Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, A

Percentage Accurate: 87.4% → 98.8%

Time: 5.7s

Alternatives: 12

Speedup: 0.3×

Specification

Math

\[\begin{array}{l} \\ \frac{x + y}{1 - \frac{y}{z}} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 87.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x + y}{1 - \frac{y}{z}} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t_0 \leq -5 \cdot 10^{-226} \lor \neg \left(t_0 \leq 0\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(x + z\right)}{y} \cdot \left(-1 - \frac{z}{y}\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -5e-226) (not (<= t_0 0.0)))
     t_0
     (- (* (/ (* z (+ x z)) y) (- -1.0 (/ z y))) z))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -5e-226) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = (((z * (x + z)) / y) * (-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) :: t_0
    real(8) :: tmp
    t_0 = (x + y) / (1.0d0 - (y / z))
    if ((t_0 <= (-5d-226)) .or. (.not. (t_0 <= 0.0d0))) then
        tmp = t_0
    else
        tmp = (((z * (x + z)) / y) * ((-1.0d0) - (z / y))) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -5e-226) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = (((z * (x + z)) / y) * (-1.0 - (z / y))) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -5e-226) or not (t_0 <= 0.0):
		tmp = t_0
	else:
		tmp = (((z * (x + z)) / y) * (-1.0 - (z / y))) - z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if ((t_0 <= -5e-226) || !(t_0 <= 0.0))
		tmp = t_0;
	else
		tmp = Float64(Float64(Float64(Float64(z * Float64(x + z)) / y) * Float64(-1.0 - Float64(z / y))) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + y) / (1.0 - (y / z));
	tmp = 0.0;
	if ((t_0 <= -5e-226) || ~((t_0 <= 0.0)))
		tmp = t_0;
	else
		tmp = (((z * (x + z)) / y) * (-1.0 - (z / y))) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -5e-226], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], t$95$0, N[(N[(N[(N[(z * N[(x + z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] * N[(-1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < -4.9999999999999998e-226 or 0.0 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

   1. Initial program 99.9%

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

   if -4.9999999999999998e-226 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < 0.0

   1. Initial program 10.9%

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

   2. Taylor expanded in y around inf 97.3%

      \[\leadsto \color{blue}{\left(-1 \cdot z + \left(-1 \cdot \frac{x \cdot z}{y} + \frac{z \cdot \left(-1 \cdot \left(x \cdot z\right) - {z}^{2}\right)}{{y}^{2}}\right)\right) - \frac{{z}^{2}}{y}} \]

   4. Simplified 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -5 \cdot 10^{-226} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(x + z\right)}{y} \cdot \left(-1 - \frac{z}{y}\right) - z\\ \end{array} \]

Alternative 2: 99.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t_0 \leq -5 \cdot 10^{-226} \lor \neg \left(t_0 \leq 0\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{y}{x + y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -5e-226) (not (<= t_0 0.0))) t_0 (/ (- z) (/ y (+ x y))))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -5e-226) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = -z / (y / (x + 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) :: t_0
    real(8) :: tmp
    t_0 = (x + y) / (1.0d0 - (y / z))
    if ((t_0 <= (-5d-226)) .or. (.not. (t_0 <= 0.0d0))) then
        tmp = t_0
    else
        tmp = -z / (y / (x + y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -5e-226) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = -z / (y / (x + y));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -5e-226) or not (t_0 <= 0.0):
		tmp = t_0
	else:
		tmp = -z / (y / (x + y))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if ((t_0 <= -5e-226) || !(t_0 <= 0.0))
		tmp = t_0;
	else
		tmp = Float64(Float64(-z) / Float64(y / Float64(x + y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + y) / (1.0 - (y / z));
	tmp = 0.0;
	if ((t_0 <= -5e-226) || ~((t_0 <= 0.0)))
		tmp = t_0;
	else
		tmp = -z / (y / (x + y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -5e-226], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], t$95$0, N[((-z) / N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < -4.9999999999999998e-226 or 0.0 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

