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

Percentage Accurate: 87.6% → 99.9%

Time: 9.6s

Alternatives: 11

Speedup: 1.0×

• 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: 87.6% 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: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ y - \frac{x}{z} \cdot \left(y + -1\right) \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = y - ((x / z) * (y + (-1.0d0)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.8%

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

2. Taylor expanded in y around inf 85.4%

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

3. Taylor expanded in z around -inf 95.9%

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

   1. mul-1-neg 95.9%

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

   2. unsub-neg 95.9%

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

   3. distribute-rgt-out 95.9%

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

   4. associate-/l* 97.4%

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

   5. +-commutative 97.4%

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

5. Simplified 97.4%

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

6. Taylor expanded in x around 0 95.9%

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

   1. sub-neg 95.9%

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

   2. metadata-eval 95.9%

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

   3. +-commutative 95.9%

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

   4. associate-*r/ 100.0%

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

   5. *-commutative 100.0%

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

   6. +-commutative 100.0%

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

8. Simplified 100.0%

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

9. Final simplification 100.0%

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

Alternative 2: 85.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-15} \lor \neg \left(z \leq 7.8 \cdot 10^{-62}\right):\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.1e-15) (not (<= z 7.8e-62)))
   (+ y (/ x z))
   (* (/ x z) (- 1.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.1e-15) || !(z <= 7.8e-62)) {
		tmp = y + (x / z);
	} else {
		tmp = (x / z) * (1.0 - 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 <= (-3.1d-15)) .or. (.not. (z <= 7.8d-62))) then
        tmp = y + (x / z)
    else
        tmp = (x / z) * (1.0d0 - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.1e-15) || !(z <= 7.8e-62)) {
		tmp = y + (x / z);
	} else {
		tmp = (x / z) * (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.1e-15) or not (z <= 7.8e-62):
		tmp = y + (x / z)
	else:
		tmp = (x / z) * (1.0 - y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.1e-15) || !(z <= 7.8e-62))
		tmp = Float64(y + Float64(x / z));
	else
		tmp = Float64(Float64(x / z) * Float64(1.0 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3.1e-15) || ~((z <= 7.8e-62)))
		tmp = y + (x / z);
	else
		tmp = (x / z) * (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.1e-15], N[Not[LessEqual[z, 7.8e-62]], $MachinePrecision]], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.0999999999999999e-15 or 7.8000000000000007e-62 < z

   1. Initial program 76.4%

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

   2. Taylor expanded in y around inf 76.4%

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

   3. Taylor expanded in z around inf 84.5%

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

   if -3.0999999999999999e-15 < z < 7.8000000000000007e-62

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 95.1%

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

   3. Taylor expanded in z around -inf 99.9%

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

      1. mul-1-neg 99.9%

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

      2. unsub-neg 99.9%

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

      3. distribute-rgt-out 99.9%

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

      4. associate-/l* 94.6%

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

      5. +-commutative 94.6%

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

   5. Simplified 94.6%

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

   6. Taylor expanded in x around 0 99.9%

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

      1. sub-neg 99.9%

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

      2. metadata-eval 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-*r/ 100.0%

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

      5. *-commutative 100.0%

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

      6. +-commutative 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in x around -inf 89.8%

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

       1. sub-neg 89.8%

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

       2. metadata-eval 89.8%

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

       3. associate-*r/ 89.8%

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

       4. associate-*l* 89.8%

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

       5. neg-mul-1 89.8%

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

       6. *-commutative 89.8%

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

       7. neg-sub0 89.8%

          \[\leadsto \frac{x}{z} \cdot \color{blue}{\left(0 - \left(y + -1\right)\right)} \]

       8. +-commutative 89.8%

          \[\leadsto \frac{x}{z} \cdot \left(0 - \color{blue}{\left(-1 + y\right)}\right) \]

       9. associate--r+ 89.8%

          \[\leadsto \frac{x}{z} \cdot \color{blue}{\left(\left(0 - -1\right) - y\right)} \]

