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

Percentage Accurate: 88.4% → 99.8%

Time: 8.5s

Alternatives: 7

Speedup: 0.8×

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: 88.4% 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, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+34} \lor \neg \left(z \leq 1.55 \cdot 10^{-56}\right):\\ \;\;\;\;\frac{x}{z} + \left(1 - \frac{x}{z}\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \left(z - x\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.7e+34) (not (<= z 1.55e-56)))
   (+ (/ x z) (* (- 1.0 (/ x z)) y))
   (/ (+ x (* y (- z x))) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.7e+34) || !(z <= 1.55e-56)) {
		tmp = (x / z) + ((1.0 - (x / z)) * y);
	} 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 <= (-1.7d+34)) .or. (.not. (z <= 1.55d-56))) then
        tmp = (x / z) + ((1.0d0 - (x / z)) * y)
    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 <= -1.7e+34) || !(z <= 1.55e-56)) {
		tmp = (x / z) + ((1.0 - (x / z)) * y);
	} else {
		tmp = (x + (y * (z - x))) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.7e+34) or not (z <= 1.55e-56):
		tmp = (x / z) + ((1.0 - (x / z)) * y)
	else:
		tmp = (x + (y * (z - x))) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.7e+34) || !(z <= 1.55e-56))
		tmp = Float64(Float64(x / z) + Float64(Float64(1.0 - Float64(x / z)) * y));
	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 <= -1.7e+34) || ~((z <= 1.55e-56)))
		tmp = (x / z) + ((1.0 - (x / z)) * y);
	else
		tmp = (x + (y * (z - x))) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.7e+34], N[Not[LessEqual[z, 1.55e-56]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] + N[(N[(1.0 - N[(x / z), $MachinePrecision]), $MachinePrecision] * y), $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 < -1.7e34 or 1.54999999999999994e-56 < z

   1. Initial program 77.2%

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

   2. Taylor expanded in y around 0 99.9%

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

   if -1.7e34 < z < 1.54999999999999994e-56

   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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+34} \lor \neg \left(z \leq 1.55 \cdot 10^{-56}\right):\\ \;\;\;\;\frac{x}{z} + \left(1 - \frac{x}{z}\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \left(z - x\right)}{z}\\ \end{array} \]

Alternative 2: 99.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.65 \cdot 10^{+20} \lor \neg \left(y \leq 0.0035\right):\\ \;\;\;\;y - \frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \left(z - x\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.65e+20) (not (<= y 0.0035)))
   (- y (/ y (/ z x)))
   (/ (+ x (* y (- z x))) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.65e+20) || !(y <= 0.0035)) {
		tmp = y - (y / (z / x));
	} else {
		tmp = (x + (y * (z - x))) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-2.65d+20)) .or. (.not. (y <= 0.0035d0))) then
        tmp = y - (y / (z / x))
    else
        tmp = (x + (y * (z - x))) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.65e+20) || !(y <= 0.0035)) {
		tmp = y - (y / (z / x));
	} else {
		tmp = (x + (y * (z - x))) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.65e+20) or not (y <= 0.0035):
		tmp = y - (y / (z / x))
	else:
		tmp = (x + (y * (z - x))) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.65e+20) || !(y <= 0.0035))
		tmp = Float64(y - Float64(y / Float64(z / x)));
	else
		tmp = Float64(Float64(x + Float64(y * Float64(z - x))) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.65e+20) || ~((y <= 0.0035)))
		tmp = y - (y / (z / x));
	else
		tmp = (x + (y * (z - x))) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.65e+20], N[Not[LessEqual[y, 0.0035]], $MachinePrecision]], N[(y - N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.65e20 or 0.00350000000000000007 < y

   1. Initial program 74.6%

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

   2. Taylor expanded in y around 0 93.5%

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

   3. Taylor expanded in y around inf 99.9%

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

      1. sub-neg 99.9%

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

      2. distribute-frac-neg 99.9%

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

      3. +-commutative 99.9%

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

      4. distribute-rgt1-in 99.9%

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

      5. *-commutative 99.9%

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

      6. associate-*r/ 86.9%

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

      7. distribute-rgt-neg-out 86.9%

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

      8. distribute-frac-neg 86.9%

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

      9. unsub-neg 86.9%

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

      10. associate-/l* 99.9%

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

   5. Simplified 99.9%

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

   if -2.65e20 < y < 0.00350000000000000007

   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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.65 \cdot 10^{+20} \lor \neg \left(y \leq 0.0035\right):\\ \;\;\;\;y - \frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \left(z - x\right)}{z}\\ \end{array} \]

Alternative 3: 86.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+81} \lor \neg \left(x \leq 3.8 \cdot 10^{+90}\right):\\ \;\;\;\;\frac{x}{z} \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -7e+81) (not (<= x 3.8e+90)))
   (* (/ x z) (- 1.0 y))
   (+ (/ x z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7e+81) || !(x <= 3.8e+90)) {
		tmp = (x / z) * (1.0 - y);
	} else {
		tmp = (x / z) + 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 ((x <= (-7d+81)) .or. (.not. (x <= 3.8d+90))) then
        tmp = (x / z) * (1.0d0 - y)
    else
        tmp = (x / z) + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7e+81) || !(x <= 3.8e+90)) {
		tmp = (x / z) * (1.0 - y);
	} else {
		tmp = (x / z) + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -7e+81) or not (x <= 3.8e+90):
		tmp = (x / z) * (1.0 - y)
	else:
		tmp = (x / z) + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -7e+81) || !(x <= 3.8e+90))
		tmp = Float64(Float64(x / z) * Float64(1.0 - y));
	else
		tmp = Float64(Float64(x / z) + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -7e+81) || ~((x <= 3.8e+90)))
		tmp = (x / z) * (1.0 - y);
	else
		tmp = (x / z) + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -7e+81], N[Not[LessEqual[x, 3.8e+90]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.0000000000000001e81 or 3.8000000000000001e90 < x