   1. Initial program 99.9%

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

   if -4.9999999999999998e-226 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < 0.0

   1. Initial program 10.9%

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

   2. Taylor expanded in z around 0 94.8%

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

      1. mul-1-neg 94.8%

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

      2. associate-/l* 99.9%

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

      3. distribute-neg-frac 99.9%

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

      4. +-commutative 99.9%

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

   4. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -5 \cdot 10^{-226} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{y}{x + y}}\\ \end{array} \]

Alternative 3: 67.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{1 - \frac{y}{z}}\\ \mathbf{if}\;y \leq -2.15 \cdot 10^{+99}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -4.9 \cdot 10^{+65}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y}\\ \mathbf{elif}\;y \leq -5 \cdot 10^{+27}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-57}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-187}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+85}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ x (- 1.0 (/ y z)))))
   (if (<= y -2.15e+99)
     (- z)
     (if (<= y -4.9e+65)
       (/ (* x (- z)) y)
       (if (<= y -5e+27)
         (- z)
         (if (<= y -9e-57)
           t_0
           (if (<= y -3.6e-187) (+ x y) (if (<= y 1.8e+85) t_0 (- z)))))))))

C

double code(double x, double y, double z) {
	double t_0 = x / (1.0 - (y / z));
	double tmp;
	if (y <= -2.15e+99) {
		tmp = -z;
	} else if (y <= -4.9e+65) {
		tmp = (x * -z) / y;
	} else if (y <= -5e+27) {
		tmp = -z;
	} else if (y <= -9e-57) {
		tmp = t_0;
	} else if (y <= -3.6e-187) {
		tmp = x + y;
	} else if (y <= 1.8e+85) {
		tmp = t_0;
	} else {
		tmp = -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 / (1.0d0 - (y / z))
    if (y <= (-2.15d+99)) then
        tmp = -z
    else if (y <= (-4.9d+65)) then
        tmp = (x * -z) / y
    else if (y <= (-5d+27)) then
        tmp = -z
    else if (y <= (-9d-57)) then
        tmp = t_0
    else if (y <= (-3.6d-187)) then
        tmp = x + y
    else if (y <= 1.8d+85) then
        tmp = t_0
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x / (1.0 - (y / z));
	double tmp;
	if (y <= -2.15e+99) {
		tmp = -z;
	} else if (y <= -4.9e+65) {
		tmp = (x * -z) / y;
	} else if (y <= -5e+27) {
		tmp = -z;
	} else if (y <= -9e-57) {
		tmp = t_0;
	} else if (y <= -3.6e-187) {
		tmp = x + y;
	} else if (y <= 1.8e+85) {
		tmp = t_0;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x / (1.0 - (y / z))
	tmp = 0
	if y <= -2.15e+99:
		tmp = -z
	elif y <= -4.9e+65:
		tmp = (x * -z) / y
	elif y <= -5e+27:
		tmp = -z
	elif y <= -9e-57:
		tmp = t_0
	elif y <= -3.6e-187:
		tmp = x + y
	elif y <= 1.8e+85:
		tmp = t_0
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x / Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (y <= -2.15e+99)
		tmp = Float64(-z);
	elseif (y <= -4.9e+65)
		tmp = Float64(Float64(x * Float64(-z)) / y);
	elseif (y <= -5e+27)
		tmp = Float64(-z);
	elseif (y <= -9e-57)
		tmp = t_0;
	elseif (y <= -3.6e-187)
		tmp = Float64(x + y);
	elseif (y <= 1.8e+85)
		tmp = t_0;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x / (1.0 - (y / z));
	tmp = 0.0;
	if (y <= -2.15e+99)
		tmp = -z;
	elseif (y <= -4.9e+65)
		tmp = (x * -z) / y;
	elseif (y <= -5e+27)
		tmp = -z;
	elseif (y <= -9e-57)
		tmp = t_0;
	elseif (y <= -3.6e-187)
		tmp = x + y;
	elseif (y <= 1.8e+85)
		tmp = t_0;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.15e+99], (-z), If[LessEqual[y, -4.9e+65], N[(N[(x * (-z)), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, -5e+27], (-z), If[LessEqual[y, -9e-57], t$95$0, If[LessEqual[y, -3.6e-187], N[(x + y), $MachinePrecision], If[LessEqual[y, 1.8e+85], t$95$0, (-z)]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.1500000000000001e99 or -4.89999999999999956e65 < y < -4.99999999999999979e27 or 1.7999999999999999e85 < y

