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

Percentage Accurate: 88.5% → 99.8%

Time: 9.0s

Alternatives: 10

Speedup: 0.9×

• 20.5% 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: 99.8% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.8%

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

2. Taylor expanded in x around inf 97.3%

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

   1. frac-2neg 97.3%

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

   2. div-inv 97.2%

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

4. Applied egg-rr 97.2%

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

   1. associate-*r/ 97.3%

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

   2. *-rgt-identity 97.3%

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

   3. *-commutative 97.3%

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

   4. associate-/l* 99.8%

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

6. Simplified 99.8%

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

7. Final simplification 99.8%

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

Alternative 2: 96.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+102} \lor \neg \left(z \leq 1.5 \cdot 10^{+143}\right):\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \left(z - x\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -6.5e+102) (not (<= z 1.5e+143)))
   (+ y (/ x z))
   (/ (+ x (* y (- z x))) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6.5e+102) || !(z <= 1.5e+143)) {
		tmp = y + (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 ((z <= (-6.5d+102)) .or. (.not. (z <= 1.5d+143))) then
        tmp = y + (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 ((z <= -6.5e+102) || !(z <= 1.5e+143)) {
		tmp = y + (x / z);
	} else {
		tmp = (x + (y * (z - x))) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -6.5e+102) or not (z <= 1.5e+143):
		tmp = y + (x / z)
	else:
		tmp = (x + (y * (z - x))) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -6.5e+102) || !(z <= 1.5e+143))
		tmp = Float64(y + 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 ((z <= -6.5e+102) || ~((z <= 1.5e+143)))
		tmp = y + (x / z);
	else
		tmp = (x + (y * (z - x))) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -6.5e+102], N[Not[LessEqual[z, 1.5e+143]], $MachinePrecision]], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.5000000000000004e102 or 1.5e143 < z

   1. Initial program 72.5%

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

   2. Taylor expanded in z around inf 68.8%

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

   3. Taylor expanded in x around 0 93.3%

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

      1. +-commutative 93.3%

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

   5. Simplified 93.3%

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

   if -6.5000000000000004e102 < z < 1.5e143

   1. Initial program 99.3%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+102} \lor \neg \left(z \leq 1.5 \cdot 10^{+143}\right):\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \left(z - x\right)}{z}\\ \end{array} \]

Alternative 3: 85.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-15} \lor \neg \left(x \leq 1.02 \cdot 10^{+34}\right):\\ \;\;\;\;x \cdot \frac{1 - y}{z}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -9e-15) (not (<= x 1.02e+34)))
   (* x (/ (- 1.0 y) z))
   (+ y (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -9e-15) || !(x <= 1.02e+34)) {
		tmp = x * ((1.0 - y) / 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 ((x <= (-9d-15)) .or. (.not. (x <= 1.02d+34))) then
        tmp = x * ((1.0d0 - y) / 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 ((x <= -9e-15) || !(x <= 1.02e+34)) {
		tmp = x * ((1.0 - y) / z);
	} else {
		tmp = y + (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -9e-15) or not (x <= 1.02e+34):
		tmp = x * ((1.0 - y) / z)
	else:
		tmp = y + (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -9e-15) || !(x <= 1.02e+34))
		tmp = Float64(x * Float64(Float64(1.0 - y) / z));
	else
		tmp = Float64(y + Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -9e-15) || ~((x <= 1.02e+34)))
		tmp = x * ((1.0 - y) / z);
	else
		tmp = y + (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -9e-15], N[Not[LessEqual[x, 1.02e+34]], $MachinePrecision]], N[(x * N[(N[(1.0 - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.9999999999999995e-15 or 1.02e34 < x

   1. Initial program 92.3%

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

   2. Taylor expanded in x around inf 84.9%

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

      1. associate-/l* 87.2%

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

      2. associate-/r/ 87.1%

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

      3. mul-1-neg 87.1%

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

      4. unsub-neg 87.1%

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

   4. Simplified 87.1%

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

   if -8.9999999999999995e-15 < x < 1.02e34

   1. Initial program 89.3%

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

   2. Taylor expanded in z around inf 78.6%

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

   3. Taylor expanded in x around 0 89.3%

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

      1. +-commutative 89.3%

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

   5. Simplified 89.3%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-15} \lor \neg \left(x \leq 1.02 \cdot 10^{+34}\right):\\ \;\;\;\;x \cdot \frac{1 - y}{z}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \]

Alternative 4: 95.2% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 1.0))
		tmp = Float64(y - Float64(x * Float64(y / 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 <= -1.0) || ~((y <= 1.0)))
		tmp = y - (x * (y / z));
	else
		tmp = y + (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 80.7%

