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

Percentage Accurate: 88.3% → 99.6%

Time: 8.7s

Alternatives: 11

Speedup: 0.8×

• 21.0% 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: 88.3% 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: 99.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+22} \lor \neg \left(z \leq 1.5 \cdot 10^{-77}\right):\\ \;\;\;\;y - x \cdot \frac{y + -1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \left(z - x\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.1e+22) (not (<= z 1.5e-77)))
   (- y (* x (/ (+ y -1.0) z)))
   (/ (+ x (* y (- z x))) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.1e+22) || !(z <= 1.5e-77)) {
		tmp = y - (x * ((y + -1.0) / 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 <= (-1.1d+22)) .or. (.not. (z <= 1.5d-77))) then
        tmp = y - (x * ((y + (-1.0d0)) / 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 <= -1.1e+22) || !(z <= 1.5e-77)) {
		tmp = y - (x * ((y + -1.0) / z));
	} else {
		tmp = (x + (y * (z - x))) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.1e+22) or not (z <= 1.5e-77):
		tmp = y - (x * ((y + -1.0) / z))
	else:
		tmp = (x + (y * (z - x))) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.1e+22) || !(z <= 1.5e-77))
		tmp = Float64(y - Float64(x * Float64(Float64(y + -1.0) / 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 <= -1.1e+22) || ~((z <= 1.5e-77)))
		tmp = y - (x * ((y + -1.0) / z));
	else
		tmp = (x + (y * (z - x))) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.1e+22], N[Not[LessEqual[z, 1.5e-77]], $MachinePrecision]], N[(y - N[(x * N[(N[(y + -1.0), $MachinePrecision] / 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 z < -1.1e22 or 1.50000000000000008e-77 < z

   1. Initial program 74.8%

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

   2. Taylor expanded in y around inf 74.8%

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

   3. Taylor expanded in z around -inf 92.1%

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

      1. mul-1-neg 92.1%

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

      2. unsub-neg 92.1%

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

      3. distribute-rgt-out 92.1%

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

      4. *-lft-identity 92.1%

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

      5. times-frac 99.9%

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

      6. /-rgt-identity 99.9%

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

      7. +-commutative 99.9%

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

   5. Simplified 99.9%

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

   if -1.1e22 < z < 1.50000000000000008e-77

   1. Initial program 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+22} \lor \neg \left(z \leq 1.5 \cdot 10^{-77}\right):\\ \;\;\;\;y - x \cdot \frac{y + -1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \left(z - x\right)}{z}\\ \end{array} \]

Alternative 2: 99.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+155} \lor \neg \left(y \leq 220000000\right):\\ \;\;\;\;y \cdot \frac{z - x}{z}\\ \mathbf{else}:\\ \;\;\;\;y - x \cdot \frac{y + -1}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.02e+155) (not (<= y 220000000.0)))
   (* y (/ (- z x) z))
   (- y (* x (/ (+ y -1.0) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.02e+155) || !(y <= 220000000.0)) {
		tmp = y * ((z - x) / z);
	} else {
		tmp = y - (x * ((y + -1.0) / 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 <= (-1.02d+155)) .or. (.not. (y <= 220000000.0d0))) then
        tmp = y * ((z - x) / z)
    else
        tmp = y - (x * ((y + (-1.0d0)) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.02e+155) || !(y <= 220000000.0)) {
		tmp = y * ((z - x) / z);
	} else {
		tmp = y - (x * ((y + -1.0) / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.02e+155) or not (y <= 220000000.0):
		tmp = y * ((z - x) / z)
	else:
		tmp = y - (x * ((y + -1.0) / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.02e+155) || !(y <= 220000000.0))
		tmp = Float64(y * Float64(Float64(z - x) / z));
	else
		tmp = Float64(y - Float64(x * Float64(Float64(y + -1.0) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.02e+155) || ~((y <= 220000000.0)))
		tmp = y * ((z - x) / z);
	else
		tmp = y - (x * ((y + -1.0) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.02e+155], N[Not[LessEqual[y, 220000000.0]], $MachinePrecision]], N[(y * N[(N[(z - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(y - N[(x * N[(N[(y + -1.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.02e155 or 2.2e8 < y

