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

Percentage Accurate: 88.1% → 99.7%

Time: 6.5s

Alternatives: 11

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: 88.1% 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: 99.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t_0 \leq -1 \cdot 10^{-263} \lor \neg \left(t_0 \leq 0\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-z\right) - \frac{z}{\frac{y}{x}}\right) - \frac{z}{\frac{y}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -1e-263) (not (<= t_0 0.0)))
     t_0
     (- (- (- z) (/ z (/ y x))) (/ 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 <= -1e-263) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = (-z - (z / (y / x))) - (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 <= (-1d-263)) .or. (.not. (t_0 <= 0.0d0))) then
        tmp = t_0
    else
        tmp = (-z - (z / (y / x))) - (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 <= -1e-263) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = (-z - (z / (y / x))) - (z / (y / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -1e-263) or not (t_0 <= 0.0):
		tmp = t_0
	else:
		tmp = (-z - (z / (y / x))) - (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 <= -1e-263) || !(t_0 <= 0.0))
		tmp = t_0;
	else
		tmp = Float64(Float64(Float64(-z) - Float64(z / Float64(y / x))) - Float64(z / Float64(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 <= -1e-263) || ~((t_0 <= 0.0)))
		tmp = t_0;
	else
		tmp = (-z - (z / (y / x))) - (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, -1e-263], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], t$95$0, N[(N[((-z) - N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < -1e-263 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 -1e-263 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < 0.0

   1. Initial program 10.2%

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

   2. Taylor expanded in y around inf 99.9%

      \[\leadsto \color{blue}{\left(-1 \cdot z + -1 \cdot \frac{z \cdot x}{y}\right) - \frac{{z}^{2}}{y}} \]
   3. Step-by-step derivation

      1. mul-1-neg 99.9%

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

      2. unsub-neg 99.9%

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

      3. mul-1-neg 99.9%

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

      4. associate-/l* 100.0%

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

      5. unpow2 100.0%

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

      6. associate-/l* 100.0%

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

   4. Simplified 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -1 \cdot 10^{-263} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-z\right) - \frac{z}{\frac{y}{x}}\right) - \frac{z}{\frac{y}{z}}\\ \end{array} \]

Alternative 2: 99.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t_0 \leq -1 \cdot 10^{-263} \lor \neg \left(t_0 \leq 0\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -1e-263) (not (<= t_0 0.0))) t_0 (* z (- -1.0 (/ 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 <= -1e-263) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = z * (-1.0 - (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 <= (-1d-263)) .or. (.not. (t_0 <= 0.0d0))) then
        tmp = t_0
    else
        tmp = z * ((-1.0d0) - (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 <= -1e-263) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = z * (-1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -1e-263) or not (t_0 <= 0.0):
		tmp = t_0
	else:
		tmp = z * (-1.0 - (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 <= -1e-263) || !(t_0 <= 0.0))
		tmp = t_0;
	else
		tmp = Float64(z * Float64(-1.0 - 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 <= -1e-263) || ~((t_0 <= 0.0)))
		tmp = t_0;
	else
		tmp = z * (-1.0 - (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, -1e-263], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], t$95$0, N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < -1e-263 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 -1e-263 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < 0.0

   1. Initial program 10.2%

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

   2. Taylor expanded in z around 0 95.6%

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

      1. mul-1-neg 95.6%

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

      2. +-commutative 95.6%

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

      3. *-commutative 95.6%

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

      4. +-commutative 95.6%

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

   4. Simplified 95.6%

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

   5. Taylor expanded in y around 0 99.9%

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

   6. Taylor expanded in z around 0 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -1 \cdot 10^{-263} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \]