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

   2. Taylor expanded in x around inf 94.4%

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

   3. Taylor expanded in y around inf 98.0%

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

      1. distribute-lft-in 98.1%

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

      2. *-commutative 98.1%

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

      3. associate-*r* 98.1%

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

      4. associate-*r/ 92.6%

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

      5. *-commutative 92.6%

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

      6. *-rgt-identity 92.6%

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

      7. mul-1-neg 92.6%

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

      8. unsub-neg 92.6%

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

      9. associate-*l/ 90.4%

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

      10. *-commutative 90.4%

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

   5. Simplified 90.4%

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

   if -1 < y < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 99.5%

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

   3. Taylor expanded in x around 0 99.5%

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

      1. +-commutative 99.5%

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

   5. Simplified 99.5%

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

4. Final simplification 95.2%

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

Alternative 5: 95.5% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 1.0))
		tmp = Float64(y - Float64(Float64(y * 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 <= -1.0) || ~((y <= 1.0)))
		tmp = y - ((y * x) / z);
	else
		tmp = y + (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 80.7%

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

   2. Taylor expanded in x around inf 94.4%

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

   3. Taylor expanded in y around inf 98.0%

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

      1. distribute-lft-in 98.1%

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

      2. *-commutative 98.1%

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

      3. associate-*r* 98.1%

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

      4. associate-*r/ 92.6%

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

      5. *-commutative 92.6%

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

      6. *-rgt-identity 92.6%

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

      7. mul-1-neg 92.6%

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

      8. unsub-neg 92.6%

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

      9. associate-*l/ 90.4%

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

      10. *-commutative 90.4%

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

   5. Simplified 90.4%

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

   6. Taylor expanded in x around 0 92.6%

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

   if -1 < y < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 99.5%

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

   3. Taylor expanded in x around 0 99.5%

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

      1. +-commutative 99.5%

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

   5. Simplified 99.5%

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

4. Final simplification 96.2%

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

Alternative 6: 79.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 30:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{+162}:\\ \;\;\;\;\frac{-y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 30.0)
   (+ y (/ x z))
   (if (<= y 8.6e+162) (/ (- y) (/ z x)) (- y (/ x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 30.0) {
		tmp = y + (x / z);
	} else if (y <= 8.6e+162) {
		tmp = -y / (z / x);
	} 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 <= 30.0d0) then
        tmp = y + (x / z)
    else if (y <= 8.6d+162) then
        tmp = -y / (z / x)
    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 <= 30.0) {
		tmp = y + (x / z);
	} else if (y <= 8.6e+162) {
		tmp = -y / (z / x);
	} else {
		tmp = y - (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 30.0:
		tmp = y + (x / z)
	elif y <= 8.6e+162:
		tmp = -y / (z / x)
	else:
		tmp = y - (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 30.0)
		tmp = Float64(y + Float64(x / z));
	elseif (y <= 8.6e+162)
		tmp = Float64(Float64(-y) / Float64(z / x));
	else
		tmp = Float64(y - Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 30.0)
		tmp = y + (x / z);
	elseif (y <= 8.6e+162)
		tmp = -y / (z / x);
	else
		tmp = y - (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 30.0], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.6e+162], N[((-y) / N[(z / x), $MachinePrecision]), $MachinePrecision], N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 30

   1. Initial program 94.1%

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

   2. Taylor expanded in z around inf 84.5%

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

   3. Taylor expanded in x around 0 90.1%

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

      1. +-commutative 90.1%

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

   5. Simplified 90.1%

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

   if 30 < y < 8.6000000000000004e162

   1. Initial program 86.1%

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

   2. Taylor expanded in x around inf 62.1%

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

      1. *-commutative 62.1%

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

      2. associate-/l* 58.4%

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

      3. mul-1-neg 58.4%

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

      4. unsub-neg 58.4%

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

   4. Simplified 58.4%

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

   5. Taylor expanded in y around inf 54.3%

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

      1. associate-*r/ 54.3%

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

      2. neg-mul-1 54.3%

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

   7. Simplified 54.3%

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

      1. frac-2neg 54.3%

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

      2. div-inv 53.5%

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

      3. distribute-frac-neg 53.5%

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

      4. remove-double-neg 53.5%

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

      5. clear-num 53.4%

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

   9. Applied egg-rr 53.4%

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

       1. *-commutative 53.4%

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

       2. distribute-rgt-neg-out 53.4%

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

       3. associate-/r/ 63.2%

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

       4. distribute-neg-frac 63.2%

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

   11. Applied egg-rr 63.2%

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

   if 8.6000000000000004e162 < y

   1. Initial program 73.7%

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

   2. Taylor expanded in z around inf 28.2%

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

   3. Taylor expanded in x around 0 51.2%

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

      1. +-commutative 51.2%

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

   5. Simplified 51.2%

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

      1. div-inv 51.2%

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

      2. fma-def 51.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, \frac{1}{z}, y\right)} \]

