Diagrams.Backend.Rasterific:rasterificRadialGradient from diagrams-rasterific-1.3.1.3

Percentage Accurate: 88.2% → 98.9%

Time: 7.4s

Alternatives: 9

Speedup: 1.0×

• 21.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{x + y \cdot \left(z - x\right)}{z} \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return (x + (y * (z - x))) / 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 + (y * (z - x))) / z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x + y \cdot \left(z - x\right)}{z} \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return (x + (y * (z - x))) / 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 + (y * (z - x))) / z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+15} \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.05e+15) (not (<= y 1.0)))
   (* y (- 1.0 (/ x z)))
   (+ y (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.05e+15) || !(y <= 1.0)) {
		tmp = y * (1.0 - (x / z));
	} else {
		tmp = y + (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 <= (-2.05d+15)) .or. (.not. (y <= 1.0d0))) then
        tmp = y * (1.0d0 - (x / z))
    else
        tmp = y + (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.05e+15) || !(y <= 1.0)) {
		tmp = y * (1.0 - (x / z));
	} else {
		tmp = y + (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.05e+15) or not (y <= 1.0):
		tmp = y * (1.0 - (x / z))
	else:
		tmp = y + (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.05e+15) || !(y <= 1.0))
		tmp = Float64(y * Float64(1.0 - Float64(x / z)));
	else
		tmp = Float64(y + Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.05e+15) || ~((y <= 1.0)))
		tmp = y * (1.0 - (x / z));
	else
		tmp = y + (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.05e+15], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(y * N[(1.0 - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.05e15 or 1 < y

   1. Initial program 71.3%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 71.3%

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

      1. associate-/l* 99.8%

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

      2. div-sub 99.9%

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

      3. *-inverses 99.9%

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

   5. Simplified 99.9%

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

   if -2.05e15 < y < 1

   1. Initial program 99.9%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 99.8%

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

   4. Taylor expanded in y around 0 98.4%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+15} \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 58.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-58}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-109}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-156}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.68 \cdot 10^{-49}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.8e-58)
   y
   (if (<= y -5.8e-109)
     (/ x z)
     (if (<= y -1.7e-156) y (if (<= y 1.68e-49) (/ x z) (* z (/ y z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.8e-58) {
		tmp = y;
	} else if (y <= -5.8e-109) {
		tmp = x / z;
	} else if (y <= -1.7e-156) {
		tmp = y;
	} else if (y <= 1.68e-49) {
		tmp = x / z;
	} else {
		tmp = z * (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 <= (-4.8d-58)) then
        tmp = y
    else if (y <= (-5.8d-109)) then
        tmp = x / z
    else if (y <= (-1.7d-156)) then
        tmp = y
    else if (y <= 1.68d-49) then
        tmp = x / z
    else
        tmp = z * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.8e-58) {
		tmp = y;
	} else if (y <= -5.8e-109) {
		tmp = x / z;
	} else if (y <= -1.7e-156) {
		tmp = y;
	} else if (y <= 1.68e-49) {
		tmp = x / z;
	} else {
		tmp = z * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.8e-58:
		tmp = y
	elif y <= -5.8e-109:
		tmp = x / z
	elif y <= -1.7e-156:
		tmp = y
	elif y <= 1.68e-49:
		tmp = x / z
	else:
		tmp = z * (y / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.8e-58)
		tmp = y;
	elseif (y <= -5.8e-109)
		tmp = Float64(x / z);
	elseif (y <= -1.7e-156)
		tmp = y;
	elseif (y <= 1.68e-49)
		tmp = Float64(x / z);
	else
		tmp = Float64(z * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4.8e-58)
		tmp = y;
	elseif (y <= -5.8e-109)
		tmp = x / z;
	elseif (y <= -1.7e-156)
		tmp = y;
	elseif (y <= 1.68e-49)
		tmp = x / z;
	else
		tmp = z * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.8e-58], y, If[LessEqual[y, -5.8e-109], N[(x / z), $MachinePrecision], If[LessEqual[y, -1.7e-156], y, If[LessEqual[y, 1.68e-49], N[(x / z), $MachinePrecision], N[(z * N[(y / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.8000000000000001e-58 or -5.8e-109 < y < -1.69999999999999995e-156