   1. Initial program 68.5%

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

   2. Taylor expanded in y around inf 70.9%

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

      1. mul-1-neg 70.9%

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

   4. Simplified 70.9%

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

   if -2.1500000000000001e99 < y < -4.89999999999999956e65

   1. Initial program 86.1%

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

   2. Taylor expanded in z around 0 71.7%

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

      1. mul-1-neg 71.7%

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

      2. +-commutative 71.7%

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

   4. Simplified 71.7%

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

   5. Taylor expanded in y around 0 72.1%

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

   if -4.99999999999999979e27 < y < -8.99999999999999945e-57 or -3.59999999999999994e-187 < y < 1.7999999999999999e85

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 78.5%

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

   if -8.99999999999999945e-57 < y < -3.59999999999999994e-187

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 73.2%

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

      1. +-commutative 73.2%

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

   4. Simplified 73.2%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+99}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -4.9 \cdot 10^{+65}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y}\\ \mathbf{elif}\;y \leq -5 \cdot 10^{+27}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-57}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-187}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+85}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 4: 69.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{z \cdot \left(\left(-x\right) - y\right)}{y}\\ \mathbf{if}\;y \leq -2.9 \cdot 10^{+224}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-57}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-187}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+64}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* z (- (- x) y)) y)))
   (if (<= y -2.9e+224)
     (- z)
     (if (<= y -9e-57)
       t_0
       (if (<= y -4.5e-187)
         (+ x y)
         (if (<= y 3e+64) (/ x (- 1.0 (/ y z))) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = (z * (-x - y)) / y;
	double tmp;
	if (y <= -2.9e+224) {
		tmp = -z;
	} else if (y <= -9e-57) {
		tmp = t_0;
	} else if (y <= -4.5e-187) {
		tmp = x + y;
	} else if (y <= 3e+64) {
		tmp = x / (1.0 - (y / z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (z * (-x - y)) / y
    if (y <= (-2.9d+224)) then
        tmp = -z
    else if (y <= (-9d-57)) then
        tmp = t_0
    else if (y <= (-4.5d-187)) then
        tmp = x + y
    else if (y <= 3d+64) then
        tmp = x / (1.0d0 - (y / z))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (z * (-x - y)) / y;
	double tmp;
	if (y <= -2.9e+224) {
		tmp = -z;
	} else if (y <= -9e-57) {
		tmp = t_0;
	} else if (y <= -4.5e-187) {
		tmp = x + y;
	} else if (y <= 3e+64) {
		tmp = x / (1.0 - (y / z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z * (-x - y)) / y
	tmp = 0
	if y <= -2.9e+224:
		tmp = -z
	elif y <= -9e-57:
		tmp = t_0
	elif y <= -4.5e-187:
		tmp = x + y
	elif y <= 3e+64:
		tmp = x / (1.0 - (y / z))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z * Float64(Float64(-x) - y)) / y)
	tmp = 0.0
	if (y <= -2.9e+224)
		tmp = Float64(-z);
	elseif (y <= -9e-57)
		tmp = t_0;
	elseif (y <= -4.5e-187)
		tmp = Float64(x + y);
	elseif (y <= 3e+64)
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (z * (-x - y)) / y;
	tmp = 0.0;
	if (y <= -2.9e+224)
		tmp = -z;
	elseif (y <= -9e-57)
		tmp = t_0;
	elseif (y <= -4.5e-187)
		tmp = x + y;
	elseif (y <= 3e+64)
		tmp = x / (1.0 - (y / z));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z * N[((-x) - y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -2.9e+224], (-z), If[LessEqual[y, -9e-57], t$95$0, If[LessEqual[y, -4.5e-187], N[(x + y), $MachinePrecision], If[LessEqual[y, 3e+64], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.89999999999999989e224

