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

Percentage Accurate: 88.0% → 98.2%

Time: 8.9s

Alternatives: 14

Speedup: 0.6×

• 21.0% 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: 88.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.1 \cdot 10^{+79}:\\ \;\;\;\;y + \frac{x}{\frac{z}{1 - y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 1.1e+79) (+ y (/ x (/ z (- 1.0 y)))) (* y (- 1.0 (/ x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.1e+79) {
		tmp = y + (x / (z / (1.0 - y)));
	} else {
		tmp = y * (1.0 - (x / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 1.1d+79) then
        tmp = y + (x / (z / (1.0d0 - y)))
    else
        tmp = y * (1.0d0 - (x / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.1e+79) {
		tmp = y + (x / (z / (1.0 - y)));
	} else {
		tmp = y * (1.0 - (x / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1.1e+79:
		tmp = y + (x / (z / (1.0 - y)))
	else:
		tmp = y * (1.0 - (x / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.1e+79)
		tmp = Float64(y + Float64(x / Float64(z / Float64(1.0 - y))));
	else
		tmp = Float64(y * Float64(1.0 - Float64(x / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 1.1e+79)
		tmp = y + (x / (z / (1.0 - y)));
	else
		tmp = y * (1.0 - (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1.1e+79], N[(y + N[(x / N[(z / N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(1.0 - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.0999999999999999e79

   1. Initial program 95.3%

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

   3. Taylor expanded in x around 0 96.5%

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

      1. +-commutative 96.5%

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

      2. mul-1-neg 96.5%

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

      3. sub-neg 96.5%

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

      4. div-sub 96.5%

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

      5. clear-num 96.6%

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

      6. un-div-inv 98.7%

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

   5. Applied egg-rr 98.7%

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

   if 1.0999999999999999e79 < y

   1. Initial program 67.7%

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

   3. Taylor expanded in y around inf 67.7%

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

      1. associate-/l* 99.8%

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

      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%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.1 \cdot 10^{+79}:\\ \;\;\;\;y + \frac{x}{\frac{z}{1 - y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 78.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{-y}{z}\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{+186}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+38}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+144}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;y - \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (/ (- y) z))))
   (if (<= y -3.8e+186)
     t_0
     (if (<= y 1.4e+38)
       (+ y (/ x z))
       (if (<= y 1.6e+144) t_0 (- y (/ x z)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (-y / z);
	double tmp;
	if (y <= -3.8e+186) {
		tmp = t_0;
	} else if (y <= 1.4e+38) {
		tmp = y + (x / z);
	} else if (y <= 1.6e+144) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = x * (-y / z)
    if (y <= (-3.8d+186)) then
        tmp = t_0
    else if (y <= 1.4d+38) then
        tmp = y + (x / z)
    else if (y <= 1.6d+144) then
        tmp = t_0
    else
        tmp = y - (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (-y / z);
	double tmp;
	if (y <= -3.8e+186) {
		tmp = t_0;
	} else if (y <= 1.4e+38) {
		tmp = y + (x / z);
	} else if (y <= 1.6e+144) {
		tmp = t_0;
	} else {
		tmp = y - (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (-y / z)
	tmp = 0
	if y <= -3.8e+186:
		tmp = t_0
	elif y <= 1.4e+38:
		tmp = y + (x / z)
	elif y <= 1.6e+144:
		tmp = t_0
	else:
		tmp = y - (x / z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(Float64(-y) / z))
	tmp = 0.0
	if (y <= -3.8e+186)
		tmp = t_0;
	elseif (y <= 1.4e+38)
		tmp = Float64(y + Float64(x / z));
	elseif (y <= 1.6e+144)
		tmp = t_0;
	else
		tmp = Float64(y - Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (-y / z);
	tmp = 0.0;
	if (y <= -3.8e+186)
		tmp = t_0;
	elseif (y <= 1.4e+38)
		tmp = y + (x / z);
	elseif (y <= 1.6e+144)
		tmp = t_0;
	else
		tmp = y - (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[((-y) / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.8e+186], t$95$0, If[LessEqual[y, 1.4e+38], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.6e+144], t$95$0, N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.7999999999999998e186 or 1.4e38 < y < 1.6e144

