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

Percentage Accurate: 87.8% → 99.5%

Time: 7.0s

Alternatives: 9

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: 87.8% 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: 99.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{-254} \lor \neg \left(t\_0 \leq 5 \cdot 10^{-290}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{y}{x + y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -1e-254) (not (<= t_0 5e-290)))
     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 <= -1e-254) || !(t_0 <= 5e-290)) {
		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 <= (-1d-254)) .or. (.not. (t_0 <= 5d-290))) 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 <= -1e-254) || !(t_0 <= 5e-290)) {
		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 <= -1e-254) or not (t_0 <= 5e-290):
		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 <= -1e-254) || !(t_0 <= 5e-290))
		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 <= -1e-254) || ~((t_0 <= 5e-290)))
		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, -1e-254], N[Not[LessEqual[t$95$0, 5e-290]], $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))) < -9.9999999999999991e-255 or 5.0000000000000001e-290 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

   1. Initial program 99.9%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   if -9.9999999999999991e-255 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < 5.0000000000000001e-290

   1. Initial program 17.4%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 94.5%

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

      1. mul-1-neg 94.5%

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

      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%

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

   5. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -1 \cdot 10^{-254} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 5 \cdot 10^{-290}\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{y}{x + y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 69.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{1 - \frac{y}{z}}\\ \mathbf{if}\;y \leq -1.65 \cdot 10^{+210}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1.16 \cdot 10^{-51}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-29}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+194}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ y (- 1.0 (/ y z)))))
   (if (<= y -1.65e+210)
     (- z)
     (if (<= y -1.16e-51)
       t_0
       (if (<= y 7.5e-29) (+ x y) (if (<= y 6.5e+194) t_0 (- z)))))))

C

double code(double x, double y, double z) {
	double t_0 = y / (1.0 - (y / z));
	double tmp;
	if (y <= -1.65e+210) {
		tmp = -z;
	} else if (y <= -1.16e-51) {
		tmp = t_0;
	} else if (y <= 7.5e-29) {
		tmp = x + y;
	} else if (y <= 6.5e+194) {
		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 = y / (1.0d0 - (y / z))
    if (y <= (-1.65d+210)) then
        tmp = -z
    else if (y <= (-1.16d-51)) then
        tmp = t_0
    else if (y <= 7.5d-29) then
        tmp = x + y
    else if (y <= 6.5d+194) 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 = y / (1.0 - (y / z));
	double tmp;
	if (y <= -1.65e+210) {
		tmp = -z;
	} else if (y <= -1.16e-51) {
		tmp = t_0;
	} else if (y <= 7.5e-29) {
		tmp = x + y;
	} else if (y <= 6.5e+194) {
		tmp = t_0;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y / (1.0 - (y / z))
	tmp = 0
	if y <= -1.65e+210:
		tmp = -z
	elif y <= -1.16e-51:
		tmp = t_0
	elif y <= 7.5e-29:
		tmp = x + y
	elif y <= 6.5e+194:
		tmp = t_0
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y / Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (y <= -1.65e+210)
		tmp = Float64(-z);
	elseif (y <= -1.16e-51)
		tmp = t_0;
	elseif (y <= 7.5e-29)
		tmp = Float64(x + y);
	elseif (y <= 6.5e+194)
		tmp = t_0;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y / (1.0 - (y / z));
	tmp = 0.0;
	if (y <= -1.65e+210)
		tmp = -z;
	elseif (y <= -1.16e-51)
		tmp = t_0;
	elseif (y <= 7.5e-29)
		tmp = x + y;
	elseif (y <= 6.5e+194)
		tmp = t_0;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.65e+210], (-z), If[LessEqual[y, -1.16e-51], t$95$0, If[LessEqual[y, 7.5e-29], N[(x + y), $MachinePrecision], If[LessEqual[y, 6.5e+194], t$95$0, (-z)]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.64999999999999997e210 or 6.50000000000000005e194 < y

