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

Percentage Accurate: 87.9% → 99.9%

Time: 7.5s

Alternatives: 10

Speedup: 0.5×

• 21.2% 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: 87.9% 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, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+52} \lor \neg \left(y \leq 10^{+43}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{\frac{z}{1 - y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5e+52) (not (<= y 1e+43)))
   (* y (- 1.0 (/ x z)))
   (+ y (/ x (/ z (- 1.0 y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5e+52) || !(y <= 1e+43)) {
		tmp = y * (1.0 - (x / z));
	} else {
		tmp = y + (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 ((y <= (-5d+52)) .or. (.not. (y <= 1d+43))) then
        tmp = y * (1.0d0 - (x / z))
    else
        tmp = y + (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 ((y <= -5e+52) || !(y <= 1e+43)) {
		tmp = y * (1.0 - (x / z));
	} else {
		tmp = y + (x / (z / (1.0 - y)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5e+52) or not (y <= 1e+43):
		tmp = y * (1.0 - (x / z))
	else:
		tmp = y + (x / (z / (1.0 - y)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5e+52) || !(y <= 1e+43))
		tmp = Float64(y * Float64(1.0 - Float64(x / z)));
	else
		tmp = Float64(y + Float64(x / Float64(z / Float64(1.0 - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -5e+52) || ~((y <= 1e+43)))
		tmp = y * (1.0 - (x / z));
	else
		tmp = y + (x / (z / (1.0 - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5e+52], N[Not[LessEqual[y, 1e+43]], $MachinePrecision]], N[(y * N[(1.0 - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(x / N[(z / N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5e52 or 1.00000000000000001e43 < y

   1. Initial program 74.8%

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

   3. Taylor expanded in y around inf 74.8%

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

      1. associate-/l* 99.9%

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

      2. div-sub 99.9%

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

      3. sub-neg 99.9%

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

      4. *-inverses 99.9%

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

      5. sub-neg 99.9%

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

   5. Simplified 99.9%

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

   if -5e52 < y < 1.00000000000000001e43

   1. Initial program 98.6%

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

   3. Taylor expanded in x around 0 99.7%

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

      1. +-commutative 99.7%

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

      2. mul-1-neg 99.7%

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

      3. sub-neg 99.7%

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

      4. div-sub 99.7%

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

      5. clear-num 99.7%

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

      6. un-div-inv 100.0%

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

   5. Applied egg-rr 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+52} \lor \neg \left(y \leq 10^{+43}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{\frac{z}{1 - y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 60.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-10}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-12}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+292}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5e-10)
   y
   (if (<= y 3.6e-12) (/ x z) (if (<= y 2.8e+292) y (/ (- x) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5e-10) {
		tmp = y;
	} else if (y <= 3.6e-12) {
		tmp = x / z;
	} else if (y <= 2.8e+292) {
		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 (y <= (-5d-10)) then
        tmp = y
    else if (y <= 3.6d-12) then
        tmp = x / z
    else if (y <= 2.8d+292) 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 (y <= -5e-10) {
		tmp = y;
	} else if (y <= 3.6e-12) {
		tmp = x / z;
	} else if (y <= 2.8e+292) {
		tmp = y;
	} else {
		tmp = -x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5e-10:
		tmp = y
	elif y <= 3.6e-12:
		tmp = x / z
	elif y <= 2.8e+292:
		tmp = y
	else:
		tmp = -x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5e-10)
		tmp = y;
	elseif (y <= 3.6e-12)
		tmp = Float64(x / z);
	elseif (y <= 2.8e+292)
		tmp = y;
	else
		tmp = Float64(Float64(-x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -5e-10)
		tmp = y;
	elseif (y <= 3.6e-12)
		tmp = x / z;
	elseif (y <= 2.8e+292)
		tmp = y;
	else
		tmp = -x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5e-10], y, If[LessEqual[y, 3.6e-12], N[(x / z), $MachinePrecision], If[LessEqual[y, 2.8e+292], y, N[((-x) / z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.00000000000000031e-10 or 3.6e-12 < y < 2.8000000000000002e292