   1. Initial program 82.5%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 59.0%

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

   if -4.8000000000000001e-58 < y < -5.8e-109 or -1.69999999999999995e-156 < y < 1.6800000000000001e-49

   1. Initial program 100.0%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 81.2%

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

   if 1.6800000000000001e-49 < y

   1. Initial program 73.1%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 68.7%

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

   4. Taylor expanded in z around inf 26.0%

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

      1. *-commutative 26.0%

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

      2. associate-/l* 54.9%

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

   6. Applied egg-rr 54.9%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-58}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-109}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-156}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.68 \cdot 10^{-49}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 5.5 \cdot 10^{+58}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+140} \lor \neg \left(y \leq 2.1 \cdot 10^{+219}\right):\\ \;\;\;\;x \cdot \frac{y}{-z}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 5.5e+58)
   (+ y (/ x z))
   (if (or (<= y 1.85e+140) (not (<= y 2.1e+219)))
     (* x (/ y (- z)))
     (* z (/ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 5.5e+58) {
		tmp = y + (x / z);
	} else if ((y <= 1.85e+140) || !(y <= 2.1e+219)) {
		tmp = x * (y / -z);
	} else {
		tmp = z * (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 <= 5.5d+58) then
        tmp = y + (x / z)
    else if ((y <= 1.85d+140) .or. (.not. (y <= 2.1d+219))) then
        tmp = x * (y / -z)
    else
        tmp = z * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 5.5e+58) {
		tmp = y + (x / z);
	} else if ((y <= 1.85e+140) || !(y <= 2.1e+219)) {
		tmp = x * (y / -z);
	} else {
		tmp = z * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 5.5e+58:
		tmp = y + (x / z)
	elif (y <= 1.85e+140) or not (y <= 2.1e+219):
		tmp = x * (y / -z)
	else:
		tmp = z * (y / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 5.5e+58)
		tmp = Float64(y + Float64(x / z));
	elseif ((y <= 1.85e+140) || !(y <= 2.1e+219))
		tmp = Float64(x * Float64(y / Float64(-z)));
	else
		tmp = Float64(z * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 5.5e+58)
		tmp = y + (x / z);
	elseif ((y <= 1.85e+140) || ~((y <= 2.1e+219)))
		tmp = x * (y / -z);
	else
		tmp = z * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 5.5e+58], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 1.85e+140], N[Not[LessEqual[y, 2.1e+219]], $MachinePrecision]], N[(x * N[(y / (-z)), $MachinePrecision]), $MachinePrecision], N[(z * N[(y / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 5.4999999999999999e58

   1. Initial program 91.6%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 97.5%

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

   4. Taylor expanded in y around 0 88.4%

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

   if 5.4999999999999999e58 < y < 1.85000000000000001e140 or 2.09999999999999988e219 < y