      3. frac-2neg 51.2%

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

      4. metadata-eval 51.2%

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

      5. add-sqr-sqrt 22.4%

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

      6. sqrt-unprod 54.6%

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

      7. sqr-neg 54.6%

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

      8. sqrt-unprod 32.4%

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

      9. add-sqr-sqrt 69.1%

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

   7. Applied egg-rr 69.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \frac{-1}{z}, y\right)} \]
   8. Step-by-step derivation

      1. fma-udef 69.1%

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

      2. *-commutative 69.1%

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

      3. associate-*l/ 69.1%

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

      4. associate-*r/ 69.1%

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

      5. mul-1-neg 69.1%

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

      6. +-commutative 69.1%

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

      7. sub-neg 69.1%

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

   9. Simplified 69.1%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 30:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{+162}:\\ \;\;\;\;\frac{-y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{x}{z}\\ \end{array} \]

Alternative 7: 57.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -450000000:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{+82}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -450000000.0) y (if (<= z 8.4e+82) (/ x z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -450000000.0) {
		tmp = y;
	} else if (z <= 8.4e+82) {
		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 <= (-450000000.0d0)) then
        tmp = y
    else if (z <= 8.4d+82) 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 <= -450000000.0) {
		tmp = y;
	} else if (z <= 8.4e+82) {
		tmp = x / z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -450000000.0:
		tmp = y
	elif z <= 8.4e+82:
		tmp = x / z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -450000000.0)
		tmp = y;
	elseif (z <= 8.4e+82)
		tmp = Float64(x / z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -450000000.0)
		tmp = y;
	elseif (z <= 8.4e+82)
		tmp = x / z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -450000000.0], y, If[LessEqual[z, 8.4e+82], N[(x / z), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if z < -4.5e8 or 8.4000000000000001e82 < z

   1. Initial program 79.3%

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

   2. Taylor expanded in x around 0 74.6%

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

   if -4.5e8 < z < 8.4000000000000001e82

   1. Initial program 99.3%

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

   2. Taylor expanded in y around 0 56.3%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -450000000:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{+82}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 8: 81.4% accurate, 1.3× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.0) {
		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 (y <= 1.0d0) 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 (y <= 1.0) {
		tmp = y + (x / z);
	} else {
		tmp = y - (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1.0:
		tmp = y + (x / z)
	else:
		tmp = y - (x / 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(y - Float64(x / 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 = y - (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < 1

   1. Initial program 94.1%

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

   2. Taylor expanded in z around inf 84.5%

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

   3. Taylor expanded in x around 0 90.1%

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

      1. +-commutative 90.1%

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

   5. Simplified 90.1%

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

   if 1 < y

   1. Initial program 80.6%

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

   2. Taylor expanded in z around inf 26.4%

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

   3. Taylor expanded in x around 0 41.2%

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

      1. +-commutative 41.2%

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

   5. Simplified 41.2%

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

      1. div-inv 41.2%

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

      2. fma-def 41.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, \frac{1}{z}, y\right)} \]

      3. frac-2neg 41.2%

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

      4. metadata-eval 41.2%

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

      5. add-sqr-sqrt 23.3%

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

      6. sqrt-unprod 47.7%

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

      7. sqr-neg 47.7%

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

      8. sqrt-unprod 22.1%

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

      9. add-sqr-sqrt 58.6%

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

   7. Applied egg-rr 58.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \frac{-1}{z}, y\right)} \]
   8. Step-by-step derivation

      1. fma-udef 58.6%

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

      2. *-commutative 58.6%

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

      3. associate-*l/ 58.6%

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

      4. associate-*r/ 58.6%

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

      5. mul-1-neg 58.6%

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

      6. +-commutative 58.6%

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

      7. sub-neg 58.6%

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

   9. Simplified 58.6%

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

4. Final simplification 82.3%

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

Alternative 9: 78.0% 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 90.8%

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

2. Taylor expanded in z around inf 70.2%

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

3. Taylor expanded in x around 0 78.1%

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

   1. +-commutative 78.1%

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

5. Simplified 78.1%

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

6. Final simplification 78.1%

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

Alternative 10: 41.3% 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 90.8%

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

2. Taylor expanded in x around 0 40.2%

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

3. Final simplification 40.2%

   \[\leadsto y \]

Developer target: 94.2% 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 2023221 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:rasterificRadialGradient from diagrams-rasterific-1.3.1.3"
  :precision binary64

  :herbie-target
  (- (+ y (/ x z)) (/ y (/ z x)))

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