       10. metadata-eval 89.8%

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

   11. Simplified 89.8%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-15} \lor \neg \left(z \leq 7.8 \cdot 10^{-62}\right):\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(1 - y\right)\\ \end{array} \]

Alternative 3: 99.3% accurate, 0.8× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 1.0))) (* y (/ (- z 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 * ((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 <= (-1.0d0)) .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 <= -1.0) || !(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 <= -1.0) 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 <= -1.0) || !(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 <= -1.0) || ~((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, -1.0], 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 < -1 or 1 < y

   1. Initial program 74.4%

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

   2. Taylor expanded in y around inf 73.8%

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

      1. *-commutative 73.8%

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

      2. associate-/l* 93.3%

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

      3. associate-/r/ 99.2%

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

   4. Simplified 99.2%

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

   if -1 < y < 1

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 98.4%

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

   3. Taylor expanded in z around inf 98.9%

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

4. Final simplification 99.1%

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

Alternative 4: 75.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+122} \lor \neg \left(y \leq 4.9 \cdot 10^{+225}\right):\\ \;\;\;\;\frac{y}{z} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -7.8e+122) (not (<= y 4.9e+225)))
   (* (/ y z) (- x))
   (+ y (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7.8e+122) || !(y <= 4.9e+225)) {
		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 <= (-7.8d+122)) .or. (.not. (y <= 4.9d+225))) 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 <= -7.8e+122) || !(y <= 4.9e+225)) {
		tmp = (y / z) * -x;
	} else {
		tmp = y + (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -7.8e+122) or not (y <= 4.9e+225):
		tmp = (y / z) * -x
	else:
		tmp = y + (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -7.8e+122) || !(y <= 4.9e+225))
		tmp = Float64(Float64(y / z) * Float64(-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 <= -7.8e+122) || ~((y <= 4.9e+225)))
		tmp = (y / z) * -x;
	else
		tmp = y + (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -7.8e+122], N[Not[LessEqual[y, 4.9e+225]], $MachinePrecision]], N[(N[(y / z), $MachinePrecision] * (-x)), $MachinePrecision], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.7999999999999999e122 or 4.90000000000000032e225 < y

   1. Initial program 79.9%

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

   2. Taylor expanded in y around inf 79.9%

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

   3. Taylor expanded in z around 0 60.9%

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

      1. mul-1-neg 60.9%

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

      2. associate-*l/ 65.4%

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

      3. distribute-rgt-neg-out 65.4%

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

   5. Simplified 65.4%

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

   if -7.7999999999999999e122 < y < 4.90000000000000032e225

   1. Initial program 90.2%

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

   2. Taylor expanded in y around inf 88.2%

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

   3. Taylor expanded in z around inf 88.4%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+122} \lor \neg \left(y \leq 4.9 \cdot 10^{+225}\right):\\ \;\;\;\;\frac{y}{z} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \]

Alternative 5: 75.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+123}:\\ \;\;\;\;y \cdot \left(-\frac{x}{z}\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+225}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.6e+123)
   (* y (- (/ x z)))
   (if (<= y 1.1e+225) (+ y (/ x z)) (* (/ y z) (- x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.6e+123) {
		tmp = y * -(x / z);
	} else if (y <= 1.1e+225) {
		tmp = y + (x / z);
	} else {
		tmp = (y / z) * -x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-3.6d+123)) then
        tmp = y * -(x / z)
    else if (y <= 1.1d+225) then
        tmp = y + (x / z)
    else
        tmp = (y / z) * -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.6e+123) {
		tmp = y * -(x / z);
	} else if (y <= 1.1e+225) {
		tmp = y + (x / z);
	} else {
		tmp = (y / z) * -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.6e+123:
		tmp = y * -(x / z)
	elif y <= 1.1e+225:
		tmp = y + (x / z)
	else:
		tmp = (y / z) * -x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.6e+123)
		tmp = Float64(y * Float64(-Float64(x / z)));
	elseif (y <= 1.1e+225)
		tmp = Float64(y + Float64(x / z));
	else
		tmp = Float64(Float64(y / z) * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.6e+123)
		tmp = y * -(x / z);
	elseif (y <= 1.1e+225)
		tmp = y + (x / z);
	else
		tmp = (y / z) * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.6e+123], N[(y * (-N[(x / z), $MachinePrecision])), $MachinePrecision], If[LessEqual[y, 1.1e+225], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], N[(N[(y / z), $MachinePrecision] * (-x)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.59999999999999998e123