   1. Initial program 72.8%

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

   2. Taylor expanded in y around inf 72.8%

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

      1. *-commutative 72.8%

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

      2. associate-/l* 87.9%

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

   4. Simplified 87.9%

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

      1. associate-/r/ 99.9%

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

   6. Applied egg-rr 99.9%

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

   if -1.02e155 < y < 2.2e8

   1. Initial program 96.2%

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

   2. Taylor expanded in y around inf 91.7%

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

   3. Taylor expanded in z around -inf 99.4%

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

      1. mul-1-neg 99.4%

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

      2. unsub-neg 99.4%

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

      3. distribute-rgt-out 99.3%

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

      4. *-lft-identity 99.3%

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

      5. times-frac 99.8%

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

      6. /-rgt-identity 99.8%

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

      7. +-commutative 99.8%

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

   5. Simplified 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+155} \lor \neg \left(y \leq 220000000\right):\\ \;\;\;\;y \cdot \frac{z - x}{z}\\ \mathbf{else}:\\ \;\;\;\;y - x \cdot \frac{y + -1}{z}\\ \end{array} \]

Alternative 3: 84.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.96 \lor \neg \left(x \leq 1.04 \cdot 10^{+139}\right):\\ \;\;\;\;x \cdot \frac{1 - y}{z}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -0.96) (not (<= x 1.04e+139)))
   (* x (/ (- 1.0 y) z))
   (+ y (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.96) || !(x <= 1.04e+139)) {
		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 <= (-0.96d0)) .or. (.not. (x <= 1.04d+139))) 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 <= -0.96) || !(x <= 1.04e+139)) {
		tmp = x * ((1.0 - y) / z);
	} else {
		tmp = y + (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -0.96) or not (x <= 1.04e+139):
		tmp = x * ((1.0 - y) / z)
	else:
		tmp = y + (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -0.96) || !(x <= 1.04e+139))
		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 <= -0.96) || ~((x <= 1.04e+139)))
		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, -0.96], N[Not[LessEqual[x, 1.04e+139]], $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 < -0.95999999999999996 or 1.04e139 < x

   1. Initial program 87.7%

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

   2. Taylor expanded in x around inf 82.0%

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

      1. associate-/l* 86.5%

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

      2. associate-/r/ 86.6%

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

      3. mul-1-neg 86.6%

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

      4. unsub-neg 86.6%

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

   4. Simplified 86.6%

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

   if -0.95999999999999996 < x < 1.04e139

   1. Initial program 86.6%

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

   2. Taylor expanded in z around inf 73.4%

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

   3. Taylor expanded in x around 0 86.8%

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

      1. +-commutative 86.8%

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

   5. Simplified 86.8%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.96 \lor \neg \left(x \leq 1.04 \cdot 10^{+139}\right):\\ \;\;\;\;x \cdot \frac{1 - y}{z}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \]

Alternative 4: 98.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+15} \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \frac{z - x}{z}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.4e+15) (not (<= y 1.0))) (* y (/ (- z x) z)) (+ y (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.4e+15) || !(y <= 1.0)) {
		tmp = y * ((z - 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 <= (-2.4d+15)) .or. (.not. (y <= 1.0d0))) then
        tmp = y * ((z - 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 <= -2.4e+15) || !(y <= 1.0)) {
		tmp = y * ((z - x) / z);
	} else {
		tmp = y + (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.4e+15) or not (y <= 1.0):
		tmp = y * ((z - x) / z)
	else:
		tmp = y + (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.4e+15) || !(y <= 1.0))
		tmp = Float64(y * Float64(Float64(z - 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 <= -2.4e+15) || ~((y <= 1.0)))
		tmp = y * ((z - x) / z);
	else
		tmp = y + (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.4e+15], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(y * N[(N[(z - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.4e15 or 1 < y

   1. Initial program 74.4%

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

   2. Taylor expanded in y around inf 73.5%

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

      1. *-commutative 73.5%

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

      2. associate-/l* 89.8%

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

   4. Simplified 89.8%

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

      1. associate-/r/ 99.0%

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

   6. Applied egg-rr 99.0%

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

   if -2.4e15 < y < 1

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 99.2%

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

   3. Taylor expanded in x around 0 99.3%

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

      1. +-commutative 99.3%

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

   5. Simplified 99.3%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+15} \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \frac{z - x}{z}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \]

