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

Percentage Accurate: 88.5% → 99.7%

Time: 10.2s

Alternatives: 11

Speedup: 0.6×

• 21.1% 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: 88.5% 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: 99.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+46} \lor \neg \left(y \leq 1850000000000\right):\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \left(z - x\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.2e+46) (not (<= y 1850000000000.0)))
   (* y (- 1.0 (/ x z)))
   (/ (+ x (* y (- z x))) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.2e+46) || !(y <= 1850000000000.0)) {
		tmp = y * (1.0 - (x / z));
	} else {
		tmp = (x + (y * (z - 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 <= (-4.2d+46)) .or. (.not. (y <= 1850000000000.0d0))) then
        tmp = y * (1.0d0 - (x / z))
    else
        tmp = (x + (y * (z - x))) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.2e+46) || !(y <= 1850000000000.0)) {
		tmp = y * (1.0 - (x / z));
	} else {
		tmp = (x + (y * (z - x))) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.2e+46) or not (y <= 1850000000000.0):
		tmp = y * (1.0 - (x / z))
	else:
		tmp = (x + (y * (z - x))) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.2e+46) || !(y <= 1850000000000.0))
		tmp = Float64(y * Float64(1.0 - Float64(x / z)));
	else
		tmp = Float64(Float64(x + Float64(y * Float64(z - x))) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -4.2e+46) || ~((y <= 1850000000000.0)))
		tmp = y * (1.0 - (x / z));
	else
		tmp = (x + (y * (z - x))) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.2e+46], N[Not[LessEqual[y, 1850000000000.0]], $MachinePrecision]], N[(y * N[(1.0 - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.2e46 or 1.85e12 < y

   1. Initial program 72.5%

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

   3. Taylor expanded in y around inf 72.5%

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

      1. associate-/l* 99.9%

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

      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 -4.2e46 < y < 1.85e12

   1. Initial program 99.9%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+46} \lor \neg \left(y \leq 1850000000000\right):\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \left(z - x\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 61.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \frac{y}{z}\\ \mathbf{if}\;y \leq -1.75 \cdot 10^{-51}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-154}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-125}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-43}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (/ y z))))
   (if (<= y -1.75e-51)
     t_0
     (if (<= y 7e-154)
       (/ x z)
       (if (<= y 2.3e-125) y (if (<= y 2.35e-43) (/ x z) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (y / z);
	double tmp;
	if (y <= -1.75e-51) {
		tmp = t_0;
	} else if (y <= 7e-154) {
		tmp = x / z;
	} else if (y <= 2.3e-125) {
		tmp = y;
	} else if (y <= 2.35e-43) {
		tmp = x / z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * (y / z)
    if (y <= (-1.75d-51)) then
        tmp = t_0
    else if (y <= 7d-154) then
        tmp = x / z
    else if (y <= 2.3d-125) then
        tmp = y
    else if (y <= 2.35d-43) then
        tmp = x / z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (y / z);
	double tmp;
	if (y <= -1.75e-51) {
		tmp = t_0;
	} else if (y <= 7e-154) {
		tmp = x / z;
	} else if (y <= 2.3e-125) {
		tmp = y;
	} else if (y <= 2.35e-43) {
		tmp = x / z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (y / z)
	tmp = 0
	if y <= -1.75e-51:
		tmp = t_0
	elif y <= 7e-154:
		tmp = x / z
	elif y <= 2.3e-125:
		tmp = y
	elif y <= 2.35e-43:
		tmp = x / z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(y / z))
	tmp = 0.0
	if (y <= -1.75e-51)
		tmp = t_0;
	elseif (y <= 7e-154)
		tmp = Float64(x / z);
	elseif (y <= 2.3e-125)
		tmp = y;
	elseif (y <= 2.35e-43)
		tmp = Float64(x / z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (y / z);
	tmp = 0.0;
	if (y <= -1.75e-51)
		tmp = t_0;
	elseif (y <= 7e-154)
		tmp = x / z;
	elseif (y <= 2.3e-125)
		tmp = y;
	elseif (y <= 2.35e-43)
		tmp = x / z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.75e-51], t$95$0, If[LessEqual[y, 7e-154], N[(x / z), $MachinePrecision], If[LessEqual[y, 2.3e-125], y, If[LessEqual[y, 2.35e-43], N[(x / z), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.7499999999999999e-51 or 2.35e-43 < y