   1. Initial program 84.5%

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

   3. Taylor expanded in y around inf 84.5%

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

   4. Taylor expanded in z around 0 64.4%

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

      1. mul-1-neg 64.4%

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

      2. distribute-lft-neg-out 64.4%

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

      3. *-commutative 64.4%

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

   6. Simplified 64.4%

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

      1. frac-2neg 64.4%

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

      2. distribute-frac-neg 64.4%

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

      3. add-sqr-sqrt 33.4%

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

      4. sqrt-unprod 25.1%

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

      5. sqr-neg 25.1%

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

      6. sqrt-unprod 0.3%

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

      7. add-sqr-sqrt 1.1%

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

      8. remove-double-neg 1.1%

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

      9. distribute-rgt-neg-out 1.1%

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

      10. frac-2neg 1.1%

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

      11. *-commutative 1.1%

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

      12. associate-/l* 1.4%

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

      13. add-sqr-sqrt 1.0%

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

      14. sqrt-unprod 24.7%

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

      15. sqr-neg 24.7%

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

      16. sqrt-unprod 28.9%

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

      17. add-sqr-sqrt 63.2%

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

   8. Applied egg-rr 63.2%

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

   if -3.7999999999999998e186 < y < 1.4e38

   1. Initial program 96.6%

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

   3. Taylor expanded in x around 0 98.1%

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

   4. Taylor expanded in y around 0 91.3%

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

   if 1.6e144 < y

   1. Initial program 63.3%

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

   3. Taylor expanded in x around 0 87.5%

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

   4. Taylor expanded in y around 0 54.9%

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

      1. frac-2neg 54.9%

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

      2. div-inv 54.9%

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

      3. add-sqr-sqrt 27.9%

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

      4. sqrt-unprod 64.6%

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

      5. sqr-neg 64.6%

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

      6. sqrt-unprod 35.1%

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

      7. add-sqr-sqrt 70.8%

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

      8. cancel-sign-sub-inv 70.8%

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

      9. div-inv 70.8%

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

   6. Applied egg-rr 70.8%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+186}:\\ \;\;\;\;x \cdot \frac{-y}{z}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+38}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+144}:\\ \;\;\;\;x \cdot \frac{-y}{z}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 79.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{z} \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -3.3 \cdot 10^{+186}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+39}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+144}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;y - \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ x z) (- y))))
   (if (<= y -3.3e+186)
     t_0
     (if (<= y 1.75e+39)
       (+ y (/ x z))
       (if (<= y 1.2e+144) t_0 (- y (/ x z)))))))

C

double code(double x, double y, double z) {
	double t_0 = (x / z) * -y;
	double tmp;
	if (y <= -3.3e+186) {
		tmp = t_0;
	} else if (y <= 1.75e+39) {
		tmp = y + (x / z);
	} else if (y <= 1.2e+144) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = (x / z) * -y
    if (y <= (-3.3d+186)) then
        tmp = t_0
    else if (y <= 1.75d+39) then
        tmp = y + (x / z)
    else if (y <= 1.2d+144) then
        tmp = t_0
    else
        tmp = y - (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x / z) * -y;
	double tmp;
	if (y <= -3.3e+186) {
		tmp = t_0;
	} else if (y <= 1.75e+39) {
		tmp = y + (x / z);
	} else if (y <= 1.2e+144) {
		tmp = t_0;
	} else {
		tmp = y - (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x / z) * -y
	tmp = 0
	if y <= -3.3e+186:
		tmp = t_0
	elif y <= 1.75e+39:
		tmp = y + (x / z)
	elif y <= 1.2e+144:
		tmp = t_0
	else:
		tmp = y - (x / z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x / z) * Float64(-y))
	tmp = 0.0
	if (y <= -3.3e+186)
		tmp = t_0;
	elseif (y <= 1.75e+39)
		tmp = Float64(y + Float64(x / z));
	elseif (y <= 1.2e+144)
		tmp = t_0;
	else
		tmp = Float64(y - Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x / z) * -y;
	tmp = 0.0;
	if (y <= -3.3e+186)
		tmp = t_0;
	elseif (y <= 1.75e+39)
		tmp = y + (x / z);
	elseif (y <= 1.2e+144)
		tmp = t_0;
	else
		tmp = y - (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x / z), $MachinePrecision] * (-y)), $MachinePrecision]}, If[LessEqual[y, -3.3e+186], t$95$0, If[LessEqual[y, 1.75e+39], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e+144], t$95$0, N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.30000000000000023e186 or 1.7500000000000001e39 < y < 1.2e144

   1. Initial program 84.5%

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

   3. Taylor expanded in y around inf 84.5%

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

      1. associate-/l* 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in z around 0 71.0%