   1. Initial program 50.1%

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

   2. Taylor expanded in y around inf 87.9%

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

      1. mul-1-neg 87.9%

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

   4. Simplified 87.9%

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

   if -2.89999999999999989e224 < y < -8.99999999999999945e-57 or 3.0000000000000002e64 < y

   1. Initial program 78.6%

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

   2. Taylor expanded in z around 0 73.3%

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

      1. mul-1-neg 73.3%

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

      2. +-commutative 73.3%

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

   4. Simplified 73.3%

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

   if -8.99999999999999945e-57 < y < -4.4999999999999998e-187

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 73.2%

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

      1. +-commutative 73.2%

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

   4. Simplified 73.2%

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

   if -4.4999999999999998e-187 < y < 3.0000000000000002e64

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 83.5%

      \[\leadsto \color{blue}{\frac{x}{1 - \frac{y}{z}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+224}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-57}:\\ \;\;\;\;\frac{z \cdot \left(\left(-x\right) - y\right)}{y}\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-187}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+64}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(\left(-x\right) - y\right)}{y}\\ \end{array} \]

Alternative 5: 73.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-z}{\frac{y}{x + y}}\\ \mathbf{if}\;y \leq -9.2 \cdot 10^{-57}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-187}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+64}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (- z) (/ y (+ x y)))))
   (if (<= y -9.2e-57)
     t_0
     (if (<= y -5.2e-187)
       (+ x y)
       (if (<= y 3e+64) (/ x (- 1.0 (/ y z))) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = -z / (y / (x + y));
	double tmp;
	if (y <= -9.2e-57) {
		tmp = t_0;
	} else if (y <= -5.2e-187) {
		tmp = x + y;
	} else if (y <= 3e+64) {
		tmp = x / (1.0 - (y / z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = -z / (y / (x + y))
    if (y <= (-9.2d-57)) then
        tmp = t_0
    else if (y <= (-5.2d-187)) then
        tmp = x + y
    else if (y <= 3d+64) then
        tmp = x / (1.0d0 - (y / z))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -z / (y / (x + y));
	double tmp;
	if (y <= -9.2e-57) {
		tmp = t_0;
	} else if (y <= -5.2e-187) {
		tmp = x + y;
	} else if (y <= 3e+64) {
		tmp = x / (1.0 - (y / z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -z / (y / (x + y))
	tmp = 0
	if y <= -9.2e-57:
		tmp = t_0
	elif y <= -5.2e-187:
		tmp = x + y
	elif y <= 3e+64:
		tmp = x / (1.0 - (y / z))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-z) / Float64(y / Float64(x + y)))
	tmp = 0.0
	if (y <= -9.2e-57)
		tmp = t_0;
	elseif (y <= -5.2e-187)
		tmp = Float64(x + y);
	elseif (y <= 3e+64)
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -z / (y / (x + y));
	tmp = 0.0;
	if (y <= -9.2e-57)
		tmp = t_0;
	elseif (y <= -5.2e-187)
		tmp = x + y;
	elseif (y <= 3e+64)
		tmp = x / (1.0 - (y / z));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[((-z) / N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.2e-57], t$95$0, If[LessEqual[y, -5.2e-187], N[(x + y), $MachinePrecision], If[LessEqual[y, 3e+64], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.2000000000000001e-57 or 3.0000000000000002e64 < y

