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

Percentage Accurate: 100.0% → 100.0%

Time: 6.3s

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, 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]

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. Add Preprocessing

Alternative 2: 59.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+54}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.42 \cdot 10^{-130}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-165}:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 1.38 \cdot 10^{+141}:\\ \;\;\;\;\frac{y}{-z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -7.5e+54)
   1.0
   (if (<= y -1.42e-130)
     (/ x z)
     (if (<= y -4.5e-165)
       (/ x (- y))
       (if (<= y 1.1e-11) (/ x z) (if (<= y 1.38e+141) (/ y (- z)) 1.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -7.5e+54) {
		tmp = 1.0;
	} else if (y <= -1.42e-130) {
		tmp = x / z;
	} else if (y <= -4.5e-165) {
		tmp = x / -y;
	} else if (y <= 1.1e-11) {
		tmp = x / z;
	} else if (y <= 1.38e+141) {
		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 <= (-7.5d+54)) then
        tmp = 1.0d0
    else if (y <= (-1.42d-130)) then
        tmp = x / z
    else if (y <= (-4.5d-165)) then
        tmp = x / -y
    else if (y <= 1.1d-11) then
        tmp = x / z
    else if (y <= 1.38d+141) 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 <= -7.5e+54) {
		tmp = 1.0;
	} else if (y <= -1.42e-130) {
		tmp = x / z;
	} else if (y <= -4.5e-165) {
		tmp = x / -y;
	} else if (y <= 1.1e-11) {
		tmp = x / z;
	} else if (y <= 1.38e+141) {
		tmp = y / -z;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -7.5e+54:
		tmp = 1.0
	elif y <= -1.42e-130:
		tmp = x / z
	elif y <= -4.5e-165:
		tmp = x / -y
	elif y <= 1.1e-11:
		tmp = x / z
	elif y <= 1.38e+141:
		tmp = y / -z
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -7.5e+54)
		tmp = 1.0;
	elseif (y <= -1.42e-130)
		tmp = Float64(x / z);
	elseif (y <= -4.5e-165)
		tmp = Float64(x / Float64(-y));
	elseif (y <= 1.1e-11)
		tmp = Float64(x / z);
	elseif (y <= 1.38e+141)
		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 <= -7.5e+54)
		tmp = 1.0;
	elseif (y <= -1.42e-130)
		tmp = x / z;
	elseif (y <= -4.5e-165)
		tmp = x / -y;
	elseif (y <= 1.1e-11)
		tmp = x / z;
	elseif (y <= 1.38e+141)
		tmp = y / -z;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -7.5e+54], 1.0, If[LessEqual[y, -1.42e-130], N[(x / z), $MachinePrecision], If[LessEqual[y, -4.5e-165], N[(x / (-y)), $MachinePrecision], If[LessEqual[y, 1.1e-11], N[(x / z), $MachinePrecision], If[LessEqual[y, 1.38e+141], N[(y / (-z)), $MachinePrecision], 1.0]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.50000000000000042e54 or 1.38e141 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 73.5%

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

   if -7.50000000000000042e54 < y < -1.4199999999999999e-130 or -4.49999999999999992e-165 < y < 1.1000000000000001e-11

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 62.2%

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

   if -1.4199999999999999e-130 < y < -4.49999999999999992e-165

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 79.5%

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

   4. Taylor expanded in z around 0 79.1%

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

      1. mul-1-neg 79.1%

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

      2. distribute-frac-neg2 79.1%

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

   6. Simplified 79.1%

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

   if 1.1000000000000001e-11 < y < 1.38e141

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 68.0%

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

   4. Taylor expanded in x around 0 45.8%

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

      1. neg-mul-1 45.8%

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

      2. distribute-neg-frac2 45.8%

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

   6. Simplified 45.8%

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

Alternative 3: 68.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.05 \cdot 10^{+43} \lor \neg \left(y \leq -4.3 \cdot 10^{-63}\right) \land \left(y \leq -4.5 \cdot 10^{-165} \lor \neg \left(y \leq 1.55 \cdot 10^{-43}\right)\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.05e+43)
         (and (not (<= y -4.3e-63))
              (or (<= y -4.5e-165) (not (<= y 1.55e-43)))))
   (- 1.0 (/ x y))
   (/ x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.05e+43) || (!(y <= -4.3e-63) && ((y <= -4.5e-165) || !(y <= 1.55e-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 <= (-3.05d+43)) .or. (.not. (y <= (-4.3d-63))) .and. (y <= (-4.5d-165)) .or. (.not. (y <= 1.55d-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 <= -3.05e+43) || (!(y <= -4.3e-63) && ((y <= -4.5e-165) || !(y <= 1.55e-43)))) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.05e+43) or (not (y <= -4.3e-63) and ((y <= -4.5e-165) or not (y <= 1.55e-43))):
		tmp = 1.0 - (x / y)
	else:
		tmp = x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.05e+43) || (!(y <= -4.3e-63) && ((y <= -4.5e-165) || !(y <= 1.55e-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 <= -3.05e+43) || (~((y <= -4.3e-63)) && ((y <= -4.5e-165) || ~((y <= 1.55e-43)))))
		tmp = 1.0 - (x / y);
	else
		tmp = x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.05e+43], And[N[Not[LessEqual[y, -4.3e-63]], $MachinePrecision], Or[LessEqual[y, -4.5e-165], N[Not[LessEqual[y, 1.55e-43]], $MachinePrecision]]]], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.0499999999999999e43 or -4.2999999999999999e-63 < y < -4.49999999999999992e-165 or 1.55e-43 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 76.2%