   1. Initial program 69.6%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 69.6%

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

   4. Taylor expanded in z around 0 63.1%

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

      1. mul-1-neg 63.1%

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

      2. distribute-lft-neg-out 63.1%

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

      3. *-commutative 63.1%

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

   6. Simplified 63.1%

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

      1. frac-2neg 63.1%

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

      2. distribute-frac-neg 63.1%

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

      3. add-sqr-sqrt 33.0%

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

      4. sqrt-unprod 33.6%

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

      5. sqr-neg 33.6%

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

      6. sqrt-unprod 0.4%

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

      7. add-sqr-sqrt 0.7%

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

      8. remove-double-neg 0.7%

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

      9. distribute-rgt-neg-out 0.7%

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

      10. frac-2neg 0.7%

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

      11. *-commutative 0.7%

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

      12. associate-/l* 0.8%

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

      13. add-sqr-sqrt 0.3%

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

      14. sqrt-unprod 26.0%

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

      15. sqr-neg 26.0%

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

      16. sqrt-unprod 32.8%

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

      17. add-sqr-sqrt 70.8%

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

   8. Applied egg-rr 70.8%

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

   if 1.85000000000000001e140 < y < 2.09999999999999988e219

   1. Initial program 63.7%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 63.7%

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

   4. Taylor expanded in z around inf 27.3%

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

      1. *-commutative 27.3%

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

      2. associate-/l* 63.0%

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

   6. Applied egg-rr 63.0%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 5.5 \cdot 10^{+58}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+140} \lor \neg \left(y \leq 2.1 \cdot 10^{+219}\right):\\ \;\;\;\;x \cdot \frac{y}{-z}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.6 \cdot 10^{+57}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 10^{+141}:\\ \;\;\;\;-\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+219}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{-z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 1.6e+57)
   (+ y (/ x z))
   (if (<= y 1e+141)
     (- (/ x (/ z y)))
     (if (<= y 2.8e+219) (* z (/ y z)) (* x (/ y (- z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.6e+57) {
		tmp = y + (x / z);
	} else if (y <= 1e+141) {
		tmp = -(x / (z / y));
	} else if (y <= 2.8e+219) {
		tmp = z * (y / z);
	} else {
		tmp = x * (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 <= 1.6d+57) then
        tmp = y + (x / z)
    else if (y <= 1d+141) then
        tmp = -(x / (z / y))
    else if (y <= 2.8d+219) then
        tmp = z * (y / z)
    else
        tmp = x * (y / -z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.6e+57) {
		tmp = y + (x / z);
	} else if (y <= 1e+141) {
		tmp = -(x / (z / y));
	} else if (y <= 2.8e+219) {
		tmp = z * (y / z);
	} else {
		tmp = x * (y / -z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1.6e+57:
		tmp = y + (x / z)
	elif y <= 1e+141:
		tmp = -(x / (z / y))
	elif y <= 2.8e+219:
		tmp = z * (y / z)
	else:
		tmp = x * (y / -z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.6e+57)
		tmp = Float64(y + Float64(x / z));
	elseif (y <= 1e+141)
		tmp = Float64(-Float64(x / Float64(z / y)));
	elseif (y <= 2.8e+219)
		tmp = Float64(z * Float64(y / z));
	else
		tmp = Float64(x * Float64(y / Float64(-z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 1.6e+57)
		tmp = y + (x / z);
	elseif (y <= 1e+141)
		tmp = -(x / (z / y));
	elseif (y <= 2.8e+219)
		tmp = z * (y / z);
	else
		tmp = x * (y / -z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1.6e+57], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e+141], (-N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]), If[LessEqual[y, 2.8e+219], N[(z * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / (-z)), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < 1.60000000000000015e57