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

      1. neg-mul-1 71.0%

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

      2. distribute-neg-frac2 71.0%

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

   8. Simplified 71.0%

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

   if -3.30000000000000023e186 < y < 1.7500000000000001e39

   1. Initial program 96.6%

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

   3. Taylor expanded in x around 0 98.1%

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

   4. Taylor expanded in y around 0 91.3%

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

   if 1.2e144 < y

   1. Initial program 63.3%

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

   3. Taylor expanded in x around 0 87.5%

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

   4. Taylor expanded in y around 0 54.9%

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

      1. frac-2neg 54.9%

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

      2. div-inv 54.9%

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

      3. add-sqr-sqrt 27.9%

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

      4. sqrt-unprod 64.6%

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

      5. sqr-neg 64.6%

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

      6. sqrt-unprod 35.1%

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

      7. add-sqr-sqrt 70.8%

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

      8. cancel-sign-sub-inv 70.8%

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

      9. div-inv 70.8%

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

   6. Applied egg-rr 70.8%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+186}:\\ \;\;\;\;\frac{x}{z} \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+39}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+144}:\\ \;\;\;\;\frac{x}{z} \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;y - \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+186}:\\ \;\;\;\;\frac{x}{z} \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+34}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+144}:\\ \;\;\;\;\frac{-y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.8e+186)
   (* (/ x z) (- y))
   (if (<= y 1.55e+34)
     (+ y (/ x z))
     (if (<= y 2.1e+144) (/ (- y) (/ z x)) (- y (/ x z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.8e+186) {
		tmp = (x / z) * -y;
	} else if (y <= 1.55e+34) {
		tmp = y + (x / z);
	} else if (y <= 2.1e+144) {
		tmp = -y / (z / x);
	} 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 <= (-2.8d+186)) then
        tmp = (x / z) * -y
    else if (y <= 1.55d+34) then
        tmp = y + (x / z)
    else if (y <= 2.1d+144) then
        tmp = -y / (z / x)
    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 <= -2.8e+186) {
		tmp = (x / z) * -y;
	} else if (y <= 1.55e+34) {
		tmp = y + (x / z);
	} else if (y <= 2.1e+144) {
		tmp = -y / (z / x);
	} else {
		tmp = y - (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.8e+186:
		tmp = (x / z) * -y
	elif y <= 1.55e+34:
		tmp = y + (x / z)
	elif y <= 2.1e+144:
		tmp = -y / (z / x)
	else:
		tmp = y - (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.8e+186)
		tmp = Float64(Float64(x / z) * Float64(-y));
	elseif (y <= 1.55e+34)
		tmp = Float64(y + Float64(x / z));
	elseif (y <= 2.1e+144)
		tmp = Float64(Float64(-y) / Float64(z / x));
	else
		tmp = Float64(y - Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.8e+186)
		tmp = (x / z) * -y;
	elseif (y <= 1.55e+34)
		tmp = y + (x / z);
	elseif (y <= 2.1e+144)
		tmp = -y / (z / x);
	else
		tmp = y - (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.8e+186], N[(N[(x / z), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[y, 1.55e+34], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.1e+144], N[((-y) / N[(z / x), $MachinePrecision]), $MachinePrecision], N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.80000000000000018e186

   1. Initial program 87.4%

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

   3. Taylor expanded in y around inf 87.4%

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

      1. associate-/l* 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in z around 0 70.9%

