y <= -9.5e+56:
		tmp = t_0
	elif y <= -9.8e-126:
		tmp = (x - y) / z
	elif y <= 1.95e-77:
		tmp = x / (z - y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y / Float64(y - z))
	tmp = 0.0
	if (y <= -9.5e+56)
		tmp = t_0;
	elseif (y <= -9.8e-126)
		tmp = Float64(Float64(x - y) / z);
	elseif (y <= 1.95e-77)
		tmp = Float64(x / Float64(z - y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y / (y - z);
	tmp = 0.0;
	if (y <= -9.5e+56)
		tmp = t_0;
	elseif (y <= -9.8e-126)
		tmp = (x - y) / z;
	elseif (y <= 1.95e-77)
		tmp = x / (z - y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.5e+56], t$95$0, If[LessEqual[y, -9.8e-126], N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 1.95e-77], N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.4999999999999997e56 or 1.9499999999999999e-77 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 87.2%

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

      1. +-commutative 87.2%

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

      2. mul-1-neg 87.2%

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

      3. unsub-neg 87.2%

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

      4. *-commutative 87.2%

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

   5. Simplified 87.2%

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

   6. Taylor expanded in x around 0 78.8%

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

      1. mul-1-neg 78.8%

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

      2. distribute-neg-frac2 78.8%

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

      3. neg-sub0 78.8%

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

      4. associate-+l- 78.8%

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

      5. neg-sub0 78.8%

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

      6. +-commutative 78.8%

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

      7. unsub-neg 78.8%

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

   8. Simplified 78.8%

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

   if -9.4999999999999997e56 < y < -9.8000000000000002e-126

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 77.0%

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

   if -9.8000000000000002e-126 < y < 1.9499999999999999e-77

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 94.8%

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

Alternative 6: 60.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+56}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-74}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+50}:\\ \;\;\;\;\frac{y}{-z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.1e+56)
   1.0
   (if (<= y 2.5e-74) (/ x z) (if (<= y 3.8e+50) (/ y (- z)) 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.1e+56) {
		tmp = 1.0;
	} else if (y <= 2.5e-74) {
		tmp = x / z;
	} else if (y <= 3.8e+50) {
		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 <= (-4.1d+56)) then
        tmp = 1.0d0
    else if (y <= 2.5d-74) then
        tmp = x / z
    else if (y <= 3.8d+50) 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 <= -4.1e+56) {
		tmp = 1.0;
	} else if (y <= 2.5e-74) {
		tmp = x / z;
	} else if (y <= 3.8e+50) {
		tmp = y / -z;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.1e+56:
		tmp = 1.0
	elif y <= 2.5e-74:
		tmp = x / z
	elif y <= 3.8e+50:
		tmp = y / -z
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.1e+56)
		tmp = 1.0;
	elseif (y <= 2.5e-74)
		tmp = Float64(x / z);
	elseif (y <= 3.8e+50)
		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 <= -4.1e+56)
		tmp = 1.0;
	elseif (y <= 2.5e-74)
		tmp = x / z;
	elseif (y <= 3.8e+50)
		tmp = y / -z;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.1e+56], 1.0, If[LessEqual[y, 2.5e-74], N[(x / z), $MachinePrecision], If[LessEqual[y, 3.8e+50], N[(y / (-z)), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.1000000000000004e56 or 3.79999999999999987e50 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 68.0%

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

   if -4.1000000000000004e56 < y < 2.49999999999999999e-74

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 69.9%

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

   if 2.49999999999999999e-74 < y < 3.79999999999999987e50

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 55.8%

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

   4. Taylor expanded in x around 0 41.4%

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

      1. neg-mul-1 41.4%

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

      2. distribute-neg-frac2 41.4%

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

   6. Simplified 41.4%

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

Alternative 7: 70.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.000155 \lor \neg \left(y \leq 3.9 \cdot 10^{-81}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.000155) (not (<= y 3.9e-81))) (- 1.0 (/ x y)) (/ x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.000155) || !(y <= 3.9e-81)) {
		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 <= (-0.000155d0)) .or. (.not. (y <= 3.9d-81))) 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 <= -0.000155) || !(y <= 3.9e-81)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.000155) or not (y <= 3.9e-81):
		tmp = 1.0 - (x / y)
	else:
		tmp = x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.000155) || !(y <= 3.9e-81))
		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 <= -0.000155) || ~((y <= 3.9e-81)))
		tmp = 1.0 - (x / y);
	else
		tmp = x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.000155], N[Not[LessEqual[y, 3.9e-81]], $MachinePrecision]], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.55e-4 or 3.89999999999999985e-81 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 71.2%

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

      1. div-sub 71.2%

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

      2. sub-neg 71.2%

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

      3. *-inverses 71.2%

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

      4. metadata-eval 71.2%

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

      5. distribute-lft-in 71.2%

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

      6. metadata-eval 71.2%

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

      7. +-commutative 71.2%

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

      8. mul-1-neg 71.2%

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

      9. unsub-neg 71.2%

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

   5. Simplified 71.2%

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

   if -1.55e-4 < y < 3.89999999999999985e-81

   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 2 regimes into one program.

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.000155 \lor \neg \left(y \leq 3.9 \cdot 10^{-81}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 60.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+56}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-6}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.8e+56) 1.0 (if (<= y 7.2e-6) (/ x z) 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.8e+56) {
		tmp = 1.0;
	} else if (y <= 7.2e-6) {
		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 <= (-3.8d+56)) then
        tmp = 1.0d0
    else if (y <= 7.2d-6) 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 <= -3.8e+56) {
		tmp = 1.0;
	} else if (y <= 7.2e-6) {
		tmp = x / z;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.8e+56:
		tmp = 1.0
	elif y <= 7.2e-6:
		tmp = x / z
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.8e+56)
		tmp = 1.0;
	elseif (y <= 7.2e-6)
		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 <= -3.8e+56)
		tmp = 1.0;
	elseif (y <= 7.2e-6)
		tmp = x / z;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.8e+56], 1.0, If[LessEqual[y, 7.2e-6], N[(x / z), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -3.79999999999999996e56 or 7.19999999999999967e-6 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 62.9%

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

   if -3.79999999999999996e56 < y < 7.19999999999999967e-6

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 65.2%

      \[\leadsto \color{blue}{\frac{x}{z}} \]
3. Recombined 2 regimes into one program.
4. 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 99.9%

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

3. Final simplification 99.9%

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

Alternative 10: 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 99.9%

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

3. Taylor expanded in y around inf 33.2%

   \[\leadsto \color{blue}{1} \]
4. Add Preprocessing

Developer target: 100.0% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024084 
(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)))