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

Percentage Accurate: 88.7% → 98.4%

Time: 5.8s

Alternatives: 7

Speedup: 0.8×

• 21.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.7% 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: 98.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+14} \lor \neg \left(y \leq 8.6 \cdot 10^{-5}\right):\\ \;\;\;\;y \cdot \frac{z - x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} + \frac{y \cdot \left(z - x\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6.2e+14) (not (<= y 8.6e-5)))
   (* y (/ (- z x) z))
   (+ (/ x z) (/ (* y (- z x)) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.2e+14) || !(y <= 8.6e-5)) {
		tmp = y * ((z - x) / z);
	} else {
		tmp = (x / z) + ((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 <= (-6.2d+14)) .or. (.not. (y <= 8.6d-5))) then
        tmp = y * ((z - x) / z)
    else
        tmp = (x / z) + ((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 <= -6.2e+14) || !(y <= 8.6e-5)) {
		tmp = y * ((z - x) / z);
	} else {
		tmp = (x / z) + ((y * (z - x)) / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6.2e+14) or not (y <= 8.6e-5):
		tmp = y * ((z - x) / z)
	else:
		tmp = (x / z) + ((y * (z - x)) / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6.2e+14) || !(y <= 8.6e-5))
		tmp = Float64(y * Float64(Float64(z - x) / z));
	else
		tmp = Float64(Float64(x / z) + Float64(Float64(y * Float64(z - x)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -6.2e+14) || ~((y <= 8.6e-5)))
		tmp = y * ((z - x) / z);
	else
		tmp = (x / z) + ((y * (z - x)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6.2e+14], N[Not[LessEqual[y, 8.6e-5]], $MachinePrecision]], N[(y * N[(N[(z - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] + N[(N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.2e14 or 8.6000000000000003e-5 < y

   1. Initial program 78.9%

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

   2. Taylor expanded in y around inf 78.9%

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

      1. *-lft-identity 78.9%

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

      2. associate-*l/ 78.8%

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

      3. *-commutative 78.8%

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

      4. associate-*l* 99.8%

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

      5. associate-*r/ 100.0%

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

      6. *-rgt-identity 100.0%

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

   4. Simplified 100.0%

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

   if -6.2e14 < y < 8.6000000000000003e-5

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+14} \lor \neg \left(y \leq 8.6 \cdot 10^{-5}\right):\\ \;\;\;\;y \cdot \frac{z - x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} + \frac{y \cdot \left(z - x\right)}{z}\\ \end{array} \]

Alternative 2: 99.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+14} \lor \neg \left(y \leq 9.5 \cdot 10^{+45}\right):\\ \;\;\;\;y \cdot \frac{z - x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \left(z - x\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -9e+14) (not (<= y 9.5e+45)))
   (* y (/ (- z x) z))
   (/ (+ x (* y (- z x))) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -9e+14) || !(y <= 9.5e+45)) {
		tmp = y * ((z - x) / z);
	} else {
		tmp = (x + (y * (z - x))) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-9d+14)) .or. (.not. (y <= 9.5d+45))) then
        tmp = y * ((z - x) / z)
    else
        tmp = (x + (y * (z - x))) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -9e+14) || !(y <= 9.5e+45)) {
		tmp = y * ((z - x) / z);
	} else {
		tmp = (x + (y * (z - x))) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -9e+14) or not (y <= 9.5e+45):
		tmp = y * ((z - x) / z)
	else:
		tmp = (x + (y * (z - x))) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -9e+14) || !(y <= 9.5e+45))
		tmp = Float64(y * Float64(Float64(z - x) / z));
	else
		tmp = Float64(Float64(x + Float64(y * Float64(z - x))) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -9e+14) || ~((y <= 9.5e+45)))
		tmp = y * ((z - x) / z);
	else
		tmp = (x + (y * (z - x))) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -9e+14], N[Not[LessEqual[y, 9.5e+45]], $MachinePrecision]], N[(y * N[(N[(z - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9e14 or 9.4999999999999998e45 < y

   1. Initial program 77.8%

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

   2. Taylor expanded in y around inf 77.8%

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

      1. *-lft-identity 77.8%

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

      2. associate-*l/ 77.7%

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

      3. *-commutative 77.7%

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

      4. associate-*l* 99.8%

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

      5. associate-*r/ 100.0%

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

      6. *-rgt-identity 100.0%

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

   4. Simplified 100.0%

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

   if -9e14 < y < 9.4999999999999998e45

   1. Initial program 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+14} \lor \neg \left(y \leq 9.5 \cdot 10^{+45}\right):\\ \;\;\;\;y \cdot \frac{z - x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \left(z - x\right)}{z}\\ \end{array} \]

Alternative 3: 98.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+15} \lor \neg \left(y \leq 8.6 \cdot 10^{-5}\right):\\ \;\;\;\;y \cdot \frac{z - x}{z}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.1e+15) (not (<= y 8.6e-5)))
   (* y (/ (- z x) z))
   (+ y (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.1e+15) || !(y <= 8.6e-5)) {
		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 <= (-1.1d+15)) .or. (.not. (y <= 8.6d-5))) 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 <= -1.1e+15) || !(y <= 8.6e-5)) {
		tmp = y * ((z - x) / z);
	} else {
		tmp = y + (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.1e+15) or not (y <= 8.6e-5):
		tmp = y * ((z - x) / z)
	else:
		tmp = y + (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.1e+15) || !(y <= 8.6e-5))
		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 <= -1.1e+15) || ~((y <= 8.6e-5)))
		tmp = y * ((z - x) / z);
	else
		tmp = y + (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.1e+15], N[Not[LessEqual[y, 8.6e-5]], $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 < -1.1e15 or 8.6000000000000003e-5 < y

