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

Percentage Accurate: 87.7% → 99.6%

Time: 6.7s

Alternatives: 12

Speedup: 0.6×

• 20.6% 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: 87.7% 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: 99.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{-72} \lor \neg \left(z \leq 10^{-74}\right):\\ \;\;\;\;\frac{x}{z} + y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \left(z - x\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -9.2e-72) (not (<= z 1e-74)))
   (+ (/ x z) (* y (- 1.0 (/ x z))))
   (/ (+ x (* y (- z x))) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -9.2e-72) || !(z <= 1e-74)) {
		tmp = (x / z) + (y * (1.0 - (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 ((z <= (-9.2d-72)) .or. (.not. (z <= 1d-74))) then
        tmp = (x / z) + (y * (1.0d0 - (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 ((z <= -9.2e-72) || !(z <= 1e-74)) {
		tmp = (x / z) + (y * (1.0 - (x / z)));
	} else {
		tmp = (x + (y * (z - x))) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -9.2e-72) or not (z <= 1e-74):
		tmp = (x / z) + (y * (1.0 - (x / z)))
	else:
		tmp = (x + (y * (z - x))) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -9.2e-72) || !(z <= 1e-74))
		tmp = Float64(Float64(x / z) + Float64(y * Float64(1.0 - Float64(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 ((z <= -9.2e-72) || ~((z <= 1e-74)))
		tmp = (x / z) + (y * (1.0 - (x / z)));
	else
		tmp = (x + (y * (z - x))) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -9.2e-72], N[Not[LessEqual[z, 1e-74]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] + N[(y * N[(1.0 - N[(x / z), $MachinePrecision]), $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 z < -9.19999999999999978e-72 or 9.99999999999999958e-75 < z

   1. Initial program 77.8%

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

   3. Taylor expanded in y around 0 100.0%

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

   if -9.19999999999999978e-72 < z < 9.99999999999999958e-75

   1. Initial program 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{-72} \lor \neg \left(z \leq 10^{-74}\right):\\ \;\;\;\;\frac{x}{z} + y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \left(z - x\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 78.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.2 \cdot 10^{+28}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+62} \lor \neg \left(y \leq 4.8 \cdot 10^{+216}\right):\\ \;\;\;\;x \cdot \frac{y}{-z}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 2.2e+28)
   (+ y (/ x z))
   (if (or (<= y 3.5e+62) (not (<= y 4.8e+216)))
     (* x (/ y (- z)))
     (/ z (/ z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.2e+28) {
		tmp = y + (x / z);
	} else if ((y <= 3.5e+62) || !(y <= 4.8e+216)) {
		tmp = x * (y / -z);
	} else {
		tmp = z / (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 <= 2.2d+28) then
        tmp = y + (x / z)
    else if ((y <= 3.5d+62) .or. (.not. (y <= 4.8d+216))) then
        tmp = x * (y / -z)
    else
        tmp = z / (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.2e+28) {
		tmp = y + (x / z);
	} else if ((y <= 3.5e+62) || !(y <= 4.8e+216)) {
		tmp = x * (y / -z);
	} else {
		tmp = z / (z / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 2.2e+28:
		tmp = y + (x / z)
	elif (y <= 3.5e+62) or not (y <= 4.8e+216):
		tmp = x * (y / -z)
	else:
		tmp = z / (z / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 2.2e+28)
		tmp = Float64(y + Float64(x / z));
	elseif ((y <= 3.5e+62) || !(y <= 4.8e+216))
		tmp = Float64(x * Float64(y / Float64(-z)));
	else
		tmp = Float64(z / Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 2.2e+28)
		tmp = y + (x / z);
	elseif ((y <= 3.5e+62) || ~((y <= 4.8e+216)))
		tmp = x * (y / -z);
	else
		tmp = z / (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 2.2e+28], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 3.5e+62], N[Not[LessEqual[y, 4.8e+216]], $MachinePrecision]], N[(x * N[(y / (-z)), $MachinePrecision]), $MachinePrecision], N[(z / N[(z / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 2.19999999999999986e28

   1. Initial program 88.5%

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

   3. Taylor expanded in x around 0 97.4%

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

   4. Taylor expanded in y around 0 85.0%

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

   if 2.19999999999999986e28 < y < 3.49999999999999984e62 or 4.7999999999999999e216 < y