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

      1. neg-mul-1 70.9%

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

      2. distribute-neg-frac2 70.9%

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

   8. Simplified 70.9%

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

   if -2.80000000000000018e186 < y < 1.54999999999999989e34

   1. Initial program 96.6%

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

   3. Taylor expanded in x around 0 98.1%

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

   4. Taylor expanded in y around 0 91.3%

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

   if 1.54999999999999989e34 < y < 2.09999999999999996e144

   1. Initial program 81.6%

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

   3. Taylor expanded in y around inf 81.6%

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

      1. associate-/l* 99.6%

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

   5. Simplified 99.6%

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

      1. clear-num 99.5%

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

      2. un-div-inv 99.6%

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

   7. Applied egg-rr 99.6%

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

   8. Taylor expanded in z around 0 71.2%

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

      1. associate-*r/ 71.2%

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

      2. neg-mul-1 71.2%

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

   10. Simplified 71.2%

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

   if 2.09999999999999996e144 < y

   1. Initial program 63.3%

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

   3. Taylor expanded in x around 0 87.5%

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

   4. Taylor expanded in y around 0 54.9%

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

      1. frac-2neg 54.9%

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

      2. div-inv 54.9%

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

      3. add-sqr-sqrt 27.9%

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

      4. sqrt-unprod 64.6%

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

      5. sqr-neg 64.6%

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

      6. sqrt-unprod 35.1%

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

      7. add-sqr-sqrt 70.8%

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

      8. cancel-sign-sub-inv 70.8%

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

      9. div-inv 70.8%

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

   6. Applied egg-rr 70.8%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+186}:\\ \;\;\;\;\frac{x}{z} \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+34}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+144}:\\ \;\;\;\;\frac{-y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+186}:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{z}\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{+36}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+144}:\\ \;\;\;\;\frac{-y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.6e+186)
   (/ (* x (- y)) z)
   (if (<= y 2.45e+36)
     (+ y (/ x z))
     (if (<= y 1.25e+144) (/ (- y) (/ z x)) (- y (/ x z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.6e+186) {
		tmp = (x * -y) / z;
	} else if (y <= 2.45e+36) {
		tmp = y + (x / z);
	} else if (y <= 1.25e+144) {
		tmp = -y / (z / x);
	} 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 <= (-3.6d+186)) then
        tmp = (x * -y) / z
    else if (y <= 2.45d+36) then
        tmp = y + (x / z)
    else if (y <= 1.25d+144) then
        tmp = -y / (z / x)
    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 <= -3.6e+186) {
		tmp = (x * -y) / z;
	} else if (y <= 2.45e+36) {
		tmp = y + (x / z);
	} else if (y <= 1.25e+144) {
		tmp = -y / (z / x);
	} else {
		tmp = y - (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.6e+186:
		tmp = (x * -y) / z
	elif y <= 2.45e+36:
		tmp = y + (x / z)
	elif y <= 1.25e+144:
		tmp = -y / (z / x)
	else:
		tmp = y - (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.6e+186)
		tmp = Float64(Float64(x * Float64(-y)) / z);
	elseif (y <= 2.45e+36)
		tmp = Float64(y + Float64(x / z));
	elseif (y <= 1.25e+144)
		tmp = Float64(Float64(-y) / Float64(z / x));
	else
		tmp = Float64(y - Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.6e+186)
		tmp = (x * -y) / z;
	elseif (y <= 2.45e+36)
		tmp = y + (x / z);
	elseif (y <= 1.25e+144)
		tmp = -y / (z / x);
	else
		tmp = y - (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.6e+186], N[(N[(x * (-y)), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 2.45e+36], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.25e+144], N[((-y) / N[(z / x), $MachinePrecision]), $MachinePrecision], N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.6000000000000002e186