Alternative 3: 67.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+105}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{+49}:\\ \;\;\;\;\frac{-z}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-134}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 3.75 \cdot 10^{-6}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+29}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.7e+105)
   (- z)
   (if (<= y -2.15e+49)
     (/ (- z) (/ y x))
     (if (<= y 5.6e-134)
       (+ x y)
       (if (<= y 3.75e-6)
         (/ x (- 1.0 (/ y z)))
         (if (<= y 9.2e+29) (+ x y) (- z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.7e+105) {
		tmp = -z;
	} else if (y <= -2.15e+49) {
		tmp = -z / (y / x);
	} else if (y <= 5.6e-134) {
		tmp = x + y;
	} else if (y <= 3.75e-6) {
		tmp = x / (1.0 - (y / z));
	} else if (y <= 9.2e+29) {
		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 <= (-2.7d+105)) then
        tmp = -z
    else if (y <= (-2.15d+49)) then
        tmp = -z / (y / x)
    else if (y <= 5.6d-134) then
        tmp = x + y
    else if (y <= 3.75d-6) then
        tmp = x / (1.0d0 - (y / z))
    else if (y <= 9.2d+29) 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 <= -2.7e+105) {
		tmp = -z;
	} else if (y <= -2.15e+49) {
		tmp = -z / (y / x);
	} else if (y <= 5.6e-134) {
		tmp = x + y;
	} else if (y <= 3.75e-6) {
		tmp = x / (1.0 - (y / z));
	} else if (y <= 9.2e+29) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.7e+105:
		tmp = -z
	elif y <= -2.15e+49:
		tmp = -z / (y / x)
	elif y <= 5.6e-134:
		tmp = x + y
	elif y <= 3.75e-6:
		tmp = x / (1.0 - (y / z))
	elif y <= 9.2e+29:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.7e+105)
		tmp = Float64(-z);
	elseif (y <= -2.15e+49)
		tmp = Float64(Float64(-z) / Float64(y / x));
	elseif (y <= 5.6e-134)
		tmp = Float64(x + y);
	elseif (y <= 3.75e-6)
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	elseif (y <= 9.2e+29)
		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 <= -2.7e+105)
		tmp = -z;
	elseif (y <= -2.15e+49)
		tmp = -z / (y / x);
	elseif (y <= 5.6e-134)
		tmp = x + y;
	elseif (y <= 3.75e-6)
		tmp = x / (1.0 - (y / z));
	elseif (y <= 9.2e+29)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.7e+105], (-z), If[LessEqual[y, -2.15e+49], N[((-z) / N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.6e-134], N[(x + y), $MachinePrecision], If[LessEqual[y, 3.75e-6], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.2e+29], N[(x + y), $MachinePrecision], (-z)]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.70000000000000016e105 or 9.2000000000000004e29 < y

   1. Initial program 67.1%

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

   2. Taylor expanded in y around inf 64.7%

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

      1. mul-1-neg 64.7%

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

   4. Simplified 64.7%

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

   if -2.70000000000000016e105 < y < -2.15e49

   1. Initial program 81.3%

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

   2. Taylor expanded in z around 0 80.4%

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

      1. mul-1-neg 80.4%

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

      2. +-commutative 80.4%

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

      3. *-commutative 80.4%

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

      4. +-commutative 80.4%

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

   4. Simplified 80.4%

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

   5. Taylor expanded in y around 0 67.9%

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

      1. associate-/l* 68.3%

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

   7. Simplified 68.3%

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

   if -2.15e49 < y < 5.5999999999999997e-134 or 3.7500000000000001e-6 < y < 9.2000000000000004e29

   1. Initial program 98.3%

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

   2. Taylor expanded in z around inf 80.7%

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

   if 5.5999999999999997e-134 < y < 3.7500000000000001e-6

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 70.1%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+105}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{+49}:\\ \;\;\;\;\frac{-z}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-134}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 3.75 \cdot 10^{-6}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+29}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 4: 68.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+105}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{+49}:\\ \;\;\;\;\frac{-z}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-10}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+172}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.3e+105)
   (- z)
   (if (<= y -2.6e+49)
     (/ (- z) (/ y x))
     (if (<= y 3e-10)
       (+ x y)
       (if (<= y 1.9e+172) (/ y (- 1.0 (/ y z))) (- z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.3e+105) {
		tmp = -z;
	} else if (y <= -2.6e+49) {
		tmp = -z / (y / x);
	} else if (y <= 3e-10) {
		tmp = x + y;
	} else if (y <= 1.9e+172) {
		tmp = y / (1.0 - (y / z));
	} 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 <= (-2.3d+105)) then
        tmp = -z
    else if (y <= (-2.6d+49)) then
        tmp = -z / (y / x)
    else if (y <= 3d-10) then
        tmp = x + y
    else if (y <= 1.9d+172) then
        tmp = y / (1.0d0 - (y / z))
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.3e+105) {
		tmp = -z;
	} else if (y <= -2.6e+49) {
		tmp = -z / (y / x);
	} else if (y <= 3e-10) {
		tmp = x + y;
	} else if (y <= 1.9e+172) {
		tmp = y / (1.0 - (y / z));
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.3e+105:
		tmp = -z
	elif y <= -2.6e+49:
		tmp = -z / (y / x)
	elif y <= 3e-10:
		tmp = x + y
	elif y <= 1.9e+172:
		tmp = y / (1.0 - (y / z))
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.3e+105)
		tmp = Float64(-z);
	elseif (y <= -2.6e+49)
		tmp = Float64(Float64(-z) / Float64(y / x));
	elseif (y <= 3e-10)
		tmp = Float64(x + y);
	elseif (y <= 1.9e+172)
		tmp = Float64(y / Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.3e+105)
		tmp = -z;
	elseif (y <= -2.6e+49)
		tmp = -z / (y / x);
	elseif (y <= 3e-10)
		tmp = x + y;
	elseif (y <= 1.9e+172)
		tmp = y / (1.0 - (y / z));
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.3e+105], (-z), If[LessEqual[y, -2.6e+49], N[((-z) / N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3e-10], N[(x + y), $MachinePrecision], If[LessEqual[y, 1.9e+172], N[(y / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], (-z)]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.2999999999999998e105 or 1.89999999999999985e172 < y