   1. Initial program 83.3%

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

   3. Taylor expanded in x around inf 68.9%

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

      1. associate-/l* 65.7%

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

      2. mul-1-neg 65.7%

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

      3. unsub-neg 65.7%

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

   5. Simplified 65.7%

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

   6. Taylor expanded in y around inf 68.9%

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

      1. mul-1-neg 68.9%

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

      2. associate-/l* 65.7%

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

      3. distribute-rgt-neg-in 65.7%

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

      4. distribute-neg-frac 65.7%

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

   8. Simplified 65.7%

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

   if 3.49999999999999984e62 < y < 4.7999999999999999e216

   1. Initial program 65.9%

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

   3. Taylor expanded in x around 0 46.4%

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

      1. *-commutative 46.4%

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

      2. associate-/l* 77.9%

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

   5. Applied egg-rr 77.9%

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

      1. clear-num 77.8%

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

      2. un-div-inv 78.1%

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

   7. Applied egg-rr 78.1%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.2 \cdot 10^{+28}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+62} \lor \neg \left(y \leq 4.8 \cdot 10^{+216}\right):\\ \;\;\;\;x \cdot \frac{y}{-z}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 78.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.6 \cdot 10^{+28}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+62}:\\ \;\;\;\;x \cdot \frac{y}{-z}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+216}:\\ \;\;\;\;\frac{z}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{-y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 2.6e+28)
   (+ y (/ x z))
   (if (<= y 3.8e+62)
     (* x (/ y (- z)))
     (if (<= y 3.3e+216) (/ z (/ z y)) (/ x (/ z (- y)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.6e+28) {
		tmp = y + (x / z);
	} else if (y <= 3.8e+62) {
		tmp = x * (y / -z);
	} else if (y <= 3.3e+216) {
		tmp = z / (z / 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 (y <= 2.6d+28) then
        tmp = y + (x / z)
    else if (y <= 3.8d+62) then
        tmp = x * (y / -z)
    else if (y <= 3.3d+216) then
        tmp = z / (z / 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 (y <= 2.6e+28) {
		tmp = y + (x / z);
	} else if (y <= 3.8e+62) {
		tmp = x * (y / -z);
	} else if (y <= 3.3e+216) {
		tmp = z / (z / y);
	} else {
		tmp = x / (z / -y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 2.6e+28:
		tmp = y + (x / z)
	elif y <= 3.8e+62:
		tmp = x * (y / -z)
	elif y <= 3.3e+216:
		tmp = z / (z / y)
	else:
		tmp = x / (z / -y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 2.6e+28)
		tmp = Float64(y + Float64(x / z));
	elseif (y <= 3.8e+62)
		tmp = Float64(x * Float64(y / Float64(-z)));
	elseif (y <= 3.3e+216)
		tmp = Float64(z / Float64(z / y));
	else
		tmp = Float64(x / Float64(z / Float64(-y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 2.6e+28)
		tmp = y + (x / z);
	elseif (y <= 3.8e+62)
		tmp = x * (y / -z);
	elseif (y <= 3.3e+216)
		tmp = z / (z / y);
	else
		tmp = x / (z / -y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 2.6e+28], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.8e+62], N[(x * N[(y / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.3e+216], N[(z / N[(z / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / (-y)), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < 2.6000000000000002e28