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

      1. mul-1-neg 76.2%

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

      2. div-sub 76.2%

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

      3. sub-neg 76.2%

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

      4. *-inverses 76.2%

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

      5. metadata-eval 76.2%

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

      6. distribute-neg-in 76.2%

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

      7. mul-1-neg 76.2%

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

      8. metadata-eval 76.2%

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

      9. +-commutative 76.2%

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

      10. mul-1-neg 76.2%

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

      11. unsub-neg 76.2%

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

   5. Simplified 76.2%

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

   if -3.0499999999999999e43 < y < -4.2999999999999999e-63 or -4.49999999999999992e-165 < y < 1.55e-43

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 67.7%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.05 \cdot 10^{+43} \lor \neg \left(y \leq -4.3 \cdot 10^{-63}\right) \land \left(y \leq -4.5 \cdot 10^{-165} \lor \neg \left(y \leq 1.55 \cdot 10^{-43}\right)\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+54}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-130}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-165}:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+67}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -7.5e+54)
   1.0
   (if (<= y -2.8e-130)
     (/ x z)
     (if (<= y -4.5e-165) (/ x (- y)) (if (<= y 1.55e+67) (/ x z) 1.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -7.5e+54) {
		tmp = 1.0;
	} else if (y <= -2.8e-130) {
		tmp = x / z;
	} else if (y <= -4.5e-165) {
		tmp = x / -y;
	} else if (y <= 1.55e+67) {
		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 <= (-7.5d+54)) then
        tmp = 1.0d0
    else if (y <= (-2.8d-130)) then
        tmp = x / z
    else if (y <= (-4.5d-165)) then
        tmp = x / -y
    else if (y <= 1.55d+67) 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 <= -7.5e+54) {
		tmp = 1.0;
	} else if (y <= -2.8e-130) {
		tmp = x / z;
	} else if (y <= -4.5e-165) {
		tmp = x / -y;
	} else if (y <= 1.55e+67) {
		tmp = x / z;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -7.5e+54:
		tmp = 1.0
	elif y <= -2.8e-130:
		tmp = x / z
	elif y <= -4.5e-165:
		tmp = x / -y
	elif y <= 1.55e+67:
		tmp = x / z
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -7.5e+54)
		tmp = 1.0;
	elseif (y <= -2.8e-130)
		tmp = Float64(x / z);
	elseif (y <= -4.5e-165)
		tmp = Float64(x / Float64(-y));
	elseif (y <= 1.55e+67)
		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 <= -7.5e+54)
		tmp = 1.0;
	elseif (y <= -2.8e-130)
		tmp = x / z;
	elseif (y <= -4.5e-165)
		tmp = x / -y;
	elseif (y <= 1.55e+67)
		tmp = x / z;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -7.5e+54], 1.0, If[LessEqual[y, -2.8e-130], N[(x / z), $MachinePrecision], If[LessEqual[y, -4.5e-165], N[(x / (-y)), $MachinePrecision], If[LessEqual[y, 1.55e+67], N[(x / z), $MachinePrecision], 1.0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.50000000000000042e54 or 1.54999999999999998e67 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 67.1%

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

   if -7.50000000000000042e54 < y < -2.80000000000000016e-130 or -4.49999999999999992e-165 < y < 1.54999999999999998e67

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 59.1%

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

   if -2.80000000000000016e-130 < y < -4.49999999999999992e-165

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 79.5%

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

   4. Taylor expanded in z around 0 79.1%

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

      1. mul-1-neg 79.1%

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

      2. distribute-frac-neg2 79.1%

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

   6. Simplified 79.1%

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

Alternative 5: 76.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+43} \lor \neg \left(y \leq 1.55 \cdot 10^{+67}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.2e+43) (not (<= y 1.55e+67))) (- 1.0 (/ x y)) (/ x (- z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.2e+43) || !(y <= 1.55e+67)) {
		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 <= (-3.2d+43)) .or. (.not. (y <= 1.55d+67))) 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 <= -3.2e+43) || !(y <= 1.55e+67)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x / (z - y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.2e+43) or not (y <= 1.55e+67):
		tmp = 1.0 - (x / y)
	else:
		tmp = x / (z - y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.2e+43) || !(y <= 1.55e+67))
		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 <= -3.2e+43) || ~((y <= 1.55e+67)))
		tmp = 1.0 - (x / y);
	else
		tmp = x / (z - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.2e+43], N[Not[LessEqual[y, 1.55e+67]], $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 < -3.20000000000000014e43 or 1.54999999999999998e67 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 83.0%