   1. Initial program 91.6%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 97.5%

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

   4. Taylor expanded in y around 0 88.4%

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

   if 1.60000000000000015e57 < y < 1.00000000000000002e141

   1. Initial program 67.0%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 67.0%

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

   4. Taylor expanded in z around 0 57.0%

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

      1. mul-1-neg 57.0%

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

      2. distribute-lft-neg-out 57.0%

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

      3. *-commutative 57.0%

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

   6. Simplified 57.0%

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

      1. frac-2neg 57.0%

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

      2. distribute-frac-neg 57.0%

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

      3. add-sqr-sqrt 31.0%

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

      4. sqrt-unprod 31.7%

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

      5. sqr-neg 31.7%

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

      6. sqrt-unprod 0.6%

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

      7. add-sqr-sqrt 0.9%

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

      8. remove-double-neg 0.9%

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

      9. distribute-rgt-neg-out 0.9%

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

      10. frac-2neg 0.9%

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

      11. *-commutative 0.9%

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

      12. associate-/l* 1.0%

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

      13. add-sqr-sqrt 0.3%

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

      14. sqrt-unprod 18.9%

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

      15. sqr-neg 18.9%

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

      16. sqrt-unprod 30.9%

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

      17. add-sqr-sqrt 70.2%

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

   8. Applied egg-rr 70.2%

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

      1. clear-num 70.2%

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

      2. un-div-inv 70.3%

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

   10. Applied egg-rr 70.3%

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

   if 1.00000000000000002e141 < y < 2.80000000000000015e219

   1. Initial program 63.7%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 63.7%

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

   4. Taylor expanded in z around inf 27.3%

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

      1. *-commutative 27.3%

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

      2. associate-/l* 63.0%

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

   6. Applied egg-rr 63.0%

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

   if 2.80000000000000015e219 < y

   1. Initial program 73.0%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 73.0%

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

   4. Taylor expanded in z around 0 71.3%

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

      1. mul-1-neg 71.3%

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

      2. distribute-lft-neg-out 71.3%

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

      3. *-commutative 71.3%

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

   6. Simplified 71.3%

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

      1. frac-2neg 71.3%

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

      2. distribute-frac-neg 71.3%

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

      3. add-sqr-sqrt 35.7%

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

      4. sqrt-unprod 36.1%

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

      5. sqr-neg 36.1%

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

      6. sqrt-unprod 0.2%

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

      7. add-sqr-sqrt 0.5%

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

      8. remove-double-neg 0.5%

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

      9. distribute-rgt-neg-out 0.5%

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

      10. frac-2neg 0.5%

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

      11. *-commutative 0.5%

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

      12. associate-/l* 0.5%

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

      13. add-sqr-sqrt 0.3%

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

      14. sqrt-unprod 35.6%

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

      15. sqr-neg 35.6%

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

      16. sqrt-unprod 35.4%

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

      17. add-sqr-sqrt 71.5%

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

   8. Applied egg-rr 71.5%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.6 \cdot 10^{+57}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 10^{+141}:\\ \;\;\;\;-\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+219}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{-z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 97.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 880:\\ \;\;\;\;y + \frac{1}{z} \cdot \frac{x}{\frac{1}{1 - y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 880.0)
   (+ y (* (/ 1.0 z) (/ x (/ 1.0 (- 1.0 y)))))
   (* y (- 1.0 (/ x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 880.0) {
		tmp = y + ((1.0 / z) * (x / (1.0 / (1.0 - y))));
	} else {
		tmp = y * (1.0 - (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 <= 880.0d0) then
        tmp = y + ((1.0d0 / z) * (x / (1.0d0 / (1.0d0 - y))))
    else
        tmp = y * (1.0d0 - (x / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 880.0) {
		tmp = y + ((1.0 / z) * (x / (1.0 / (1.0 - y))));
	} else {
		tmp = y * (1.0 - (x / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 880.0:
		tmp = y + ((1.0 / z) * (x / (1.0 / (1.0 - y))))
	else:
		tmp = y * (1.0 - (x / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 880.0)
		tmp = Float64(y + Float64(Float64(1.0 / z) * Float64(x / Float64(1.0 / Float64(1.0 - y)))));
	else
		tmp = Float64(y * Float64(1.0 - Float64(x / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 880.0)
		tmp = y + ((1.0 / z) * (x / (1.0 / (1.0 - y))));
	else
		tmp = y * (1.0 - (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 880.0], N[(y + N[(N[(1.0 / z), $MachinePrecision] * N[(x / N[(1.0 / N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(1.0 - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 880