   1. Initial program 78.0%

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

   3. Taylor expanded in z around inf 46.0%

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

   4. Taylor expanded in x around 0 33.1%

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

      1. *-commutative 33.1%

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

   6. Simplified 33.1%

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

      1. associate-/l* 59.7%

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

      2. *-commutative 59.7%

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

   8. Applied egg-rr 59.7%

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

   if -1.7499999999999999e-51 < y < 7.0000000000000001e-154 or 2.2999999999999999e-125 < y < 2.35e-43

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 78.9%

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

   if 7.0000000000000001e-154 < y < 2.2999999999999999e-125

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 86.0%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{-51}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-154}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-125}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-43}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{-58} \lor \neg \left(z \leq 2.7 \cdot 10^{-6}\right):\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1 - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.65e-58) (not (<= z 2.7e-6)))
   (+ y (/ x z))
   (* x (/ (- 1.0 y) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.65e-58) || !(z <= 2.7e-6)) {
		tmp = y + (x / z);
	} else {
		tmp = x * ((1.0 - 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 ((z <= (-2.65d-58)) .or. (.not. (z <= 2.7d-6))) then
        tmp = y + (x / z)
    else
        tmp = x * ((1.0d0 - y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.65e-58) || !(z <= 2.7e-6)) {
		tmp = y + (x / z);
	} else {
		tmp = x * ((1.0 - y) / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.65e-58) or not (z <= 2.7e-6):
		tmp = y + (x / z)
	else:
		tmp = x * ((1.0 - y) / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.65e-58) || !(z <= 2.7e-6))
		tmp = Float64(y + Float64(x / z));
	else
		tmp = Float64(x * Float64(Float64(1.0 - y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.65e-58) || ~((z <= 2.7e-6)))
		tmp = y + (x / z);
	else
		tmp = x * ((1.0 - y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.65e-58], N[Not[LessEqual[z, 2.7e-6]], $MachinePrecision]], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(1.0 - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.6500000000000002e-58 or 2.69999999999999998e-6 < z

   1. Initial program 77.8%

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

   3. Taylor expanded in z around inf 71.4%

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

   4. Taylor expanded in x around 0 89.9%

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

      1. +-commutative 89.9%

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

   6. Simplified 89.9%

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

   if -2.6500000000000002e-58 < z < 2.69999999999999998e-6

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 91.7%

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

      1. associate-/l* 87.7%

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

      2. mul-1-neg 87.7%

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

      3. unsub-neg 87.7%

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

   5. Simplified 87.7%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{-58} \lor \neg \left(z \leq 2.7 \cdot 10^{-6}\right):\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1 - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -480000 \lor \neg \left(y \leq 7.6 \cdot 10^{-6}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -480000.0) (not (<= y 7.6e-6)))
   (* y (- 1.0 (/ x z)))
   (+ y (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -480000.0) || !(y <= 7.6e-6)) {
		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 <= (-480000.0d0)) .or. (.not. (y <= 7.6d-6))) 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 <= -480000.0) || !(y <= 7.6e-6)) {
		tmp = y * (1.0 - (x / z));
	} else {
		tmp = y + (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -480000.0) or not (y <= 7.6e-6):
		tmp = y * (1.0 - (x / z))
	else:
		tmp = y + (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -480000.0) || !(y <= 7.6e-6))
		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 <= -480000.0) || ~((y <= 7.6e-6)))
		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, -480000.0], N[Not[LessEqual[y, 7.6e-6]], $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 < -4.8e5 or 7.6000000000000001e-6 < y