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

      1. mul-1-neg 83.0%

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

      2. div-sub 83.0%

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

      3. sub-neg 83.0%

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

      4. *-inverses 83.0%

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

      5. metadata-eval 83.0%

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

      6. distribute-neg-in 83.0%

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

      7. mul-1-neg 83.0%

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

      8. metadata-eval 83.0%

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

      9. +-commutative 83.0%

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

      10. mul-1-neg 83.0%

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

      11. unsub-neg 83.0%

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

   5. Simplified 83.0%

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

   if -3.20000000000000014e43 < y < 1.54999999999999998e67

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 75.8%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+43} \lor \neg \left(y \leq 1.55 \cdot 10^{+67}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+44}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+43}:\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.3e+44)
   (- 1.0 (/ x y))
   (if (<= y 6.6e+43) (/ x (- z y)) (/ y (- y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.3e+44) {
		tmp = 1.0 - (x / y);
	} else if (y <= 6.6e+43) {
		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 <= (-2.3d+44)) then
        tmp = 1.0d0 - (x / y)
    else if (y <= 6.6d+43) 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 <= -2.3e+44) {
		tmp = 1.0 - (x / y);
	} else if (y <= 6.6e+43) {
		tmp = x / (z - y);
	} else {
		tmp = y / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.3e+44:
		tmp = 1.0 - (x / y)
	elif y <= 6.6e+43:
		tmp = x / (z - y)
	else:
		tmp = y / (y - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.3e+44)
		tmp = Float64(1.0 - Float64(x / y));
	elseif (y <= 6.6e+43)
		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 <= -2.3e+44)
		tmp = 1.0 - (x / y);
	elseif (y <= 6.6e+43)
		tmp = x / (z - y);
	else
		tmp = y / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.3e+44], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.6e+43], N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision], N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.30000000000000004e44

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 92.2%

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

      1. mul-1-neg 92.2%

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

      2. div-sub 92.3%

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

      3. sub-neg 92.3%

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

      4. *-inverses 92.3%

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

      5. metadata-eval 92.3%

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

      6. distribute-neg-in 92.3%

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

      7. mul-1-neg 92.3%

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

      8. metadata-eval 92.3%

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

      9. +-commutative 92.3%

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

      10. mul-1-neg 92.3%

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

      11. unsub-neg 92.3%

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

   5. Simplified 92.3%

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

   if -2.30000000000000004e44 < y < 6.6000000000000003e43

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 76.7%

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

   if 6.6000000000000003e43 < y

   1. Initial program 100.0%

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

      1. clear-num 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in x around 0 82.7%

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

      1. associate-*r/ 82.7%

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

      2. neg-mul-1 82.7%

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

   7. Simplified 82.7%

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

      1. frac-2neg 82.7%

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

      2. div-inv 82.5%

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

      3. remove-double-neg 82.5%

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

      4. sub-neg 82.5%

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

      5. distribute-neg-in 82.5%

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

      6. remove-double-neg 82.5%

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

   9. Applied egg-rr 82.5%

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

       1. associate-*r/ 82.7%

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

       2. *-rgt-identity 82.7%

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

       3. +-commutative 82.7%

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

       4. unsub-neg 82.7%

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

   11. Simplified 82.7%

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

Alternative 7: 61.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+54} \lor \neg \left(y \leq 1.55 \cdot 10^{+67}\right):\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -8e+54) (not (<= y 1.55e+67))) 1.0 (/ x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -8e+54) || !(y <= 1.55e+67)) {
		tmp = 1.0;
	} else {
		tmp = x / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-8d+54)) .or. (.not. (y <= 1.55d+67))) then
        tmp = 1.0d0
    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 <= -8e+54) || !(y <= 1.55e+67)) {
		tmp = 1.0;
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -8e+54) or not (y <= 1.55e+67):
		tmp = 1.0
	else:
		tmp = x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -8e+54) || !(y <= 1.55e+67))
		tmp = 1.0;
	else
		tmp = Float64(x / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -8e+54) || ~((y <= 1.55e+67)))
		tmp = 1.0;
	else
		tmp = x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -8e+54], N[Not[LessEqual[y, 1.55e+67]], $MachinePrecision]], 1.0, N[(x / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.0000000000000006e54 or 1.54999999999999998e67 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 67.1%

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

   if -8.0000000000000006e54 < y < 1.54999999999999998e67

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 55.3%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+54} \lor \neg \left(y \leq 1.55 \cdot 10^{+67}\right):\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 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 99.9%

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

Alternative 9: 35.0% 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 38.9%

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

Developer target: 100.0% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024096 
(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)))