   1. Initial program 88.5%

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

   3. Taylor expanded in x around 0 97.4%

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

   4. Taylor expanded in y around 0 85.0%

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

   if 2.6000000000000002e28 < y < 3.79999999999999984e62

   1. Initial program 86.8%

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

   3. Taylor expanded in x around inf 67.5%

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

      1. associate-/l* 61.6%

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

      2. mul-1-neg 61.6%

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

      3. unsub-neg 61.6%

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

   5. Simplified 61.6%

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

   6. Taylor expanded in y around inf 67.5%

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

      1. mul-1-neg 67.5%

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

      2. associate-/l* 61.6%

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

      3. distribute-rgt-neg-in 61.6%

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

      4. distribute-neg-frac 61.6%

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

   8. Simplified 61.6%

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

   if 3.79999999999999984e62 < y < 3.3e216

   1. Initial program 65.9%

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

   3. Taylor expanded in x around 0 46.4%

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

      1. *-commutative 46.4%

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

      2. associate-/l* 77.9%

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

   5. Applied egg-rr 77.9%

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

      1. clear-num 77.8%

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

      2. un-div-inv 78.1%

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

   7. Applied egg-rr 78.1%

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

   if 3.3e216 < y

   1. Initial program 79.1%

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

   3. Taylor expanded in y around inf 79.1%

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

   4. Taylor expanded in x around inf 70.5%

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

      1. *-commutative 70.5%

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

      2. associate-/l* 77.5%

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

      3. sub-neg 77.5%

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

      4. metadata-eval 77.5%

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

      5. distribute-lft-in 77.5%

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

      6. *-commutative 77.5%

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

      7. neg-mul-1 77.5%

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

      8. unsub-neg 77.5%

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

      9. rgt-mult-inverse 77.5%

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

      10. *-commutative 77.5%

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

      11. associate-/r/ 70.6%

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

   6. Simplified 70.6%

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

   7. Taylor expanded in y around inf 70.6%

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

      1. associate-*r/ 70.6%

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

      2. mul-1-neg 70.6%

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

   9. Simplified 70.6%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.6 \cdot 10^{+28}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+62}:\\ \;\;\;\;x \cdot \frac{y}{-z}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+216}:\\ \;\;\;\;\frac{z}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{-y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+43}:\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+15}:\\ \;\;\;\;\frac{x + y \cdot \left(z - x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;y - y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6e+43)
   (* y (- 1.0 (/ x z)))
   (if (<= y 4.2e+15) (/ (+ x (* y (- z x))) z) (- y (* y (/ x z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6e+43) {
		tmp = y * (1.0 - (x / z));
	} else if (y <= 4.2e+15) {
		tmp = (x + (y * (z - x))) / z;
	} else {
		tmp = y - (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 <= (-6d+43)) then
        tmp = y * (1.0d0 - (x / z))
    else if (y <= 4.2d+15) then
        tmp = (x + (y * (z - x))) / z
    else
        tmp = y - (y * (x / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -6e+43) {
		tmp = y * (1.0 - (x / z));
	} else if (y <= 4.2e+15) {
		tmp = (x + (y * (z - x))) / z;
	} else {
		tmp = y - (y * (x / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -6e+43:
		tmp = y * (1.0 - (x / z))
	elif y <= 4.2e+15:
		tmp = (x + (y * (z - x))) / z
	else:
		tmp = y - (y * (x / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6e+43)
		tmp = Float64(y * Float64(1.0 - Float64(x / z)));
	elseif (y <= 4.2e+15)
		tmp = Float64(Float64(x + Float64(y * Float64(z - x))) / z);
	else
		tmp = Float64(y - Float64(y * Float64(x / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -6e+43)
		tmp = y * (1.0 - (x / z));
	elseif (y <= 4.2e+15)
		tmp = (x + (y * (z - x))) / z;
	else
		tmp = y - (y * (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6e+43], N[(y * N[(1.0 - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e+15], N[(N[(x + N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(y - N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.00000000000000033e43

   1. Initial program 66.0%

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

   3. Taylor expanded in y around inf 66.0%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - x\right)}{z}} \]
   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. *-inverses 99.9%

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

   5. Simplified 99.9%

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

   if -6.00000000000000033e43 < y < 4.2e15

   1. Initial program 99.9%

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

   if 4.2e15 < y

   1. Initial program 75.5%

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

   3. Taylor expanded in y around inf 75.5%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - x\right)}{z}} \]
   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. *-inverses 99.9%

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

   5. Simplified 99.9%

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

      1. sub-neg 99.9%

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

      2. distribute-rgt-in 99.9%

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

      3. *-un-lft-identity 99.9%

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

      4. distribute-neg-frac2 99.9%

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

   7. Applied egg-rr 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+43}:\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+15}:\\ \;\;\;\;\frac{x + y \cdot \left(z - x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;y - y \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.1% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 1.0))) (* y (- 1.0 (/ x z))) (+ y (/ x z))))

