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

Percentage Accurate: 88.1% → 99.9%

Time: 8.2s

Alternatives: 6

Speedup: 1.0×

• 20.4% 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: 88.1% 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

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.6%

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

3. Taylor expanded in x around 0

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

   1. distribute-lft-in N/A

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

   2. mul-1-neg N/A

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

   3. distribute-rgt-neg-in N/A

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

   4. associate-/l* N/A

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

   5. mul-1-neg N/A

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

   6. associate-+r+ N/A

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

   7. associate-*r/ N/A

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

   8. *-rgt-identity N/A

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

   9. associate-+r+ N/A

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

   10. +-commutative N/A

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

   11. mul-1-neg N/A

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

   12. unsub-neg N/A

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

   13. div-sub N/A

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

   14. unsub-neg N/A

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

   15. mul-1-neg N/A

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

   16. +-lowering-+.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(\frac{x + -1 \cdot \left(x \cdot y\right)}{z}\right)}\right) \]

5. Simplified 100.0%

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

Alternative 2: 99.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 0.37:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- 1.0 (/ x z)))))
   (if (<= y -1.0) t_0 (if (<= y 0.37) (+ y (/ x z)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = y * (1.0 - (x / z));
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= 0.37) {
		tmp = y + (x / z);
	} else {
		tmp = t_0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = y * (1.0d0 - (x / z))
    if (y <= (-1.0d0)) then
        tmp = t_0
    else if (y <= 0.37d0) then
        tmp = y + (x / z)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (1.0 - (x / z));
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= 0.37) {
		tmp = y + (x / z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (1.0 - (x / z))
	tmp = 0
	if y <= -1.0:
		tmp = t_0
	elif y <= 0.37:
		tmp = y + (x / z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(1.0 - Float64(x / z)))
	tmp = 0.0
	if (y <= -1.0)
		tmp = t_0;
	elseif (y <= 0.37)
		tmp = Float64(y + Float64(x / z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (1.0 - (x / z));
	tmp = 0.0;
	if (y <= -1.0)
		tmp = t_0;
	elseif (y <= 0.37)
		tmp = y + (x / z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(1.0 - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.0], t$95$0, If[LessEqual[y, 0.37], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 0.37 < y

   1. Initial program 73.3%

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

   3. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{z - x}{z}\right)}\right) \]

      3. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(\frac{z}{z} - \color{blue}{\frac{x}{z}}\right)\right) \]

      4. *-inverses N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(1 - \frac{\color{blue}{x}}{z}\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{x}{z}\right)}\right)\right) \]

      6. /-lowering-/.f64 99.5%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(x, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 99.5%

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

   if -1 < y < 0.37

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. distribute-lft-in N/A

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

      2. mul-1-neg N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. associate-/l* N/A

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

      5. mul-1-neg N/A

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

      6. associate-+r+ N/A

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

      7. associate-*r/ N/A

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

      8. *-rgt-identity N/A

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

      9. associate-+r+ N/A

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

      10. +-commutative N/A

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

      11. mul-1-neg N/A

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

      12. unsub-neg N/A

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

      13. div-sub N/A

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

      14. unsub-neg N/A

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

      15. mul-1-neg N/A

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

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(\frac{x + -1 \cdot \left(x \cdot y\right)}{z}\right)}\right) \]

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(\frac{x}{z}\right)}\right) \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{/.f64}\left(x, \color{blue}{z}\right)\right) \]