   1. Initial program 83.1%

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

   2. Taylor expanded in x around inf 81.3%

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

      1. *-commutative 81.3%

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

      2. associate-/l* 86.8%

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

      3. mul-1-neg 86.8%

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

      4. unsub-neg 86.8%

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

   4. Simplified 86.8%

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

      1. associate-/r/ 86.7%

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

   6. Applied egg-rr 86.7%

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

   if -7.0000000000000001e81 < x < 3.8000000000000001e90

   1. Initial program 90.0%

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

   2. Taylor expanded in y around 0 98.7%

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

   3. Taylor expanded in x around 0 88.2%

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

   4. Taylor expanded in y around 0 88.2%

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

      1. +-commutative 88.2%

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

   6. Simplified 88.2%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+81} \lor \neg \left(x \leq 3.8 \cdot 10^{+90}\right):\\ \;\;\;\;\frac{x}{z} \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} + y\\ \end{array} \]

Alternative 4: 99.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -11200 \lor \neg \left(y \leq 0.0035\right):\\ \;\;\;\;y - \frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -11200.0) (not (<= y 0.0035)))
   (- y (/ y (/ z x)))
   (+ (/ x z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -11200.0) || !(y <= 0.0035)) {
		tmp = y - (y / (z / x));
	} else {
		tmp = (x / z) + 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 <= (-11200.0d0)) .or. (.not. (y <= 0.0035d0))) then
        tmp = y - (y / (z / x))
    else
        tmp = (x / z) + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -11200.0) || !(y <= 0.0035)) {
		tmp = y - (y / (z / x));
	} else {
		tmp = (x / z) + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -11200.0) or not (y <= 0.0035):
		tmp = y - (y / (z / x))
	else:
		tmp = (x / z) + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -11200.0) || !(y <= 0.0035))
		tmp = Float64(y - Float64(y / Float64(z / x)));
	else
		tmp = Float64(Float64(x / z) + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -11200.0) || ~((y <= 0.0035)))
		tmp = y - (y / (z / x));
	else
		tmp = (x / z) + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -11200.0], N[Not[LessEqual[y, 0.0035]], $MachinePrecision]], N[(y - N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -11200 or 0.00350000000000000007 < y

   1. Initial program 75.2%

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

   2. Taylor expanded in y around 0 93.6%

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

   3. Taylor expanded in y around inf 99.8%

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

      1. sub-neg 99.8%

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

      2. distribute-frac-neg 99.8%

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

      3. +-commutative 99.8%

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

      4. distribute-rgt1-in 99.8%

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

      5. *-commutative 99.8%

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

      6. associate-*r/ 87.1%

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

      7. distribute-rgt-neg-out 87.1%

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

      8. distribute-frac-neg 87.1%

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

      9. unsub-neg 87.1%

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

      10. associate-/l* 99.9%

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

   5. Simplified 99.9%

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

   if -11200 < y < 0.00350000000000000007

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 92.9%

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

   3. Taylor expanded in x around 0 99.1%

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

   4. Taylor expanded in y around 0 99.1%

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

      1. +-commutative 99.1%

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

   6. Simplified 99.1%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -11200 \lor \neg \left(y \leq 0.0035\right):\\ \;\;\;\;y - \frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} + y\\ \end{array} \]

Alternative 5: 55.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+72}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-127}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -8.6e+72) y (if (<= z 6.5e-127) (/ x z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -8.6e+72) {
		tmp = y;
	} else if (z <= 6.5e-127) {
		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 <= (-8.6d+72)) then
        tmp = y
    else if (z <= 6.5d-127) 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 <= -8.6e+72) {
		tmp = y;
	} else if (z <= 6.5e-127) {
		tmp = x / z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -8.6e+72:
		tmp = y
	elif z <= 6.5e-127:
		tmp = x / z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -8.6e+72)
		tmp = y;
	elseif (z <= 6.5e-127)
		tmp = Float64(x / z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -8.6e+72)
		tmp = y;
	elseif (z <= 6.5e-127)
		tmp = x / z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -8.6e+72], y, If[LessEqual[z, 6.5e-127], N[(x / z), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if z < -8.6000000000000003e72 or 6.49999999999999998e-127 < z

   1. Initial program 79.1%

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

   2. Taylor expanded in x around 0 65.9%

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

   if -8.6000000000000003e72 < z < 6.49999999999999998e-127

   1. Initial program 99.0%

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

   2. Taylor expanded in y around 0 53.1%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+72}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-127}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 6: 78.8% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.4%

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

2. Taylor expanded in y around 0 93.3%

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

3. Taylor expanded in x around 0 76.9%

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

4. Taylor expanded in y around 0 76.9%

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

   1. +-commutative 76.9%

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

6. Simplified 76.9%

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

7. Final simplification 76.9%

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

Alternative 7: 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 87.4%

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

2. Taylor expanded in x around 0 44.2%

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

3. Final simplification 44.2%

   \[\leadsto y \]

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 2023224 
(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))