   1. Initial program 59.1%

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

   2. Taylor expanded in y around inf 70.0%

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

      1. mul-1-neg 70.0%

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

   4. Simplified 70.0%

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

   if -2.2999999999999998e105 < y < -2.59999999999999989e49

   1. Initial program 81.3%

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

   2. Taylor expanded in z around 0 80.4%

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

      1. mul-1-neg 80.4%

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

      2. +-commutative 80.4%

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

      3. *-commutative 80.4%

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

      4. +-commutative 80.4%

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

   4. Simplified 80.4%

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

   5. Taylor expanded in y around 0 67.9%

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

      1. associate-/l* 68.3%

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

   7. Simplified 68.3%

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

   if -2.59999999999999989e49 < y < 3e-10

   1. Initial program 99.2%

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

   2. Taylor expanded in z around inf 76.8%

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

   if 3e-10 < y < 1.89999999999999985e172

   1. Initial program 91.0%

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

   2. Taylor expanded in x around 0 67.8%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+105}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{+49}:\\ \;\;\;\;\frac{-z}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-10}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+172}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 5: 73.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{+14}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-60}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+44}:\\ \;\;\;\;\left(-z\right) - \frac{x \cdot z}{y}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+162}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- -1.0 (/ x y)))))
   (if (<= y -1.6e+14)
     t_0
     (if (<= y 1.85e-60)
       (+ x y)
       (if (<= y 2.5e+44)
         (- (- z) (/ (* x z) y))
         (if (<= y 1.15e+162) (/ y (- 1.0 (/ y z))) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (-1.0 - (x / y));
	double tmp;
	if (y <= -1.6e+14) {
		tmp = t_0;
	} else if (y <= 1.85e-60) {
		tmp = x + y;
	} else if (y <= 2.5e+44) {
		tmp = -z - ((x * z) / y);
	} else if (y <= 1.15e+162) {
		tmp = 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 = z * ((-1.0d0) - (x / y))
    if (y <= (-1.6d+14)) then
        tmp = t_0
    else if (y <= 1.85d-60) then
        tmp = x + y
    else if (y <= 2.5d+44) then
        tmp = -z - ((x * z) / y)
    else if (y <= 1.15d+162) then
        tmp = 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 = z * (-1.0 - (x / y));
	double tmp;
	if (y <= -1.6e+14) {
		tmp = t_0;
	} else if (y <= 1.85e-60) {
		tmp = x + y;
	} else if (y <= 2.5e+44) {
		tmp = -z - ((x * z) / y);
	} else if (y <= 1.15e+162) {
		tmp = y / (1.0 - (y / z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (-1.0 - (x / y))
	tmp = 0
	if y <= -1.6e+14:
		tmp = t_0
	elif y <= 1.85e-60:
		tmp = x + y
	elif y <= 2.5e+44:
		tmp = -z - ((x * z) / y)
	elif y <= 1.15e+162:
		tmp = y / (1.0 - (y / z))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -1.6e+14)
		tmp = t_0;
	elseif (y <= 1.85e-60)
		tmp = Float64(x + y);
	elseif (y <= 2.5e+44)
		tmp = Float64(Float64(-z) - Float64(Float64(x * z) / y));
	elseif (y <= 1.15e+162)
		tmp = Float64(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 = z * (-1.0 - (x / y));
	tmp = 0.0;
	if (y <= -1.6e+14)
		tmp = t_0;
	elseif (y <= 1.85e-60)
		tmp = x + y;
	elseif (y <= 2.5e+44)
		tmp = -z - ((x * z) / y);
	elseif (y <= 1.15e+162)
		tmp = y / (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[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.6e+14], t$95$0, If[LessEqual[y, 1.85e-60], N[(x + y), $MachinePrecision], If[LessEqual[y, 2.5e+44], N[((-z) - N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.15e+162], N[(y / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.6e14 or 1.14999999999999997e162 < y