   1. Initial program 74.5%

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

   2. Taylor expanded in z around 0 71.3%

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

      1. mul-1-neg 71.3%

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

      2. associate-/l* 81.7%

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

      3. distribute-neg-frac 81.7%

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

      4. +-commutative 81.7%

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

   4. Simplified 81.7%

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

   if -9.2000000000000001e-57 < y < -5.1999999999999999e-187

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 73.2%

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

      1. +-commutative 73.2%

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

   4. Simplified 73.2%

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

   if -5.1999999999999999e-187 < y < 3.0000000000000002e64

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 83.5%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{-57}:\\ \;\;\;\;\frac{-z}{\frac{y}{x + y}}\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-187}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+64}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{y}{x + y}}\\ \end{array} \]

Alternative 6: 73.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-z}{\frac{y}{x + y}}\\ \mathbf{if}\;y \leq -9.2 \cdot 10^{-57}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-187}:\\ \;\;\;\;\left(x + y\right) \cdot \left(1 + \frac{y}{z}\right)\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+64}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (- z) (/ y (+ x y)))))
   (if (<= y -9.2e-57)
     t_0
     (if (<= y -4.8e-187)
       (* (+ x y) (+ 1.0 (/ y z)))
       (if (<= y 3e+64) (/ x (- 1.0 (/ y z))) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = -z / (y / (x + y));
	double tmp;
	if (y <= -9.2e-57) {
		tmp = t_0;
	} else if (y <= -4.8e-187) {
		tmp = (x + y) * (1.0 + (y / z));
	} else if (y <= 3e+64) {
		tmp = x / (1.0 - (y / z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = -z / (y / (x + y))
    if (y <= (-9.2d-57)) then
        tmp = t_0
    else if (y <= (-4.8d-187)) then
        tmp = (x + y) * (1.0d0 + (y / z))
    else if (y <= 3d+64) then
        tmp = x / (1.0d0 - (y / z))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -z / (y / (x + y));
	double tmp;
	if (y <= -9.2e-57) {
		tmp = t_0;
	} else if (y <= -4.8e-187) {
		tmp = (x + y) * (1.0 + (y / z));
	} else if (y <= 3e+64) {
		tmp = x / (1.0 - (y / z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -z / (y / (x + y))
	tmp = 0
	if y <= -9.2e-57:
		tmp = t_0
	elif y <= -4.8e-187:
		tmp = (x + y) * (1.0 + (y / z))
	elif y <= 3e+64:
		tmp = x / (1.0 - (y / z))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-z) / Float64(y / Float64(x + y)))
	tmp = 0.0
	if (y <= -9.2e-57)
		tmp = t_0;
	elseif (y <= -4.8e-187)
		tmp = Float64(Float64(x + y) * Float64(1.0 + Float64(y / z)));
	elseif (y <= 3e+64)
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -z / (y / (x + y));
	tmp = 0.0;
	if (y <= -9.2e-57)
		tmp = t_0;
	elseif (y <= -4.8e-187)
		tmp = (x + y) * (1.0 + (y / z));
	elseif (y <= 3e+64)
		tmp = x / (1.0 - (y / z));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[((-z) / N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.2e-57], t$95$0, If[LessEqual[y, -4.8e-187], N[(N[(x + y), $MachinePrecision] * N[(1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3e+64], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.2000000000000001e-57 or 3.0000000000000002e64 < y

   1. Initial program 74.5%

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

   2. Taylor expanded in z around 0 71.3%

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

      1. mul-1-neg 71.3%

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

      2. associate-/l* 81.7%

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

      3. distribute-neg-frac 81.7%

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

      4. +-commutative 81.7%

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

   4. Simplified 81.7%

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

   if -9.2000000000000001e-57 < y < -4.80000000000000027e-187

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 73.7%

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

      1. associate-+r+ 73.7%

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

      2. *-lft-identity 73.7%

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

      3. associate-/l* 73.5%

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

      4. associate-/r/ 73.5%

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

      5. distribute-rgt-in 73.5%

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

      6. +-commutative 73.5%

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

   4. Simplified 73.5%

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

   if -4.80000000000000027e-187 < y < 3.0000000000000002e64

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 83.5%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{-57}:\\ \;\;\;\;\frac{-z}{\frac{y}{x + y}}\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-187}:\\ \;\;\;\;\left(x + y\right) \cdot \left(1 + \frac{y}{z}\right)\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+64}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{y}{x + y}}\\ \end{array} \]