   1. Initial program 76.0%

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

   3. Taylor expanded in x around 0 51.9%

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

   if -5.00000000000000031e-10 < y < 3.6e-12

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 78.6%

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

   if 2.8000000000000002e292 < y

   1. Initial program 91.0%

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

   3. Taylor expanded in y around 0 0.3%

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

      1. div-inv 0.3%

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

   5. Applied egg-rr 0.3%

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

      1. un-div-inv 0.3%

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

      2. frac-2neg 0.3%

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

      3. add-sqr-sqrt 0.2%

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

      4. sqrt-unprod 20.6%

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

      5. sqr-neg 20.6%

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

      6. sqrt-unprod 10.9%

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

      7. add-sqr-sqrt 52.0%

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

   7. Applied egg-rr 52.0%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-10}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-12}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+292}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{+20} \lor \neg \left(y \leq 5.5 \cdot 10^{-9}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.55e+20) (not (<= y 5.5e-9)))
   (* y (- 1.0 (/ x z)))
   (+ y (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.55e+20) || !(y <= 5.5e-9)) {
		tmp = y * (1.0 - (x / z));
	} else {
		tmp = y + (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-2.55d+20)) .or. (.not. (y <= 5.5d-9))) then
        tmp = y * (1.0d0 - (x / z))
    else
        tmp = y + (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.55e+20) || !(y <= 5.5e-9)) {
		tmp = y * (1.0 - (x / z));
	} else {
		tmp = y + (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.55e+20) or not (y <= 5.5e-9):
		tmp = y * (1.0 - (x / z))
	else:
		tmp = y + (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.55e+20) || !(y <= 5.5e-9))
		tmp = Float64(y * Float64(1.0 - 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 <= -2.55e+20) || ~((y <= 5.5e-9)))
		tmp = y * (1.0 - (x / z));
	else
		tmp = y + (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.55e+20], N[Not[LessEqual[y, 5.5e-9]], $MachinePrecision]], N[(y * N[(1.0 - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.55e20 or 5.4999999999999996e-9 < y

   1. Initial program 76.6%

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

   3. Taylor expanded in y around inf 76.6%

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

      1. associate-/l* 99.9%

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

      2. div-sub 99.9%

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

      3. sub-neg 99.9%

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

      4. *-inverses 99.9%

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

      5. sub-neg 99.9%

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

   5. Simplified 99.9%

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

   if -2.55e20 < y < 5.4999999999999996e-9

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 99.6%

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

   4. Taylor expanded in y around 0 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{+20} \lor \neg \left(y \leq 5.5 \cdot 10^{-9}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 80.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 5.5 \cdot 10^{-9}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+251}:\\ \;\;\;\;y - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(-x\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 5.5e-9)
   (+ y (/ x z))
   (if (<= y 1.35e+251) (- y (/ x z)) (/ (* y (- x)) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 5.5e-9) {
		tmp = y + (x / z);
	} else if (y <= 1.35e+251) {
		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 <= 5.5d-9) then
        tmp = y + (x / z)
    else if (y <= 1.35d+251) 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 <= 5.5e-9) {
		tmp = y + (x / z);
	} else if (y <= 1.35e+251) {
		tmp = y - (x / z);
	} else {
		tmp = (y * -x) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 5.5e-9:
		tmp = y + (x / z)
	elif y <= 1.35e+251:
		tmp = y - (x / z)
	else:
		tmp = (y * -x) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 5.5e-9)
		tmp = Float64(y + Float64(x / z));
	elseif (y <= 1.35e+251)
		tmp = Float64(y - Float64(x / z));
	else
		tmp = Float64(Float64(y * Float64(-x)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 5.5e-9)
		tmp = y + (x / z);
	elseif (y <= 1.35e+251)
		tmp = y - (x / z);
	else
		tmp = (y * -x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 5.5e-9], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.35e+251], N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision], N[(N[(y * (-x)), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 5.4999999999999996e-9