   1. Initial program 65.3%

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

   2. Taylor expanded in z around 0 67.2%

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

      1. mul-1-neg 67.2%

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

      2. +-commutative 67.2%

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

      3. *-commutative 67.2%

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

      4. +-commutative 67.2%

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

   4. Simplified 67.2%

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

   5. Taylor expanded in y around 0 75.2%

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

   6. Taylor expanded in z around 0 81.8%

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

   if -1.6e14 < y < 1.85000000000000012e-60

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 81.4%

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

   if 1.85000000000000012e-60 < y < 2.4999999999999998e44

   1. Initial program 88.1%

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

   2. Taylor expanded in z around 0 75.4%

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

      1. mul-1-neg 75.4%

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

      2. +-commutative 75.4%

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

      3. *-commutative 75.4%

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

      4. +-commutative 75.4%

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

   4. Simplified 75.4%

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

   5. Taylor expanded in y around 0 75.4%

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

   if 2.4999999999999998e44 < y < 1.14999999999999997e162

   1. Initial program 94.4%

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

   2. Taylor expanded in x around 0 78.2%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+14}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-60}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+44}:\\ \;\;\;\;\left(-z\right) - \frac{x \cdot z}{y}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+162}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \]

Alternative 6: 65.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.16 \cdot 10^{+113}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{+49}:\\ \;\;\;\;\frac{-z}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-60}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{\frac{-y}{z}}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+29}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.16e+113)
   (- z)
   (if (<= y -2.6e+49)
     (/ (- z) (/ y x))
     (if (<= y 6.2e-60)
       (+ x y)
       (if (<= y 6.2e-7)
         (/ x (/ (- y) z))
         (if (<= y 6.6e+29) (+ x y) (- z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.16e+113) {
		tmp = -z;
	} else if (y <= -2.6e+49) {
		tmp = -z / (y / x);
	} else if (y <= 6.2e-60) {
		tmp = x + y;
	} else if (y <= 6.2e-7) {
		tmp = x / (-y / z);
	} else if (y <= 6.6e+29) {
		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 <= (-1.16d+113)) then
        tmp = -z
    else if (y <= (-2.6d+49)) then
        tmp = -z / (y / x)
    else if (y <= 6.2d-60) then
        tmp = x + y
    else if (y <= 6.2d-7) then
        tmp = x / (-y / z)
    else if (y <= 6.6d+29) 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 <= -1.16e+113) {
		tmp = -z;
	} else if (y <= -2.6e+49) {
		tmp = -z / (y / x);
	} else if (y <= 6.2e-60) {
		tmp = x + y;
	} else if (y <= 6.2e-7) {
		tmp = x / (-y / z);
	} else if (y <= 6.6e+29) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.16e+113:
		tmp = -z
	elif y <= -2.6e+49:
		tmp = -z / (y / x)
	elif y <= 6.2e-60:
		tmp = x + y
	elif y <= 6.2e-7:
		tmp = x / (-y / z)
	elif y <= 6.6e+29:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.16e+113)
		tmp = Float64(-z);
	elseif (y <= -2.6e+49)
		tmp = Float64(Float64(-z) / Float64(y / x));
	elseif (y <= 6.2e-60)
		tmp = Float64(x + y);
	elseif (y <= 6.2e-7)
		tmp = Float64(x / Float64(Float64(-y) / z));
	elseif (y <= 6.6e+29)
		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 <= -1.16e+113)
		tmp = -z;
	elseif (y <= -2.6e+49)
		tmp = -z / (y / x);
	elseif (y <= 6.2e-60)
		tmp = x + y;
	elseif (y <= 6.2e-7)
		tmp = x / (-y / z);
	elseif (y <= 6.6e+29)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.16e+113], (-z), If[LessEqual[y, -2.6e+49], N[((-z) / N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.2e-60], N[(x + y), $MachinePrecision], If[LessEqual[y, 6.2e-7], N[(x / N[((-y) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.6e+29], N[(x + y), $MachinePrecision], (-z)]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.1600000000000001e113 or 6.59999999999999968e29 < y