C

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

Python

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

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 1.0))
		tmp = Float64(y * Float64(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 <= -1.0) || ~((y <= 1.0)))
		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, -1.0], N[Not[LessEqual[y, 1.0]], $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 < -1 or 1 < y

   1. Initial program 74.2%

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

   3. Taylor expanded in y around inf 73.4%

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

      1. associate-/l* 99.1%

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

      2. div-sub 99.1%

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

      3. *-inverses 99.1%

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

   5. Simplified 99.1%

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

   if -1 < y < 1

   1. Initial program 99.9%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   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. Taylor expanded in y around 0 99.6%

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

4. Final simplification 99.3%

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

Alternative 6: 84.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-71} \lor \neg \left(z \leq 6 \cdot 10^{-120}\right):\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1 - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -8.5e-71) (not (<= z 6e-120)))
   (+ y (/ x z))
   (* x (/ (- 1.0 y) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8.5e-71) || !(z <= 6e-120)) {
		tmp = y + (x / z);
	} else {
		tmp = x * ((1.0 - 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 ((z <= (-8.5d-71)) .or. (.not. (z <= 6d-120))) then
        tmp = y + (x / z)
    else
        tmp = x * ((1.0d0 - y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8.5e-71) || !(z <= 6e-120)) {
		tmp = y + (x / z);
	} else {
		tmp = x * ((1.0 - y) / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -8.5e-71) or not (z <= 6e-120):
		tmp = y + (x / z)
	else:
		tmp = x * ((1.0 - y) / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -8.5e-71) || !(z <= 6e-120))
		tmp = Float64(y + Float64(x / z));
	else
		tmp = Float64(x * Float64(Float64(1.0 - y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -8.5e-71) || ~((z <= 6e-120)))
		tmp = y + (x / z);
	else
		tmp = x * ((1.0 - y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -8.5e-71], N[Not[LessEqual[z, 6e-120]], $MachinePrecision]], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(1.0 - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.49999999999999988e-71 or 6.00000000000000022e-120 < z

   1. Initial program 78.6%

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

   3. Taylor expanded in x around 0 99.3%

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

   4. Taylor expanded in y around 0 85.5%

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

   if -8.49999999999999988e-71 < z < 6.00000000000000022e-120

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 91.7%

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

      1. associate-/l* 85.4%

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

      2. mul-1-neg 85.4%

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

      3. unsub-neg 85.4%

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

   5. Simplified 85.4%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-71} \lor \neg \left(z \leq 6 \cdot 10^{-120}\right):\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1 - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.1% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if y < -1

   1. Initial program 71.0%

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

   3. Taylor expanded in y around inf 70.1%

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

      1. associate-/l* 98.9%

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

      2. div-sub 98.9%

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

      3. *-inverses 98.9%

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

   5. Simplified 98.9%

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

   if -1 < y < 1

   1. Initial program 99.9%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   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. Taylor expanded in y around 0 99.6%

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

   if 1 < y

   1. Initial program 78.3%

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

   3. Taylor expanded in y around inf 77.9%

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

      1. associate-/l* 99.4%

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

      2. div-sub 99.4%

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

      3. *-inverses 99.4%

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

   5. Simplified 99.4%

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

      1. sub-neg 99.4%

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

      2. distribute-rgt-in 99.5%

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

      3. *-un-lft-identity 99.5%

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

      4. distribute-neg-frac2 99.5%

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

   7. Applied egg-rr 99.5%

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

4. Final simplification 99.3%

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

Alternative 8: 97.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.25 \cdot 10^{-289}:\\ \;\;\;\;\frac{x}{z} + y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot \left(\frac{1}{z} - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.25e-289)
   (+ (/ x z) (* y (- 1.0 (/ x z))))
   (+ y (* x (- (/ 1.0 z) (/ y z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.25e-289) {
		tmp = (x / z) + (y * (1.0 - (x / z)));
	} else {
		tmp = y + (x * ((1.0 / 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 <= (-3.25d-289)) then
        tmp = (x / z) + (y * (1.0d0 - (x / z)))
    else
        tmp = y + (x * ((1.0d0 / z) - (y / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.25e-289) {
		tmp = (x / z) + (y * (1.0 - (x / z)));
	} else {
		tmp = y + (x * ((1.0 / z) - (y / z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.25e-289:
		tmp = (x / z) + (y * (1.0 - (x / z)))
	else:
		tmp = y + (x * ((1.0 / z) - (y / z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.25e-289)
		tmp = Float64(Float64(x / z) + Float64(y * Float64(1.0 - Float64(x / z))));
	else
		tmp = Float64(y + Float64(x * Float64(Float64(1.0 / z) - Float64(y / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.25e-289)
		tmp = (x / z) + (y * (1.0 - (x / z)));
	else
		tmp = y + (x * ((1.0 / z) - (y / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.25e-289], N[(N[(x / z), $MachinePrecision] + N[(y * N[(1.0 - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(x * N[(N[(1.0 / z), $MachinePrecision] - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.24999999999999987e-289