Alternative 7: 68.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ \mathbf{if}\;y \leq -5.6 \cdot 10^{+216}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-28}:\\ \;\;\;\;\frac{y}{t_0}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+86}:\\ \;\;\;\;\frac{x}{t_0}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))))
   (if (<= y -5.6e+216)
     (- z)
     (if (<= y -1.1e-28) (/ y t_0) (if (<= y 8e+86) (/ x t_0) (- z))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double tmp;
	if (y <= -5.6e+216) {
		tmp = -z;
	} else if (y <= -1.1e-28) {
		tmp = y / t_0;
	} else if (y <= 8e+86) {
		tmp = x / t_0;
	} else {
		tmp = -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 = 1.0d0 - (y / z)
    if (y <= (-5.6d+216)) then
        tmp = -z
    else if (y <= (-1.1d-28)) then
        tmp = y / t_0
    else if (y <= 8d+86) then
        tmp = x / t_0
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double tmp;
	if (y <= -5.6e+216) {
		tmp = -z;
	} else if (y <= -1.1e-28) {
		tmp = y / t_0;
	} else if (y <= 8e+86) {
		tmp = x / t_0;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	tmp = 0
	if y <= -5.6e+216:
		tmp = -z
	elif y <= -1.1e-28:
		tmp = y / t_0
	elif y <= 8e+86:
		tmp = x / t_0
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y / z))
	tmp = 0.0
	if (y <= -5.6e+216)
		tmp = Float64(-z);
	elseif (y <= -1.1e-28)
		tmp = Float64(y / t_0);
	elseif (y <= 8e+86)
		tmp = Float64(x / t_0);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y / z);
	tmp = 0.0;
	if (y <= -5.6e+216)
		tmp = -z;
	elseif (y <= -1.1e-28)
		tmp = y / t_0;
	elseif (y <= 8e+86)
		tmp = x / t_0;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.6e+216], (-z), If[LessEqual[y, -1.1e-28], N[(y / t$95$0), $MachinePrecision], If[LessEqual[y, 8e+86], N[(x / t$95$0), $MachinePrecision], (-z)]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.59999999999999963e216 or 8.0000000000000001e86 < y