   8. Simplified 100.0%

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

Alternative 3: 62.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \frac{y}{z}\\ \mathbf{if}\;y \leq -1.05 \cdot 10^{+33}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 0.0055:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (/ y z))))
   (if (<= y -1.05e+33) t_0 (if (<= y 0.0055) (/ x z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z * (y / z);
	double tmp;
	if (y <= -1.05e+33) {
		tmp = t_0;
	} else if (y <= 0.0055) {
		tmp = x / z;
	} else {
		tmp = t_0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = z * (y / z)
    if (y <= (-1.05d+33)) then
        tmp = t_0
    else if (y <= 0.0055d0) then
        tmp = x / z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (y / z);
	double tmp;
	if (y <= -1.05e+33) {
		tmp = t_0;
	} else if (y <= 0.0055) {
		tmp = x / z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (y / z)
	tmp = 0
	if y <= -1.05e+33:
		tmp = t_0
	elif y <= 0.0055:
		tmp = x / z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(y / z))
	tmp = 0.0
	if (y <= -1.05e+33)
		tmp = t_0;
	elseif (y <= 0.0055)
		tmp = Float64(x / z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (y / z);
	tmp = 0.0;
	if (y <= -1.05e+33)
		tmp = t_0;
	elseif (y <= 0.0055)
		tmp = x / z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.05e+33], t$95$0, If[LessEqual[y, 0.0055], N[(x / z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.05e33 or 0.0054999999999999997 < y

   1. Initial program 72.1%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(y \cdot z\right)}, z\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 30.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), z\right) \]

   5. Simplified 30.4%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{y}{z}\right)}\right) \]

      4. /-lowering-/.f64 60.3%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right) \]

   7. Applied egg-rr 60.3%

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

   if -1.05e33 < y < 0.0054999999999999997

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 76.7%

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{z}\right) \]

   5. Simplified 76.7%

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

Alternative 4: 58.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+97}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 0.048:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -7.8e+97) y (if (<= y 0.048) (/ x z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -7.8e+97) {
		tmp = y;
	} else if (y <= 0.048) {
		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 <= (-7.8d+97)) then
        tmp = y
    else if (y <= 0.048d0) 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 <= -7.8e+97) {
		tmp = y;
	} else if (y <= 0.048) {
		tmp = x / z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -7.8e+97:
		tmp = y
	elif y <= 0.048:
		tmp = x / z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -7.8e+97)
		tmp = y;
	elseif (y <= 0.048)
		tmp = Float64(x / z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -7.8e+97)
		tmp = y;
	elseif (y <= 0.048)
		tmp = x / z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -7.8e+97], y, If[LessEqual[y, 0.048], N[(x / z), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if y < -7.7999999999999999e97 or 0.048000000000000001 < y

   1. Initial program 70.7%

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

   3. Taylor expanded in x around 0

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

   5. Simplified 57.1%

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

   if -7.7999999999999999e97 < y < 0.048000000000000001

   1. Initial program 98.5%

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

   3. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 72.7%

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{z}\right) \]

   5. Simplified 72.7%

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

Alternative 5: 78.3% 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 85.6%

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

3. Taylor expanded in x around 0

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

   1. distribute-lft-in N/A

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

   2. mul-1-neg N/A

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

   3. distribute-rgt-neg-in N/A

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

   4. associate-/l* N/A

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

   5. mul-1-neg N/A

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

   6. associate-+r+ N/A

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

   7. associate-*r/ N/A

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

   8. *-rgt-identity N/A

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

   9. associate-+r+ N/A

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

   10. +-commutative N/A

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

   11. mul-1-neg N/A

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

   12. unsub-neg N/A

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

   13. div-sub N/A

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

   14. unsub-neg N/A

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

   15. mul-1-neg N/A

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

   16. +-lowering-+.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(\frac{x + -1 \cdot \left(x \cdot y\right)}{z}\right)}\right) \]

5. Simplified 100.0%

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

6. Taylor expanded in y around 0

   \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(\frac{x}{z}\right)}\right) \]
7. Step-by-step derivation

   1. /-lowering-/.f64 79.7%

      \[\leadsto \mathsf{+.f64}\left(y, \mathsf{/.f64}\left(x, \color{blue}{z}\right)\right) \]

8. Simplified 79.7%

   \[\leadsto y + \color{blue}{\frac{x}{z}} \]
9. Add Preprocessing

Alternative 6: 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 85.6%

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

3. Taylor expanded in x around 0

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

5. Simplified 39.0%

   \[\leadsto \color{blue}{y} \]
6. Add Preprocessing

Developer Target 1: 94.3% 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 2024191 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:rasterificRadialGradient from diagrams-rasterific-1.3.1.3"
  :precision binary64

  :alt
  (! :herbie-platform default (- (+ y (/ x z)) (/ y (/ z x))))

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