   1. Initial program 83.0%

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

   2. Taylor expanded in y around inf 83.0%

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

      1. *-commutative 83.0%

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

      2. associate-/l* 95.8%

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

      3. associate-/r/ 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in z around 0 65.9%

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

      1. neg-mul-1 65.9%

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

      2. distribute-neg-frac 65.9%

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

   7. Simplified 65.9%

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

   if -3.59999999999999998e123 < y < 1.10000000000000007e225

   1. Initial program 90.2%

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

   2. Taylor expanded in y around inf 88.2%

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

   3. Taylor expanded in z around inf 88.4%

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

   if 1.10000000000000007e225 < y

   1. Initial program 71.4%

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

   2. Taylor expanded in y around inf 71.4%

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

   3. Taylor expanded in z around 0 52.8%

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

      1. mul-1-neg 52.8%

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

      2. associate-*l/ 66.4%

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

      3. distribute-rgt-neg-out 66.4%

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

   5. Simplified 66.4%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+123}:\\ \;\;\;\;y \cdot \left(-\frac{x}{z}\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+225}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot \left(-x\right)\\ \end{array} \]

Alternative 6: 75.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{+123}:\\ \;\;\;\;\frac{y}{\frac{-z}{x}}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+225}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.06e+123)
   (/ y (/ (- z) x))
   (if (<= y 1.3e+225) (+ y (/ x z)) (* (/ y z) (- x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.06e+123) {
		tmp = y / (-z / x);
	} else if (y <= 1.3e+225) {
		tmp = y + (x / z);
	} else {
		tmp = (y / z) * -x;
	}
	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 <= (-1.06d+123)) then
        tmp = y / (-z / x)
    else if (y <= 1.3d+225) then
        tmp = y + (x / z)
    else
        tmp = (y / z) * -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.06e+123) {
		tmp = y / (-z / x);
	} else if (y <= 1.3e+225) {
		tmp = y + (x / z);
	} else {
		tmp = (y / z) * -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.06e+123:
		tmp = y / (-z / x)
	elif y <= 1.3e+225:
		tmp = y + (x / z)
	else:
		tmp = (y / z) * -x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.06e+123)
		tmp = Float64(y / Float64(Float64(-z) / x));
	elseif (y <= 1.3e+225)
		tmp = Float64(y + Float64(x / z));
	else
		tmp = Float64(Float64(y / z) * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.06e+123)
		tmp = y / (-z / x);
	elseif (y <= 1.3e+225)
		tmp = y + (x / z);
	else
		tmp = (y / z) * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.06e+123], N[(y / N[((-z) / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.3e+225], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], N[(N[(y / z), $MachinePrecision] * (-x)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.06e123

   1. Initial program 83.0%

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

   2. Taylor expanded in y around inf 83.0%

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

      1. associate-/l* 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in z around 0 66.0%

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

      1. mul-1-neg 66.0%

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

   7. Simplified 66.0%

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

   if -1.06e123 < y < 1.30000000000000002e225

   1. Initial program 90.2%

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

   2. Taylor expanded in y around inf 88.2%

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

   3. Taylor expanded in z around inf 88.4%

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

   if 1.30000000000000002e225 < y

   1. Initial program 71.4%

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

   2. Taylor expanded in y around inf 71.4%

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

   3. Taylor expanded in z around 0 52.8%

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

      1. mul-1-neg 52.8%

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

      2. associate-*l/ 66.4%

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

      3. distribute-rgt-neg-out 66.4%

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

   5. Simplified 66.4%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{+123}:\\ \;\;\;\;\frac{y}{\frac{-z}{x}}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+225}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot \left(-x\right)\\ \end{array} \]