   1. Initial program 74.9%

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

   3. Taylor expanded in y around inf 74.7%

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

      1. associate-/l* 99.7%

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

      2. div-sub 99.7%

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

      3. *-inverses 99.7%

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

   5. Simplified 99.7%

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

   if -4.8e5 < y < 7.6000000000000001e-6

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 99.1%

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

   4. Taylor expanded in x around 0 99.2%

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

      1. +-commutative 99.2%

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

   6. Simplified 99.2%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -480000 \lor \neg \left(y \leq 7.6 \cdot 10^{-6}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-140} \lor \neg \left(z \leq -1.16 \cdot 10^{-200}\right):\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{-z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -8.5e-140) (not (<= z -1.16e-200)))
   (+ y (/ x z))
   (* y (/ x (- z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8.5e-140) || !(z <= -1.16e-200)) {
		tmp = y + (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 ((z <= (-8.5d-140)) .or. (.not. (z <= (-1.16d-200)))) then
        tmp = y + (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 ((z <= -8.5e-140) || !(z <= -1.16e-200)) {
		tmp = y + (x / z);
	} else {
		tmp = y * (x / -z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -8.5e-140) or not (z <= -1.16e-200):
		tmp = y + (x / z)
	else:
		tmp = y * (x / -z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -8.5e-140) || !(z <= -1.16e-200))
		tmp = Float64(y + Float64(x / z));
	else
		tmp = Float64(y * Float64(x / Float64(-z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -8.5e-140) || ~((z <= -1.16e-200)))
		tmp = y + (x / z);
	else
		tmp = y * (x / -z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -8.5e-140], N[Not[LessEqual[z, -1.16e-200]], $MachinePrecision]], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / (-z)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.49999999999999997e-140 or -1.1600000000000001e-200 < z

   1. Initial program 86.8%

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

   3. Taylor expanded in z around inf 71.2%

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

   4. Taylor expanded in x around 0 82.2%

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

      1. +-commutative 82.2%

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

   6. Simplified 82.2%

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

   if -8.49999999999999997e-140 < z < -1.1600000000000001e-200

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-rgt-neg-out 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in x around 0 100.0%

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

       1. mul-1-neg 100.0%

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

       2. *-commutative 100.0%

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

       3. associate-*r/ 99.9%

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

       4. distribute-rgt-neg-in 99.9%

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

       5. distribute-neg-frac2 99.9%

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

   11. Simplified 99.9%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-140} \lor \neg \left(z \leq -1.16 \cdot 10^{-200}\right):\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{-z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-140} \lor \neg \left(z \leq -2.3 \cdot 10^{-200}\right):\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-y \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -8.5e-140) (not (<= z -2.3e-200)))
   (+ y (/ x z))
   (/ (- (* y x)) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8.5e-140) || !(z <= -2.3e-200)) {
		tmp = y + (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 ((z <= (-8.5d-140)) .or. (.not. (z <= (-2.3d-200)))) then
        tmp = y + (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 ((z <= -8.5e-140) || !(z <= -2.3e-200)) {
		tmp = y + (x / z);
	} else {
		tmp = -(y * x) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -8.5e-140) or not (z <= -2.3e-200):
		tmp = y + (x / z)
	else:
		tmp = -(y * x) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -8.5e-140) || !(z <= -2.3e-200))
		tmp = Float64(y + Float64(x / z));
	else
		tmp = Float64(Float64(-Float64(y * x)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -8.5e-140) || ~((z <= -2.3e-200)))
		tmp = y + (x / z);
	else
		tmp = -(y * x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -8.5e-140], N[Not[LessEqual[z, -2.3e-200]], $MachinePrecision]], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], N[((-N[(y * x), $MachinePrecision]) / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.49999999999999997e-140 or -2.30000000000000007e-200 < z

   1. Initial program 86.8%

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

   3. Taylor expanded in z around inf 71.2%

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

   4. Taylor expanded in x around 0 82.2%

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

      1. +-commutative 82.2%

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

   6. Simplified 82.2%

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

   if -8.49999999999999997e-140 < z < -2.30000000000000007e-200

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-rgt-neg-out 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-140} \lor \neg \left(z \leq -2.3 \cdot 10^{-200}\right):\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-y \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 97.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+52}:\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot \left(\frac{1}{z} - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2e+52) (* y (- 1.0 (/ x z))) (+ y (* x (- (/ 1.0 z) (/ y z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2e+52) {
		tmp = y * (1.0 - (x / z));
	} else {
		tmp = y + (x * ((1.0 / 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 <= (-2d+52)) then
        tmp = y * (1.0d0 - (x / z))
    else
        tmp = y + (x * ((1.0d0 / z) - (y / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2e+52) {
		tmp = y * (1.0 - (x / z));
	} else {
		tmp = y + (x * ((1.0 / z) - (y / z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2e+52:
		tmp = y * (1.0 - (x / z))
	else:
		tmp = y + (x * ((1.0 / z) - (y / z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2e+52)
		tmp = Float64(y * Float64(1.0 - Float64(x / z)));
	else
		tmp = Float64(y + Float64(x * Float64(Float64(1.0 / z) - Float64(y / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2e+52)
		tmp = y * (1.0 - (x / z));
	else
		tmp = y + (x * ((1.0 / z) - (y / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2e+52], N[(y * N[(1.0 - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(x * N[(N[(1.0 / z), $MachinePrecision] - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2e52