   1. Initial program 87.4%

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

   3. Taylor expanded in y around inf 87.4%

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

   4. Taylor expanded in z around 0 71.0%

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

      1. mul-1-neg 71.0%

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

      2. distribute-lft-neg-out 71.0%

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

      3. *-commutative 71.0%

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

   6. Simplified 71.0%

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

   if -3.6000000000000002e186 < y < 2.4499999999999999e36

   1. Initial program 96.6%

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

   3. Taylor expanded in x around 0 98.1%

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

   4. Taylor expanded in y around 0 91.3%

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

   if 2.4499999999999999e36 < y < 1.25e144

   1. Initial program 81.6%

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

   3. Taylor expanded in y around inf 81.6%

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

      1. associate-/l* 99.6%

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

   5. Simplified 99.6%

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

      1. clear-num 99.5%

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

      2. un-div-inv 99.6%

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

   7. Applied egg-rr 99.6%

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

   8. Taylor expanded in z around 0 71.2%

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

      1. associate-*r/ 71.2%

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

      2. neg-mul-1 71.2%

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

   10. Simplified 71.2%

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

   if 1.25e144 < y

   1. Initial program 63.3%

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

   3. Taylor expanded in x around 0 87.5%

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

   4. Taylor expanded in y around 0 54.9%

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

      1. frac-2neg 54.9%

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

      2. div-inv 54.9%

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

      3. add-sqr-sqrt 27.9%

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

      4. sqrt-unprod 64.6%

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

      5. sqr-neg 64.6%

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

      6. sqrt-unprod 35.1%

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

      7. add-sqr-sqrt 70.8%

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

      8. cancel-sign-sub-inv 70.8%

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

      9. div-inv 70.8%

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

   6. Applied egg-rr 70.8%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+186}:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{z}\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{+36}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+144}:\\ \;\;\;\;\frac{-y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+97} \lor \neg \left(x \leq 7.6 \cdot 10^{-59}\right):\\ \;\;\;\;x \cdot \frac{1 - y}{z}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.8e+97) (not (<= x 7.6e-59)))
   (* x (/ (- 1.0 y) z))
   (+ y (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.8e+97) || !(x <= 7.6e-59)) {
		tmp = x * ((1.0 - y) / 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 ((x <= (-5.8d+97)) .or. (.not. (x <= 7.6d-59))) then
        tmp = x * ((1.0d0 - y) / 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 ((x <= -5.8e+97) || !(x <= 7.6e-59)) {
		tmp = x * ((1.0 - y) / z);
	} else {
		tmp = y + (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.8e+97) or not (x <= 7.6e-59):
		tmp = x * ((1.0 - y) / z)
	else:
		tmp = y + (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.8e+97) || !(x <= 7.6e-59))
		tmp = Float64(x * Float64(Float64(1.0 - y) / z));
	else
		tmp = Float64(y + Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -5.8e+97) || ~((x <= 7.6e-59)))
		tmp = x * ((1.0 - y) / z);
	else
		tmp = y + (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.8e+97], N[Not[LessEqual[x, 7.6e-59]], $MachinePrecision]], N[(x * N[(N[(1.0 - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.79999999999999974e97 or 7.59999999999999966e-59 < x

   1. Initial program 90.9%

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

   3. Taylor expanded in x around inf 83.5%

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

      1. associate-/l* 88.3%

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

      2. mul-1-neg 88.3%

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

      3. unsub-neg 88.3%

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

   5. Simplified 88.3%

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

   if -5.79999999999999974e97 < x < 7.59999999999999966e-59

   1. Initial program 88.7%

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

   3. Taylor expanded in x around 0 90.5%

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

   4. Taylor expanded in y around 0 88.0%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+97} \lor \neg \left(x \leq 7.6 \cdot 10^{-59}\right):\\ \;\;\;\;x \cdot \frac{1 - y}{z}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.1% accurate, 0.5× speedup

Math

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

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 79.6%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   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* 98.1%

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

      2. div-sub 98.1%

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

      3. sub-neg 98.1%

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

      4. *-inverses 98.1%

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

      5. sub-neg 98.1%

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

   5. Simplified 98.1%

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

   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 98.4%

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

4. Final simplification 98.3%

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

Alternative 8: 99.1% accurate, 0.5× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.0) {
		tmp = y * ((z - x) / z);
	} else if (y <= 1.0) {
		tmp = y + (x / z);
	} else {
		tmp = y * (1.0 - (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 * ((z - x) / z)
    else if (y <= 1.0d0) then
        tmp = y + (x / z)
    else
        tmp = y * (1.0d0 - (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 * ((z - x) / z);
	} else if (y <= 1.0) {
		tmp = y + (x / z);
	} else {
		tmp = y * (1.0 - (x / z));
	}
	return tmp;
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if y < -1

   1. Initial program 88.4%

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

   3. Taylor expanded in y around inf 85.8%

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

      1. associate-/l* 97.3%

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

   5. Simplified 97.3%

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

   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 98.4%

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

   if 1 < y

   1. Initial program 70.7%

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

   3. Taylor expanded in y around inf 69.9%

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

      1. associate-/l* 99.0%

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

      2. div-sub 99.0%

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

      3. sub-neg 99.0%

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

      4. *-inverses 99.0%

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

      5. sub-neg 99.0%

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

   5. Simplified 99.0%

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

4. Final simplification 98.3%

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

Alternative 9: 99.1% accurate, 0.5× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.0) {
		tmp = y / (z / (z - x));
	} else if (y <= 1.0) {
		tmp = y + (x / z);
	} else {
		tmp = y * (1.0 - (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 / (z / (z - x))
    else if (y <= 1.0d0) then
        tmp = y + (x / z)
    else
        tmp = y * (1.0d0 - (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 / (z / (z - x));
	} else if (y <= 1.0) {
		tmp = y + (x / z);
	} else {
		tmp = y * (1.0 - (x / z));
	}
	return tmp;
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if y < -1