   1. Initial program 83.5%

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

   3. Taylor expanded in y around 0 99.9%

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

   if -3.24999999999999987e-289 < y

   1. Initial program 88.4%

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

   3. Taylor expanded in x around 0 97.4%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.25 \cdot 10^{-289}:\\ \;\;\;\;\frac{x}{z} + y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot \left(\frac{1}{z} - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 62.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-7}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-90}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.2e-7) (* z (/ y z)) (if (<= y 2.7e-90) (/ x z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.2e-7) {
		tmp = z * (y / z);
	} else if (y <= 2.7e-90) {
		tmp = x / z;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-3.2d-7)) then
        tmp = z * (y / z)
    else if (y <= 2.7d-90) then
        tmp = x / z
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.2e-7) {
		tmp = z * (y / z);
	} else if (y <= 2.7e-90) {
		tmp = x / z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.2e-7:
		tmp = z * (y / z)
	elif y <= 2.7e-90:
		tmp = x / z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.2e-7)
		tmp = Float64(z * Float64(y / z));
	elseif (y <= 2.7e-90)
		tmp = Float64(x / z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.2e-7)
		tmp = z * (y / z);
	elseif (y <= 2.7e-90)
		tmp = x / z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.2e-7], N[(z * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.7e-90], N[(x / z), $MachinePrecision], y]]

Derivation

1. Split input into 3 regimes

2. if y < -3.2000000000000001e-7

   1. Initial program 71.4%

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

   3. Taylor expanded in x around 0 34.7%

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

      1. *-commutative 34.7%

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

      2. associate-/l* 66.7%

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

   5. Applied egg-rr 66.7%

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

   if -3.2000000000000001e-7 < y < 2.69999999999999996e-90

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 77.6%

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

   if 2.69999999999999996e-90 < y

   1. Initial program 82.1%

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

   3. Taylor expanded in x around 0 53.0%

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

Alternative 10: 61.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{-6}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-90}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.05e-6) y (if (<= y 2.5e-90) (/ x z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.05e-6) {
		tmp = y;
	} else if (y <= 2.5e-90) {
		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 <= (-2.05d-6)) then
        tmp = y
    else if (y <= 2.5d-90) 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 <= -2.05e-6) {
		tmp = y;
	} else if (y <= 2.5e-90) {
		tmp = x / z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.05e-6:
		tmp = y
	elif y <= 2.5e-90:
		tmp = x / z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.05e-6)
		tmp = y;
	elseif (y <= 2.5e-90)
		tmp = Float64(x / z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.05e-6)
		tmp = y;
	elseif (y <= 2.5e-90)
		tmp = x / z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.05e-6], y, If[LessEqual[y, 2.5e-90], N[(x / z), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if y < -2.0499999999999999e-6 or 2.5000000000000001e-90 < y

   1. Initial program 76.5%

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

   3. Taylor expanded in x around 0 55.3%

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

   if -2.0499999999999999e-6 < y < 2.5000000000000001e-90

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 77.6%

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

Alternative 11: 79.0% 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 85.7%

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

3. Taylor expanded in x around 0 96.9%

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

4. Taylor expanded in y around 0 77.6%

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

Alternative 12: 41.4% 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 85.7%

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

3. Taylor expanded in x around 0 43.0%

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

Developer target: 94.2% 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 2024101 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:rasterificRadialGradient from diagrams-rasterific-1.3.1.3"
  :precision binary64

  :alt
  (- (+ y (/ x z)) (/ y (/ z x)))

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