   1. Initial program 57.1%

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

   2. Taylor expanded in y around inf 83.0%

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

      1. mul-1-neg 83.0%

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

   4. Simplified 83.0%

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

   if -5.59999999999999963e216 < y < -1.09999999999999998e-28

   1. Initial program 88.6%

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

   2. Taylor expanded in x around 0 64.9%

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

   if -1.09999999999999998e-28 < y < 8.0000000000000001e86

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 74.9%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+216}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-28}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+86}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 8: 66.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+96}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{+65}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y}\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-49}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+83}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.8e+96)
   (- z)
   (if (<= y -4.4e+65)
     (/ (* x (- z)) y)
     (if (<= y -2.8e-49) (- z) (if (<= y 9.5e+83) (+ x y) (- z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.8e+96) {
		tmp = -z;
	} else if (y <= -4.4e+65) {
		tmp = (x * -z) / y;
	} else if (y <= -2.8e-49) {
		tmp = -z;
	} else if (y <= 9.5e+83) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-4.8d+96)) then
        tmp = -z
    else if (y <= (-4.4d+65)) then
        tmp = (x * -z) / y
    else if (y <= (-2.8d-49)) then
        tmp = -z
    else if (y <= 9.5d+83) then
        tmp = x + y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.8e+96) {
		tmp = -z;
	} else if (y <= -4.4e+65) {
		tmp = (x * -z) / y;
	} else if (y <= -2.8e-49) {
		tmp = -z;
	} else if (y <= 9.5e+83) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.8e+96:
		tmp = -z
	elif y <= -4.4e+65:
		tmp = (x * -z) / y
	elif y <= -2.8e-49:
		tmp = -z
	elif y <= 9.5e+83:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.8e+96)
		tmp = Float64(-z);
	elseif (y <= -4.4e+65)
		tmp = Float64(Float64(x * Float64(-z)) / y);
	elseif (y <= -2.8e-49)
		tmp = Float64(-z);
	elseif (y <= 9.5e+83)
		tmp = Float64(x + y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4.8e+96)
		tmp = -z;
	elseif (y <= -4.4e+65)
		tmp = (x * -z) / y;
	elseif (y <= -2.8e-49)
		tmp = -z;
	elseif (y <= 9.5e+83)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.8e+96], (-z), If[LessEqual[y, -4.4e+65], N[(N[(x * (-z)), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, -2.8e-49], (-z), If[LessEqual[y, 9.5e+83], N[(x + y), $MachinePrecision], (-z)]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.79999999999999986e96 or -4.3999999999999997e65 < y < -2.79999999999999997e-49 or 9.5000000000000002e83 < y

   1. Initial program 71.8%

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

   2. Taylor expanded in y around inf 66.6%

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

      1. mul-1-neg 66.6%

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

   4. Simplified 66.6%

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

   if -4.79999999999999986e96 < y < -4.3999999999999997e65

   1. Initial program 86.1%

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

   2. Taylor expanded in z around 0 71.7%

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

      1. mul-1-neg 71.7%

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

      2. +-commutative 71.7%

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

   4. Simplified 71.7%

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

   5. Taylor expanded in y around 0 72.1%

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

   if -2.79999999999999997e-49 < y < 9.5000000000000002e83

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 71.6%

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

      1. +-commutative 71.6%

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

   4. Simplified 71.6%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+96}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{+65}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y}\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-49}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+83}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 9: 66.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-49}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+83}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.8e-49) (- z) (if (<= y 9.2e+83) (+ x y) (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.8e-49) {
		tmp = -z;
	} else if (y <= 9.2e+83) {
		tmp = x + y;
	} else {
		tmp = -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-49)) then
        tmp = -z
    else if (y <= 9.2d+83) then
        tmp = x + y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.8e-49) {
		tmp = -z;
	} else if (y <= 9.2e+83) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.8e-49:
		tmp = -z
	elif y <= 9.2e+83:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.8e-49)
		tmp = Float64(-z);
	elseif (y <= 9.2e+83)
		tmp = Float64(x + y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.8e-49)
		tmp = -z;
	elseif (y <= 9.2e+83)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.8e-49], (-z), If[LessEqual[y, 9.2e+83], N[(x + y), $MachinePrecision], (-z)]]

Derivation

1. Split input into 2 regimes

2. if y < -2.79999999999999997e-49 or 9.1999999999999998e83 < y

   1. Initial program 72.6%

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

   2. Taylor expanded in y around inf 62.9%

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

      1. mul-1-neg 62.9%

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

   4. Simplified 62.9%

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

   if -2.79999999999999997e-49 < y < 9.1999999999999998e83

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 71.6%

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

      1. +-commutative 71.6%

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

   4. Simplified 71.6%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-49}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+83}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 10: 57.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-49}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+64}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.8e-49) (- z) (if (<= y 3e+64) x (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.8e-49) {
		tmp = -z;
	} else if (y <= 3e+64) {
		tmp = x;
	} else {
		tmp = -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-49)) then
        tmp = -z
    else if (y <= 3d+64) then
        tmp = x
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.8e-49) {
		tmp = -z;
	} else if (y <= 3e+64) {
		tmp = x;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.8e-49:
		tmp = -z
	elif y <= 3e+64:
		tmp = x
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.8e-49)
		tmp = Float64(-z);
	elseif (y <= 3e+64)
		tmp = x;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.8e-49)
		tmp = -z;
	elseif (y <= 3e+64)
		tmp = x;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.8e-49], (-z), If[LessEqual[y, 3e+64], x, (-z)]]