Alternative 5: 97.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 220000000:\\ \;\;\;\;y + \frac{\left(1 - y\right) \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 220000000.0) (+ y (/ (* (- 1.0 y) x) z)) (* y (/ (- z x) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 220000000.0) {
		tmp = y + (((1.0 - y) * x) / z);
	} else {
		tmp = 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 <= 220000000.0d0) then
        tmp = y + (((1.0d0 - y) * x) / z)
    else
        tmp = 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 <= 220000000.0) {
		tmp = y + (((1.0 - y) * x) / z);
	} else {
		tmp = y * ((z - x) / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 220000000.0:
		tmp = y + (((1.0 - y) * x) / z)
	else:
		tmp = y * ((z - x) / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 220000000.0)
		tmp = Float64(y + Float64(Float64(Float64(1.0 - y) * x) / z));
	else
		tmp = Float64(y * Float64(Float64(z - x) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 220000000.0)
		tmp = y + (((1.0 - y) * x) / z);
	else
		tmp = y * ((z - x) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 220000000.0], N[(y + N[(N[(N[(1.0 - y), $MachinePrecision] * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.2e8

   1. Initial program 93.3%

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

   2. Taylor expanded in x around inf 98.5%

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

   if 2.2e8 < y

   1. Initial program 70.4%

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

   2. Taylor expanded in y around inf 70.4%

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

      1. *-commutative 70.4%

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

      2. associate-/l* 89.2%

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

   4. Simplified 89.2%

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

      1. associate-/r/ 99.9%

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

   6. Applied egg-rr 99.9%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 220000000:\\ \;\;\;\;y + \frac{\left(1 - y\right) \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - x}{z}\\ \end{array} \]

Alternative 6: 77.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 7 \cdot 10^{+270}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 7e+270) (+ y (/ x z)) (* y (/ (- x) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 7e+270) {
		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 (x <= 7d+270) 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 (x <= 7e+270) {
		tmp = y + (x / z);
	} else {
		tmp = y * (-x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 7e+270:
		tmp = y + (x / z)
	else:
		tmp = y * (-x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 7e+270)
		tmp = Float64(y + Float64(x / z));
	else
		tmp = Float64(y * Float64(Float64(-x) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 7e+270)
		tmp = y + (x / z);
	else
		tmp = y * (-x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 7e+270], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], N[(y * N[((-x) / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 6.9999999999999999e270

   1. Initial program 87.3%

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

   2. Taylor expanded in z around inf 67.7%

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

   3. Taylor expanded in x around 0 77.8%

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

      1. +-commutative 77.8%

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

   5. Simplified 77.8%

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

   if 6.9999999999999999e270 < x

   1. Initial program 80.9%

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

   2. Taylor expanded in y around inf 60.9%

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

      1. *-commutative 60.9%

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

      2. associate-/l* 80.0%

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

   4. Simplified 80.0%

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

      1. associate-/r/ 79.7%

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

   6. Applied egg-rr 79.7%

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

   7. Taylor expanded in z around 0 60.9%

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

      1. mul-1-neg 60.9%

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

      2. associate-*l/ 79.9%

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

      3. distribute-rgt-neg-out 79.9%

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

      4. associate-*l/ 60.9%

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

      5. associate-*r/ 79.7%

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

   9. Simplified 79.7%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 7 \cdot 10^{+270}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-x}{z}\\ \end{array} \]

Alternative 7: 77.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 5.4 \cdot 10^{+268}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-\frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 5.4e+268) (+ y (/ x z)) (* x (- (/ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 5.4e+268) {
		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 (x <= 5.4d+268) 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 (x <= 5.4e+268) {
		tmp = y + (x / z);
	} else {
		tmp = x * -(y / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 5.4e+268:
		tmp = y + (x / z)
	else:
		tmp = x * -(y / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 5.4e+268)
		tmp = Float64(y + Float64(x / z));
	else
		tmp = Float64(x * Float64(-Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 5.4e+268)
		tmp = y + (x / z);
	else
		tmp = x * -(y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 5.4e+268], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x * (-N[(y / z), $MachinePrecision])), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 5.40000000000000022e268