   1. Initial program 90.2%

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

   3. Taylor expanded in x around 0 94.8%

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

   4. Taylor expanded in y around 0 86.9%

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

   if 5.4999999999999996e-9 < y < 1.3500000000000001e251

   1. Initial program 78.2%

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

   3. Taylor expanded in x around 0 90.1%

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

   4. Taylor expanded in y around 0 52.4%

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

      1. add-sqr-sqrt 32.3%

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

      2. sqrt-unprod 48.2%

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

      3. sqr-neg 48.2%

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

      4. sqrt-unprod 23.1%

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

      5. add-sqr-sqrt 66.4%

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

      6. distribute-frac-neg2 66.4%

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

      7. sub-neg 66.4%

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

   6. Applied egg-rr 66.4%

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

   if 1.3500000000000001e251 < y

   1. Initial program 87.9%

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

   3. Taylor expanded in y around inf 87.9%

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

   4. Taylor expanded in z around 0 86.9%

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

      1. mul-1-neg 86.9%

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

      2. distribute-lft-neg-out 86.9%

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

      3. *-commutative 86.9%

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

   6. Simplified 86.9%

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

Alternative 5: 80.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 5.5 \cdot 10^{-9}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+250}:\\ \;\;\;\;y - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 5.5e-9)
   (+ y (/ x z))
   (if (<= y 2.2e+250) (- y (/ x z)) (* y (/ (- x) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 5.5e-9) {
		tmp = y + (x / z);
	} else if (y <= 2.2e+250) {
		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 <= 5.5d-9) then
        tmp = y + (x / z)
    else if (y <= 2.2d+250) 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 <= 5.5e-9) {
		tmp = y + (x / z);
	} else if (y <= 2.2e+250) {
		tmp = y - (x / z);
	} else {
		tmp = y * (-x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 5.5e-9:
		tmp = y + (x / z)
	elif y <= 2.2e+250:
		tmp = y - (x / z)
	else:
		tmp = y * (-x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 5.5e-9)
		tmp = Float64(y + Float64(x / z));
	elseif (y <= 2.2e+250)
		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 (y <= 5.5e-9)
		tmp = y + (x / z);
	elseif (y <= 2.2e+250)
		tmp = y - (x / z);
	else
		tmp = y * (-x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 5.5e-9], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.2e+250], N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision], N[(y * N[((-x) / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 5.4999999999999996e-9

   1. Initial program 90.2%

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

   3. Taylor expanded in x around 0 94.8%

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

   4. Taylor expanded in y around 0 86.9%

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

   if 5.4999999999999996e-9 < y < 2.20000000000000014e250

   1. Initial program 78.2%

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

   3. Taylor expanded in x around 0 90.1%

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

   4. Taylor expanded in y around 0 52.4%

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

      1. add-sqr-sqrt 32.3%

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

      2. sqrt-unprod 48.2%

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

      3. sqr-neg 48.2%

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

      4. sqrt-unprod 23.1%

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

      5. add-sqr-sqrt 66.4%

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

      6. distribute-frac-neg2 66.4%

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

      7. sub-neg 66.4%

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

   6. Applied egg-rr 66.4%

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

   if 2.20000000000000014e250 < y

   1. Initial program 87.9%

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

   3. Taylor expanded in y around inf 87.9%

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

      1. associate-/l* 100.0%

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

      2. div-sub 100.0%

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

      3. sub-neg 100.0%

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

      4. *-inverses 100.0%

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

      5. sub-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around inf 86.9%

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

      1. mul-1-neg 86.9%

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

      2. distribute-frac-neg2 86.9%

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

   8. Simplified 86.9%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 5.5 \cdot 10^{-9}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+250}:\\ \;\;\;\;y - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-8}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-10}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.2e-8) y (if (<= y 4.1e-10) (/ x z) (* z (/ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.2e-8) {
		tmp = y;
	} else if (y <= 4.1e-10) {
		tmp = x / z;
	} else {
		tmp = z * (y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-4.2d-8)) then
        tmp = y
    else if (y <= 4.1d-10) then
        tmp = x / z
    else
        tmp = z * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.2e-8) {
		tmp = y;
	} else if (y <= 4.1e-10) {
		tmp = x / z;
	} else {
		tmp = z * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.2e-8:
		tmp = y
	elif y <= 4.1e-10:
		tmp = x / z
	else:
		tmp = z * (y / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.2e-8)
		tmp = y;
	elseif (y <= 4.1e-10)
		tmp = Float64(x / z);
	else
		tmp = Float64(z * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4.2e-8)
		tmp = y;
	elseif (y <= 4.1e-10)
		tmp = x / z;
	else
		tmp = z * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.2e-8], y, If[LessEqual[y, 4.1e-10], N[(x / z), $MachinePrecision], N[(z * N[(y / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.19999999999999989e-8