   1. Initial program 88.4%

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

   3. Taylor expanded in y around inf 85.8%

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

      1. associate-/l* 97.3%

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

   5. Simplified 97.3%

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

      1. clear-num 97.3%

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

      2. un-div-inv 97.3%

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

   7. Applied egg-rr 97.3%

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

   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 98.4%

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

   if 1 < y

   1. Initial program 70.7%

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

   3. Taylor expanded in y around inf 69.9%

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

      1. associate-/l* 99.0%

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

      2. div-sub 99.0%

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

      3. sub-neg 99.0%

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

      4. *-inverses 99.0%

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

      5. sub-neg 99.0%

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

   5. Simplified 99.0%

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

4. Final simplification 98.3%

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

Alternative 10: 60.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-8}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-50}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.8e-8) y (if (<= y 2.1e-50) (/ x z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.8e-8) {
		tmp = y;
	} else if (y <= 2.1e-50) {
		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 <= (-3.8d-8)) then
        tmp = y
    else if (y <= 2.1d-50) 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 <= -3.8e-8) {
		tmp = y;
	} else if (y <= 2.1e-50) {
		tmp = x / z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.8e-8:
		tmp = y
	elif y <= 2.1e-50:
		tmp = x / z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.8e-8)
		tmp = y;
	elseif (y <= 2.1e-50)
		tmp = Float64(x / z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.8e-8)
		tmp = y;
	elseif (y <= 2.1e-50)
		tmp = x / z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.8e-8], y, If[LessEqual[y, 2.1e-50], N[(x / z), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if y < -3.80000000000000028e-8 or 2.1000000000000001e-50 < y

   1. Initial program 81.0%

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

   3. Taylor expanded in x around 0 51.2%

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

   if -3.80000000000000028e-8 < y < 2.1000000000000001e-50

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 73.6%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-8}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-50}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 61.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-8}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-53}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.8e-8) (* z (/ y z)) (if (<= y 1.4e-53) (/ x z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.8e-8) {
		tmp = z * (y / z);
	} else if (y <= 1.4e-53) {
		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 <= (-2.8d-8)) then
        tmp = z * (y / z)
    else if (y <= 1.4d-53) 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 <= -2.8e-8) {
		tmp = z * (y / z);
	} else if (y <= 1.4e-53) {
		tmp = x / z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.8e-8:
		tmp = z * (y / z)
	elif y <= 1.4e-53:
		tmp = x / z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.8e-8)
		tmp = Float64(z * Float64(y / z));
	elseif (y <= 1.4e-53)
		tmp = Float64(x / z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.8e-8)
		tmp = z * (y / z);
	elseif (y <= 1.4e-53)
		tmp = x / z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.8e-8], N[(z * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.4e-53], N[(x / z), $MachinePrecision], y]]

Derivation

1. Split input into 3 regimes

2. if y < -2.7999999999999999e-8

   1. Initial program 88.5%

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

   3. Taylor expanded in y around inf 86.0%

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

   4. Taylor expanded in z around inf 45.9%

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

      1. *-commutative 45.9%

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

      2. associate-/l* 56.8%

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

   6. Applied egg-rr 56.8%

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

   if -2.7999999999999999e-8 < y < 1.39999999999999993e-53

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 73.6%

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

   if 1.39999999999999993e-53 < y

   1. Initial program 74.2%

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

   3. Taylor expanded in x around 0 49.2%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-8}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-53}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 81.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.0) {
		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 <= 1.0d0) 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 <= 1.0) {
		tmp = y + (x / z);
	} else {
		tmp = y - (x / z);
	}
	return tmp;
}

Python

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < 1

   1. Initial program 96.0%

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

   3. Taylor expanded in x around 0 96.3%

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

   4. Taylor expanded in y around 0 85.7%

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

   if 1 < 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 89.5%

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

   4. Taylor expanded in y around 0 48.9%

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

      1. frac-2neg 48.9%

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

      2. div-inv 48.9%

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

      3. add-sqr-sqrt 26.2%

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

      4. sqrt-unprod 54.9%

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

      5. sqr-neg 54.9%

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

      6. sqrt-unprod 27.9%

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

      7. add-sqr-sqrt 60.8%

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

      8. cancel-sign-sub-inv 60.8%

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

      9. div-inv 60.8%

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

   6. Applied egg-rr 60.8%

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

4. Final simplification 79.5%

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

Alternative 13: 77.9% 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 89.7%

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

3. Taylor expanded in x around 0 94.6%

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

4. Taylor expanded in y around 0 76.5%

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

5. Final simplification 76.5%

   \[\leadsto y + \frac{x}{z} \]
6. Add Preprocessing

Alternative 14: 40.0% 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 89.7%

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

3. Taylor expanded in x around 0 40.9%

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

4. Final simplification 40.9%

   \[\leadsto y \]
5. Add Preprocessing

Developer target: 94.0% 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 2024115 
(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))