   1. Initial program 67.1%

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

   2. Taylor expanded in y around inf 64.7%

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

      1. mul-1-neg 64.7%

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

   4. Simplified 64.7%

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

   if -1.1600000000000001e113 < y < -2.59999999999999989e49

   1. Initial program 81.3%

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

   2. Taylor expanded in z around 0 80.4%

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

      1. mul-1-neg 80.4%

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

      2. +-commutative 80.4%

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

      3. *-commutative 80.4%

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

      4. +-commutative 80.4%

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

   4. Simplified 80.4%

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

   5. Taylor expanded in y around 0 67.9%

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

      1. associate-/l* 68.3%

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

   7. Simplified 68.3%

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

   if -2.59999999999999989e49 < y < 6.19999999999999976e-60 or 6.1999999999999999e-7 < y < 6.59999999999999968e29

   1. Initial program 98.5%

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

   2. Taylor expanded in z around inf 79.4%

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

   if 6.19999999999999976e-60 < y < 6.1999999999999999e-7

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 75.8%

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

   3. Taylor expanded in y around inf 75.7%

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

      1. mul-1-neg 75.7%

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

      2. distribute-frac-neg 75.7%

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

   5. Simplified 75.7%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.16 \cdot 10^{+113}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{+49}:\\ \;\;\;\;\frac{-z}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-60}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{\frac{-y}{z}}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+29}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 7: 75.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+14} \lor \neg \left(y \leq 5.5 \cdot 10^{-32}\right):\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.8e+14) (not (<= y 5.5e-32))) (* z (- -1.0 (/ x y))) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.8e+14) || !(y <= 5.5e-32)) {
		tmp = z * (-1.0 - (x / y));
	} else {
		tmp = 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) :: tmp
    if ((y <= (-1.8d+14)) .or. (.not. (y <= 5.5d-32))) then
        tmp = z * ((-1.0d0) - (x / y))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.8e+14) || !(y <= 5.5e-32)) {
		tmp = z * (-1.0 - (x / y));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.8e+14) or not (y <= 5.5e-32):
		tmp = z * (-1.0 - (x / y))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.8e+14) || !(y <= 5.5e-32))
		tmp = Float64(z * Float64(-1.0 - Float64(x / y)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.8e+14) || ~((y <= 5.5e-32)))
		tmp = z * (-1.0 - (x / y));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.8e+14], N[Not[LessEqual[y, 5.5e-32]], $MachinePrecision]], N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.8e14 or 5.50000000000000024e-32 < y

   1. Initial program 70.6%

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

   2. Taylor expanded in z around 0 66.3%

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

      1. mul-1-neg 66.3%

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

      2. +-commutative 66.3%

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

      3. *-commutative 66.3%

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

      4. +-commutative 66.3%

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

   4. Simplified 66.3%

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

   5. Taylor expanded in y around 0 72.6%

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

   6. Taylor expanded in z around 0 77.8%

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

   if -1.8e14 < y < 5.50000000000000024e-32

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 79.7%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+14} \lor \neg \left(y \leq 5.5 \cdot 10^{-32}\right):\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 8: 67.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.1 \cdot 10^{+113}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{+49}:\\ \;\;\;\;\frac{-z}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+23}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6.1e+113)
   (- z)
   (if (<= y -2.4e+49) (/ (- z) (/ y x)) (if (<= y 1.3e+23) (+ x y) (- z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.1e+113) {
		tmp = -z;
	} else if (y <= -2.4e+49) {
		tmp = -z / (y / x);
	} else if (y <= 1.3e+23) {
		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 <= (-6.1d+113)) then
        tmp = -z
    else if (y <= (-2.4d+49)) then
        tmp = -z / (y / x)
    else if (y <= 1.3d+23) 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 <= -6.1e+113) {
		tmp = -z;
	} else if (y <= -2.4e+49) {
		tmp = -z / (y / x);
	} else if (y <= 1.3e+23) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -6.1e+113:
		tmp = -z
	elif y <= -2.4e+49:
		tmp = -z / (y / x)
	elif y <= 1.3e+23:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6.1e+113)
		tmp = Float64(-z);
	elseif (y <= -2.4e+49)
		tmp = Float64(Float64(-z) / Float64(y / x));
	elseif (y <= 1.3e+23)
		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 <= -6.1e+113)
		tmp = -z;
	elseif (y <= -2.4e+49)
		tmp = -z / (y / x);
	elseif (y <= 1.3e+23)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6.1e+113], (-z), If[LessEqual[y, -2.4e+49], N[((-z) / N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.3e+23], N[(x + y), $MachinePrecision], (-z)]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.09999999999999996e113 or 1.29999999999999996e23 < y