   1. Initial program 92.2%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 97.4%

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

      1. +-commutative 97.4%

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

      2. mul-1-neg 97.4%

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

      3. sub-neg 97.4%

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

      4. div-sub 97.4%

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

      5. clear-num 97.4%

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

      6. un-div-inv 98.0%

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

   5. Applied egg-rr 98.0%

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

      1. *-un-lft-identity 98.0%

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

      2. div-inv 97.9%

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

      3. times-frac 98.8%

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

   7. Applied egg-rr 98.8%

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

   if 880 < y

   1. Initial program 69.1%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 69.1%

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

      1. associate-/l* 99.8%

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

      2. div-sub 99.8%

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

      3. *-inverses 99.8%

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

   5. Simplified 99.8%

      \[\leadsto \color{blue}{y \cdot \left(1 - \frac{x}{z}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 880:\\ \;\;\;\;y + \frac{1}{z} \cdot \frac{x}{\frac{1}{1 - y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 56.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-17}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-30}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -9.5e-17) y (if (<= z 2.35e-30) (/ x z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -9.5e-17) {
		tmp = y;
	} else if (z <= 2.35e-30) {
		tmp = x / z;
	} else {
		tmp = 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 (z <= (-9.5d-17)) then
        tmp = y
    else if (z <= 2.35d-30) then
        tmp = x / z
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -9.5e-17) {
		tmp = y;
	} else if (z <= 2.35e-30) {
		tmp = x / z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -9.5e-17:
		tmp = y
	elif z <= 2.35e-30:
		tmp = x / z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -9.5e-17)
		tmp = y;
	elseif (z <= 2.35e-30)
		tmp = Float64(x / z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -9.5e-17)
		tmp = y;
	elseif (z <= 2.35e-30)
		tmp = x / z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -9.5e-17], y, If[LessEqual[z, 2.35e-30], N[(x / z), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if z < -9.50000000000000029e-17 or 2.34999999999999985e-30 < z

   1. Initial program 76.8%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 65.2%

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

   if -9.50000000000000029e-17 < z < 2.34999999999999985e-30

   1. Initial program 99.9%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 57.8%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-17}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-30}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 78.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 1.0) (+ y (/ x z)) (* z (/ y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.0) {
		tmp = y + (x / z);
	} else {
		tmp = z * (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 <= 1.0d0) then
        tmp = y + (x / z)
    else
        tmp = z * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.0) {
		tmp = y + (x / z);
	} else {
		tmp = z * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1.0:
		tmp = y + (x / z)
	else:
		tmp = z * (y / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.0)
		tmp = Float64(y + Float64(x / z));
	else
		tmp = Float64(z * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 1.0)
		tmp = y + (x / z);
	else
		tmp = z * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1.0], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], N[(z * N[(y / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1

   1. Initial program 92.2%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 97.4%

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

   4. Taylor expanded in y around 0 88.4%

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

   if 1 < y

   1. Initial program 69.1%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 69.1%

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

   4. Taylor expanded in z around inf 20.1%

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

      1. *-commutative 20.1%

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

      2. associate-/l* 53.2%

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

   6. Applied egg-rr 53.2%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 96.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ y + \frac{x}{\frac{z}{1 - y}} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ y (/ x (/ z (- 1.0 y)))))

C

double code(double x, double y, double z) {
	return y + (x / (z / (1.0 - 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 = y + (x / (z / (1.0d0 - y)))
end function

Java

public static double code(double x, double y, double z) {
	return y + (x / (z / (1.0 - y)));
}

Python

def code(x, y, z):
	return y + (x / (z / (1.0 - y)))

Julia

function code(x, y, z)
	return Float64(y + Float64(x / Float64(z / Float64(1.0 - y))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = y + (x / (z / (1.0 - y)));
end

Wolfram

code[x_, y_, z_] := N[(y + N[(x / N[(z / N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 86.7%

   \[\frac{x + y \cdot \left(z - x\right)}{z} \]
2. Add Preprocessing

3. Taylor expanded in x around 0 96.5%

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

   1. +-commutative 96.5%

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

   2. mul-1-neg 96.5%

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

   3. sub-neg 96.5%

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

   4. div-sub 96.5%

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

   5. clear-num 96.5%

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

   6. un-div-inv 97.0%

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

5. Applied egg-rr 97.0%

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

6. Final simplification 97.0%

   \[\leadsto y + \frac{x}{\frac{z}{1 - y}} \]
7. Add Preprocessing

Alternative 9: 40.0% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ y \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return 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 = y
end function

Java

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

Python

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

Julia

function code(x, y, z)
	return y
end

MATLAB

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

Wolfram

code[x_, y_, z_] := y

Derivation

1. Initial program 86.7%

   \[\frac{x + y \cdot \left(z - x\right)}{z} \]
2. Add Preprocessing

3. Taylor expanded in x around 0 41.1%

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

4. Final simplification 41.1%

   \[\leadsto y \]
5. Add Preprocessing

Developer target: 93.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}} \end{array} \]

FPCore

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

C

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

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 / z)) - (y / (z / x))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024071 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:rasterificRadialGradient from diagrams-rasterific-1.3.1.3"
  :precision binary64

  :alt
  (- (+ y (/ x z)) (/ y (/ z x)))

  (/ (+ x (* y (- z x))) z))