Alternative 7: 63.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{-34} \lor \neg \left(y \leq 0.0029\right):\\ \;\;\;\;z \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.6e-34) (not (<= y 0.0029))) (* z (/ y z)) (/ x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.6e-34) || !(y <= 0.0029)) {
		tmp = z * (y / z);
	} else {
		tmp = x / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-3.6d-34)) .or. (.not. (y <= 0.0029d0))) then
        tmp = z * (y / z)
    else
        tmp = x / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.6e-34) || !(y <= 0.0029)) {
		tmp = z * (y / z);
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.6e-34) or not (y <= 0.0029):
		tmp = z * (y / z)
	else:
		tmp = x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.6e-34) || !(y <= 0.0029))
		tmp = Float64(z * Float64(y / z));
	else
		tmp = Float64(x / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.6e-34) || ~((y <= 0.0029)))
		tmp = z * (y / z);
	else
		tmp = x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.6e-34], N[Not[LessEqual[y, 0.0029]], $MachinePrecision]], N[(z * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(x / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.60000000000000008e-34 or 0.0029 < y

   1. Initial program 76.3%

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

   2. Taylor expanded in y around inf 74.4%

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

   3. Taylor expanded in z around inf 32.3%

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

      1. associate-/l* 49.2%

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

      2. associate-/r/ 55.3%

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

   5. Applied egg-rr 55.3%

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

   if -3.60000000000000008e-34 < y < 0.0029

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 80.6%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{-34} \lor \neg \left(y \leq 0.0029\right):\\ \;\;\;\;z \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]

Alternative 8: 61.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-35}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 0.0026:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.2e-35) y (if (<= y 0.0026) (/ x z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.2e-35) {
		tmp = y;
	} else if (y <= 0.0026) {
		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 <= (-3.2d-35)) then
        tmp = y
    else if (y <= 0.0026d0) 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 <= -3.2e-35) {
		tmp = y;
	} else if (y <= 0.0026) {
		tmp = x / z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.2e-35:
		tmp = y
	elif y <= 0.0026:
		tmp = x / z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.2e-35)
		tmp = y;
	elseif (y <= 0.0026)
		tmp = Float64(x / z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.2e-35)
		tmp = y;
	elseif (y <= 0.0026)
		tmp = x / z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.2e-35], y, If[LessEqual[y, 0.0026], N[(x / z), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if y < -3.1999999999999998e-35 or 0.0025999999999999999 < y

   1. Initial program 76.3%

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

   2. Taylor expanded in x around 0 49.2%

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

   if -3.1999999999999998e-35 < y < 0.0025999999999999999

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 80.6%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-35}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 0.0026:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 9: 81.7% 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 93.1%

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

   2. Taylor expanded in y around inf 92.1%

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

   3. Taylor expanded in z around inf 84.3%

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

   if 1 < y

   1. Initial program 65.4%

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

   2. Taylor expanded in y around inf 57.2%

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

   3. Taylor expanded in z around inf 46.7%

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

      1. div-inv 46.7%

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

      2. add-sqr-sqrt 28.9%

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

      3. sqrt-unprod 47.2%

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

      4. sqr-neg 47.2%

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

      5. sqrt-unprod 18.6%

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

      6. add-sqr-sqrt 56.2%

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

      7. cancel-sign-sub-inv 56.2%

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

      8. div-inv 56.2%

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

   5. Applied egg-rr 56.2%

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

4. Final simplification 78.9%

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

Alternative 10: 78.1% 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 87.8%

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

2. Taylor expanded in y around inf 85.4%

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

3. Taylor expanded in z around inf 77.1%

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

4. Final simplification 77.1%

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

Alternative 11: 40.5% 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 87.8%

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

2. Taylor expanded in x around 0 35.8%

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

3. Final simplification 35.8%

   \[\leadsto y \]

Developer target: 94.1% 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 2023182 
(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))