Derivation

1. Split input into 2 regimes

2. if y < -2.79999999999999997e-49 or 3.0000000000000002e64 < y

   1. Initial program 73.5%

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

   2. Taylor expanded in y around inf 61.8%

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

      1. mul-1-neg 61.8%

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

   4. Simplified 61.8%

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

   if -2.79999999999999997e-49 < y < 3.0000000000000002e64

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 57.4%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-49}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+64}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 11: 35.8% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-58}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y -1.6e-58) y x))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.6e-58) {
		tmp = y;
	} else {
		tmp = x;
	}
	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 <= (-1.6d-58)) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.6e-58) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.6e-58:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.6e-58)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.6e-58)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.6e-58], y, x]

Derivation

1. Split input into 2 regimes

2. if y < -1.6e-58

   1. Initial program 77.9%

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

   2. Taylor expanded in x around 0 55.1%

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

   3. Taylor expanded in y around 0 20.3%

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

   if -1.6e-58 < y

   1. Initial program 91.6%

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

   2. Taylor expanded in y around 0 46.2%

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

4. Final simplification 37.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-58}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 33.7% accurate, 9.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return 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 = x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 87.0%

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

2. Taylor expanded in y around 0 32.4%

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

3. Final simplification 32.4%

   \[\leadsto x \]

Developer target: 93.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y + x}{-y} \cdot z\\ \mathbf{if}\;y < -3.7429310762689856 \cdot 10^{+171}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y < 3.5534662456086734 \cdot 10^{+168}:\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ (+ y x) (- y)) z)))
   (if (< y -3.7429310762689856e+171)
     t_0
     (if (< y 3.5534662456086734e+168) (/ (+ x y) (- 1.0 (/ y z))) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = ((y + x) / -y) * z;
	double tmp;
	if (y < -3.7429310762689856e+171) {
		tmp = t_0;
	} else if (y < 3.5534662456086734e+168) {
		tmp = (x + y) / (1.0 - (y / z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((y + x) / -y) * z
    if (y < (-3.7429310762689856d+171)) then
        tmp = t_0
    else if (y < 3.5534662456086734d+168) then
        tmp = (x + y) / (1.0d0 - (y / z))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = ((y + x) / -y) * z;
	double tmp;
	if (y < -3.7429310762689856e+171) {
		tmp = t_0;
	} else if (y < 3.5534662456086734e+168) {
		tmp = (x + y) / (1.0 - (y / z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = ((y + x) / -y) * z
	tmp = 0
	if y < -3.7429310762689856e+171:
		tmp = t_0
	elif y < 3.5534662456086734e+168:
		tmp = (x + y) / (1.0 - (y / z))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(y + x) / Float64(-y)) * z)
	tmp = 0.0
	if (y < -3.7429310762689856e+171)
		tmp = t_0;
	elseif (y < 3.5534662456086734e+168)
		tmp = Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((y + x) / -y) * z;
	tmp = 0.0;
	if (y < -3.7429310762689856e+171)
		tmp = t_0;
	elseif (y < 3.5534662456086734e+168)
		tmp = (x + y) / (1.0 - (y / z));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(y + x), $MachinePrecision] / (-y)), $MachinePrecision] * z), $MachinePrecision]}, If[Less[y, -3.7429310762689856e+171], t$95$0, If[Less[y, 3.5534662456086734e+168], N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Reproduce

herbie shell --seed 2023271 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, A"
  :precision binary64

  :herbie-target
  (if (< y -3.7429310762689856e+171) (* (/ (+ y x) (- y)) z) (if (< y 3.5534662456086734e+168) (/ (+ x y) (- 1.0 (/ y z))) (* (/ (+ y x) (- y)) z)))

  (/ (+ x y) (- 1.0 (/ y z))))