   1. Initial program 78.8%

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

   2. Taylor expanded in y around inf 78.8%

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

      1. *-lft-identity 78.8%

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

      2. associate-*l/ 78.7%

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

      3. *-commutative 78.7%

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

      4. associate-*l* 99.8%

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

      5. associate-*r/ 100.0%

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

      6. *-rgt-identity 100.0%

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

   4. Simplified 100.0%

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

   if -1.1e15 < y < 8.6000000000000003e-5

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 99.9%

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

   3. Taylor expanded in z around inf 98.8%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+15} \lor \neg \left(y \leq 8.6 \cdot 10^{-5}\right):\\ \;\;\;\;y \cdot \frac{z - x}{z}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \]

Alternative 4: 77.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-244} \lor \neg \left(z \leq 1.3 \cdot 10^{-233}\right):\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -7.8e-244) (not (<= z 1.3e-233)))
   (+ y (/ x z))
   (* y (/ (- x) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -7.8e-244) || !(z <= 1.3e-233)) {
		tmp = y + (x / z);
	} else {
		tmp = y * (-x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-7.8d-244)) .or. (.not. (z <= 1.3d-233))) then
        tmp = y + (x / z)
    else
        tmp = y * (-x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -7.8e-244) || !(z <= 1.3e-233)) {
		tmp = y + (x / z);
	} else {
		tmp = y * (-x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -7.8e-244) or not (z <= 1.3e-233):
		tmp = y + (x / z)
	else:
		tmp = y * (-x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -7.8e-244) || !(z <= 1.3e-233))
		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 ((z <= -7.8e-244) || ~((z <= 1.3e-233)))
		tmp = y + (x / z);
	else
		tmp = y * (-x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -7.8e-244], N[Not[LessEqual[z, 1.3e-233]], $MachinePrecision]], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], N[(y * N[((-x) / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.7999999999999998e-244 or 1.2999999999999999e-233 < z

   1. Initial program 87.6%

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

   2. Taylor expanded in y around inf 86.3%

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

   3. Taylor expanded in z around inf 82.7%

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

   if -7.7999999999999998e-244 < z < 1.2999999999999999e-233

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 82.8%

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

      1. *-lft-identity 82.8%

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

      2. associate-*l/ 82.8%

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

      3. *-commutative 82.8%

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

      4. associate-*l* 86.2%

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

      5. associate-*r/ 86.2%

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

      6. *-rgt-identity 86.2%

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

   4. Simplified 86.2%

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

   5. Taylor expanded in z around 0 82.6%

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

      1. associate-*r/ 82.6%

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

      2. mul-1-neg 82.6%

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

   7. Simplified 82.6%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-244} \lor \neg \left(z \leq 1.3 \cdot 10^{-233}\right):\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-x}{z}\\ \end{array} \]

Alternative 5: 57.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{-65}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-10}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.2e-65) (/ x z) (if (<= x 2.05e-10) y (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.2e-65) {
		tmp = x / z;
	} else if (x <= 2.05e-10) {
		tmp = y;
	} 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 (x <= (-5.2d-65)) then
        tmp = x / z
    else if (x <= 2.05d-10) then
        tmp = y
    else
        tmp = x / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.2e-65) {
		tmp = x / z;
	} else if (x <= 2.05e-10) {
		tmp = y;
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.2e-65:
		tmp = x / z
	elif x <= 2.05e-10:
		tmp = y
	else:
		tmp = x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.2e-65)
		tmp = Float64(x / z);
	elseif (x <= 2.05e-10)
		tmp = y;
	else
		tmp = Float64(x / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5.2e-65)
		tmp = x / z;
	elseif (x <= 2.05e-10)
		tmp = y;
	else
		tmp = x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.2e-65], N[(x / z), $MachinePrecision], If[LessEqual[x, 2.05e-10], y, N[(x / z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.20000000000000019e-65 or 2.0499999999999999e-10 < x

   1. Initial program 91.3%

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

   2. Taylor expanded in y around 0 58.1%

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

   if -5.20000000000000019e-65 < x < 2.0499999999999999e-10

   1. Initial program 86.0%

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

   2. Taylor expanded in x around 0 69.7%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{-65}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-10}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]

Alternative 6: 78.4% 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 88.9%

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

2. Taylor expanded in y around inf 86.6%

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

3. Taylor expanded in z around inf 80.3%

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

4. Final simplification 80.3%

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

Alternative 7: 40.2% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ y \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return y;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = y
end function

Java

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

Python

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

Julia

function code(x, y, z)
	return y
end

MATLAB

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

Wolfram

code[x_, y_, z_] := y

Derivation

1. Initial program 88.9%

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

2. Taylor expanded in x around 0 43.4%

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

3. Final simplification 43.4%

   \[\leadsto y \]

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 2023297 
(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))