   1. Initial program 87.3%

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

   2. Taylor expanded in z around inf 67.7%

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

   3. Taylor expanded in x around 0 77.8%

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

      1. +-commutative 77.8%

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

   5. Simplified 77.8%

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

   if 5.40000000000000022e268 < x

   1. Initial program 80.9%

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

   2. Taylor expanded in y around inf 60.9%

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

      1. *-commutative 60.9%

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

      2. associate-/l* 80.0%

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

   4. Simplified 80.0%

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

      1. associate-/r/ 79.7%

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

   6. Applied egg-rr 79.7%

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

   7. Taylor expanded in z around 0 60.9%

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

      1. mul-1-neg 60.9%

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

      2. associate-*l/ 79.9%

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

      3. distribute-rgt-neg-out 79.9%

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

   9. Simplified 79.9%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 5.4 \cdot 10^{+268}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-\frac{y}{z}\right)\\ \end{array} \]

Alternative 8: 60.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0005:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-52}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -0.0005) y (if (<= y 1.65e-52) (/ x z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -0.0005) {
		tmp = y;
	} else if (y <= 1.65e-52) {
		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 (y <= (-0.0005d0)) then
        tmp = y
    else if (y <= 1.65d-52) 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 (y <= -0.0005) {
		tmp = y;
	} else if (y <= 1.65e-52) {
		tmp = x / z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -0.0005:
		tmp = y
	elif y <= 1.65e-52:
		tmp = x / z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -0.0005)
		tmp = y;
	elseif (y <= 1.65e-52)
		tmp = Float64(x / z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -0.0005)
		tmp = y;
	elseif (y <= 1.65e-52)
		tmp = x / z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -0.0005], y, If[LessEqual[y, 1.65e-52], N[(x / z), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if y < -5.0000000000000001e-4 or 1.64999999999999998e-52 < y

   1. Initial program 76.5%

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

   2. Taylor expanded in x around 0 52.0%

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

   if -5.0000000000000001e-4 < y < 1.64999999999999998e-52

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 71.6%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0005:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-52}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 9: 61.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00048:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-52}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -0.00048) (* z (/ y z)) (if (<= y 3.3e-52) (/ x z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -0.00048) {
		tmp = z * (y / z);
	} else if (y <= 3.3e-52) {
		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 (y <= (-0.00048d0)) then
        tmp = z * (y / z)
    else if (y <= 3.3d-52) 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 (y <= -0.00048) {
		tmp = z * (y / z);
	} else if (y <= 3.3e-52) {
		tmp = x / z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -0.00048:
		tmp = z * (y / z)
	elif y <= 3.3e-52:
		tmp = x / z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -0.00048)
		tmp = Float64(z * Float64(y / z));
	elseif (y <= 3.3e-52)
		tmp = Float64(x / z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -0.00048)
		tmp = z * (y / z);
	elseif (y <= 3.3e-52)
		tmp = x / z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -0.00048], N[(z * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.3e-52], N[(x / z), $MachinePrecision], y]]

Derivation

1. Split input into 3 regimes

2. if y < -4.80000000000000012e-4

   1. Initial program 79.8%

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

   2. Taylor expanded in z around inf 43.4%

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

   3. Taylor expanded in x around 0 34.4%

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

      1. *-commutative 34.4%

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

   5. Simplified 34.4%

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

      1. associate-/l* 50.3%

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

      2. div-inv 51.8%

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

      3. clear-num 51.9%

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

   7. Applied egg-rr 51.9%

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

   if -4.80000000000000012e-4 < y < 3.29999999999999995e-52

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 71.6%

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

   if 3.29999999999999995e-52 < y

   1. Initial program 74.1%

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

   2. Taylor expanded in x around 0 53.4%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00048:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-52}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 10: 77.5% 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 87.1%

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

2. Taylor expanded in z around inf 66.4%

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

3. Taylor expanded in x around 0 76.1%

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

   1. +-commutative 76.1%

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

5. Simplified 76.1%

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

6. Final simplification 76.1%

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

Alternative 11: 40.7% 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 87.1%

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

2. Taylor expanded in x around 0 41.9%

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

3. Final simplification 41.9%

   \[\leadsto y \]

Developer target: 94.0% 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 2023238 
(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))