   1. Initial program 72.7%

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

   3. Taylor expanded in y around inf 72.7%

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

      1. associate-/l* 99.9%

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

      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 -2e52 < y

   1. Initial program 92.5%

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

   3. Taylor expanded in x around 0 98.8%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+52}:\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot \left(\frac{1}{z} - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 58.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-6}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 38000000000:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.4e-6) y (if (<= z 38000000000.0) (/ x z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.4e-6) {
		tmp = y;
	} else if (z <= 38000000000.0) {
		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 <= (-1.4d-6)) then
        tmp = y
    else if (z <= 38000000000.0d0) 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 <= -1.4e-6) {
		tmp = y;
	} else if (z <= 38000000000.0) {
		tmp = x / z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.4e-6:
		tmp = y
	elif z <= 38000000000.0:
		tmp = x / z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.4e-6)
		tmp = y;
	elseif (z <= 38000000000.0)
		tmp = Float64(x / z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.4e-6)
		tmp = y;
	elseif (z <= 38000000000.0)
		tmp = x / z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.4e-6], y, If[LessEqual[z, 38000000000.0], N[(x / z), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if z < -1.39999999999999994e-6 or 3.8e10 < z

   1. Initial program 76.1%

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

   3. Taylor expanded in x around 0 67.7%

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

   if -1.39999999999999994e-6 < z < 3.8e10

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 57.7%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-6}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 38000000000:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 77.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.6 \cdot 10^{+208}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{-z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 1.6e+208) (+ y (/ x z)) (* x (/ y (- z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.6e+208) {
		tmp = y + (x / 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+208) then
        tmp = y + (x / 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+208) {
		tmp = y + (x / z);
	} else {
		tmp = x * (y / -z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1.6e+208:
		tmp = y + (x / z)
	else:
		tmp = x * (y / -z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.6e+208)
		tmp = Float64(y + Float64(x / 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+208)
		tmp = y + (x / z);
	else
		tmp = x * (y / -z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1.6e+208], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / (-z)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.6000000000000001e208

   1. Initial program 87.8%

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

   3. Taylor expanded in z around inf 71.7%

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

   4. Taylor expanded in x around 0 82.7%

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

      1. +-commutative 82.7%

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

   6. Simplified 82.7%

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

   if 1.6000000000000001e208 < y

   1. Initial program 78.1%

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

   3. Taylor expanded in x around inf 68.9%

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

      1. mul-1-neg 68.9%

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

      2. unsub-neg 68.9%

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

   5. Simplified 68.9%

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

   6. Taylor expanded in y around inf 68.9%

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

      1. mul-1-neg 68.9%

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

      2. distribute-rgt-neg-out 68.9%

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

   8. Simplified 68.9%

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

   9. Taylor expanded in x around 0 68.9%

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

       1. mul-1-neg 68.9%

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

       2. associate-*r/ 81.5%

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

       3. distribute-rgt-neg-in 81.5%

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

   11. Simplified 81.5%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.6 \cdot 10^{+208}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{-z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 77.8% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.4%

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

3. Taylor expanded in z around inf 69.1%

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

4. Taylor expanded in x around 0 79.6%

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

   1. +-commutative 79.6%

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

6. Simplified 79.6%

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

7. Final simplification 79.6%

   \[\leadsto y + \frac{x}{z} \]
8. Add Preprocessing

Alternative 11: 40.2% 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 87.4%

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

3. Taylor expanded in x around 0 41.4%

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

4. Final simplification 41.4%

   \[\leadsto y \]
5. Add Preprocessing

Developer target: 93.8% 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 2024043 
(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))