   1. Initial program 74.2%

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

   3. Taylor expanded in x around 0 53.1%

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

   if -4.19999999999999989e-8 < y < 4.0999999999999998e-10

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 78.6%

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

   if 4.0999999999999998e-10 < y

   1. Initial program 80.5%

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

   3. Taylor expanded in y around inf 80.5%

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

      1. div-inv 80.3%

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

      2. *-commutative 80.3%

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

      3. associate-*l* 92.2%

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

      4. div-inv 92.4%

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

   5. Applied egg-rr 92.4%

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

   6. Taylor expanded in z around inf 50.3%

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

Alternative 7: 60.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-11}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-9}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6.5e-11) y (if (<= y 1.1e-9) (/ x z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.5e-11) {
		tmp = y;
	} else if (y <= 1.1e-9) {
		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 <= (-6.5d-11)) then
        tmp = y
    else if (y <= 1.1d-9) 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 <= -6.5e-11) {
		tmp = y;
	} else if (y <= 1.1e-9) {
		tmp = x / z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -6.5e-11:
		tmp = y
	elif y <= 1.1e-9:
		tmp = x / z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6.5e-11)
		tmp = y;
	elseif (y <= 1.1e-9)
		tmp = Float64(x / z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -6.5e-11)
		tmp = y;
	elseif (y <= 1.1e-9)
		tmp = x / z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6.5e-11], y, If[LessEqual[y, 1.1e-9], N[(x / z), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if y < -6.49999999999999953e-11 or 1.0999999999999999e-9 < y

   1. Initial program 77.1%

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

   3. Taylor expanded in x around 0 48.9%

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

   if -6.49999999999999953e-11 < y < 1.0999999999999999e-9

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 78.6%

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

Alternative 8: 80.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 5.5 \cdot 10^{-9}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 5.5e-9) (+ y (/ x z)) (- y (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 5.5e-9) {
		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 <= 5.5d-9) 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 <= 5.5e-9) {
		tmp = y + (x / z);
	} else {
		tmp = y - (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 5.5e-9:
		tmp = y + (x / z)
	else:
		tmp = y - (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 5.5e-9)
		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 <= 5.5e-9)
		tmp = y + (x / z);
	else
		tmp = y - (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 5.5e-9], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 5.4999999999999996e-9

   1. Initial program 90.2%

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

   3. Taylor expanded in x around 0 94.8%

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

   4. Taylor expanded in y around 0 86.9%

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

   if 5.4999999999999996e-9 < y

   1. Initial program 80.5%

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

   3. Taylor expanded in x around 0 92.5%

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

   4. Taylor expanded in y around 0 43.5%

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

      1. add-sqr-sqrt 26.3%

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

      2. sqrt-unprod 51.0%

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

      3. sqr-neg 51.0%

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

      4. sqrt-unprod 25.9%

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

      5. add-sqr-sqrt 62.2%

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

      6. distribute-frac-neg2 62.2%

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

      7. sub-neg 62.2%

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

   6. Applied egg-rr 62.2%

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

Alternative 9: 78.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 8 \cdot 10^{+172}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 8e+172) (+ y (/ x z)) (* z (/ y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 8e+172) {
		tmp = y + (x / z);
	} else {
		tmp = z * (y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 8d+172) then
        tmp = y + (x / z)
    else
        tmp = z * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 8e+172) {
		tmp = y + (x / z);
	} else {
		tmp = z * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 8e+172:
		tmp = y + (x / z)
	else:
		tmp = z * (y / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 8e+172)
		tmp = Float64(y + Float64(x / z));
	else
		tmp = Float64(z * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 8e+172)
		tmp = y + (x / z);
	else
		tmp = z * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 8e+172], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], N[(z * N[(y / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 8.0000000000000007e172

   1. Initial program 89.1%

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

   3. Taylor expanded in x around 0 94.7%

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

   4. Taylor expanded in y around 0 82.3%

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

   if 8.0000000000000007e172 < y

   1. Initial program 78.9%

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

   3. Taylor expanded in y around inf 78.9%

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

      1. div-inv 78.8%

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

      2. *-commutative 78.8%

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

      3. associate-*l* 90.9%

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

      4. div-inv 90.9%

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

   5. Applied egg-rr 90.9%

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

   6. Taylor expanded in z around inf 45.9%

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

Alternative 10: 41.1% 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. Add Preprocessing

3. Taylor expanded in x around 0 36.9%

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

Developer Target 1: 93.9% 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 2024157 
(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))