   1. Initial program 67.1%

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

   2. Taylor expanded in y around inf 64.7%

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

      1. mul-1-neg 64.7%

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

   4. Simplified 64.7%

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

   if -6.09999999999999996e113 < y < -2.4e49

   1. Initial program 81.3%

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

   2. Taylor expanded in z around 0 80.4%

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

      1. mul-1-neg 80.4%

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

      2. +-commutative 80.4%

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

      3. *-commutative 80.4%

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

      4. +-commutative 80.4%

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

   4. Simplified 80.4%

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

   5. Taylor expanded in y around 0 67.9%

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

      1. associate-/l* 68.3%

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

   7. Simplified 68.3%

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

   if -2.4e49 < y < 1.29999999999999996e23

   1. Initial program 98.5%

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

   2. Taylor expanded in z around inf 75.7%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.1 \cdot 10^{+113}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{+49}:\\ \;\;\;\;\frac{-z}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+23}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 9: 67.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+84}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+22}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6.5e+84) (- z) (if (<= y 2.8e+22) (+ x y) (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.5e+84) {
		tmp = -z;
	} else if (y <= 2.8e+22) {
		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 <= (-6.5d+84)) then
        tmp = -z
    else if (y <= 2.8d+22) 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 <= -6.5e+84) {
		tmp = -z;
	} else if (y <= 2.8e+22) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -6.5e+84:
		tmp = -z
	elif y <= 2.8e+22:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6.5e+84)
		tmp = Float64(-z);
	elseif (y <= 2.8e+22)
		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 <= -6.5e+84)
		tmp = -z;
	elseif (y <= 2.8e+22)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6.5e+84], (-z), If[LessEqual[y, 2.8e+22], N[(x + y), $MachinePrecision], (-z)]]

Derivation

1. Split input into 2 regimes

2. if y < -6.50000000000000027e84 or 2.8e22 < y

   1. Initial program 66.9%

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

   2. Taylor expanded in y around inf 63.7%

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

      1. mul-1-neg 63.7%

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

   4. Simplified 63.7%

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

   if -6.50000000000000027e84 < y < 2.8e22

   1. Initial program 98.0%

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

   2. Taylor expanded in z around inf 73.1%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+84}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+22}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 10: 58.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+42}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.8e+42) (- z) (if (<= y 2.1e-9) x (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.8e+42) {
		tmp = -z;
	} else if (y <= 2.1e-9) {
		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 <= (-1.8d+42)) then
        tmp = -z
    else if (y <= 2.1d-9) 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 <= -1.8e+42) {
		tmp = -z;
	} else if (y <= 2.1e-9) {
		tmp = x;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.8e+42:
		tmp = -z
	elif y <= 2.1e-9:
		tmp = x
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.8e+42)
		tmp = Float64(-z);
	elseif (y <= 2.1e-9)
		tmp = x;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.8e+42)
		tmp = -z;
	elseif (y <= 2.1e-9)
		tmp = x;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.8e+42], (-z), If[LessEqual[y, 2.1e-9], x, (-z)]]

Derivation

1. Split input into 2 regimes

2. if y < -1.8e42 or 2.10000000000000019e-9 < y

   1. Initial program 69.8%

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

   2. Taylor expanded in y around inf 58.0%

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

      1. mul-1-neg 58.0%

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

   4. Simplified 58.0%

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

   if -1.8e42 < y < 2.10000000000000019e-9

   1. Initial program 99.2%

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

   2. Taylor expanded in y around 0 59.0%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+42}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 11: 35.4% 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 84.5%

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

2. Taylor expanded in y around 0 33.5%

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

3. Final simplification 33.5%

   \[\leadsto x \]

Developer target: 93.9% 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 2023238 
(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))))