   1. Initial program 59.6%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 84.7%

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

      1. mul-1-neg 84.7%

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

   5. Simplified 84.7%

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

   if -1.64999999999999997e210 < y < -1.1600000000000001e-51 or 7.50000000000000006e-29 < y < 6.50000000000000005e194

   1. Initial program 88.7%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 71.2%

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

   if -1.1600000000000001e-51 < y < 7.50000000000000006e-29

   1. Initial program 99.9%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 80.7%

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

      1. +-commutative 80.7%

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

   5. Simplified 80.7%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+210}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1.16 \cdot 10^{-51}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-29}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+194}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 66.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.65 \cdot 10^{+129} \lor \neg \left(y \leq 19000000000\right) \land \left(y \leq 1.42 \cdot 10^{+134} \lor \neg \left(y \leq 1.05 \cdot 10^{+158}\right)\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.65e+129)
         (and (not (<= y 19000000000.0))
              (or (<= y 1.42e+134) (not (<= y 1.05e+158)))))
   (- z)
   (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.65e+129) || (!(y <= 19000000000.0) && ((y <= 1.42e+134) || !(y <= 1.05e+158)))) {
		tmp = -z;
	} 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 <= (-2.65d+129)) .or. (.not. (y <= 19000000000.0d0)) .and. (y <= 1.42d+134) .or. (.not. (y <= 1.05d+158))) then
        tmp = -z
    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 <= -2.65e+129) || (!(y <= 19000000000.0) && ((y <= 1.42e+134) || !(y <= 1.05e+158)))) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.65e+129) or (not (y <= 19000000000.0) and ((y <= 1.42e+134) or not (y <= 1.05e+158))):
		tmp = -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.65e+129) || (!(y <= 19000000000.0) && ((y <= 1.42e+134) || !(y <= 1.05e+158))))
		tmp = Float64(-z);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.65e+129) || (~((y <= 19000000000.0)) && ((y <= 1.42e+134) || ~((y <= 1.05e+158)))))
		tmp = -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.65e+129], And[N[Not[LessEqual[y, 19000000000.0]], $MachinePrecision], Or[LessEqual[y, 1.42e+134], N[Not[LessEqual[y, 1.05e+158]], $MachinePrecision]]]], (-z), N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.6499999999999999e129 or 1.9e10 < y < 1.42000000000000002e134 or 1.0499999999999999e158 < y

   1. Initial program 75.0%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 66.5%

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

      1. mul-1-neg 66.5%

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

   5. Simplified 66.5%

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

   if -2.6499999999999999e129 < y < 1.9e10 or 1.42000000000000002e134 < y < 1.0499999999999999e158

   1. Initial program 97.6%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 73.9%

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

      1. +-commutative 73.9%

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

   5. Simplified 73.9%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.65 \cdot 10^{+129} \lor \neg \left(y \leq 19000000000\right) \land \left(y \leq 1.42 \cdot 10^{+134} \lor \neg \left(y \leq 1.05 \cdot 10^{+158}\right)\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+24} \lor \neg \left(z \leq 6.2 \cdot 10^{-53}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-z\right) \cdot \left(x + y\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.15e+24) (not (<= z 6.2e-53)))
   (+ x y)
   (/ (* (- z) (+ x y)) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.15e+24) || !(z <= 6.2e-53)) {
		tmp = x + y;
	} else {
		tmp = (-z * (x + y)) / 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 ((z <= (-1.15d+24)) .or. (.not. (z <= 6.2d-53))) then
        tmp = x + y
    else
        tmp = (-z * (x + y)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.15e+24) || !(z <= 6.2e-53)) {
		tmp = x + y;
	} else {
		tmp = (-z * (x + y)) / y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.15e+24) or not (z <= 6.2e-53):
		tmp = x + y
	else:
		tmp = (-z * (x + y)) / y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.15e+24) || !(z <= 6.2e-53))
		tmp = Float64(x + y);
	else
		tmp = Float64(Float64(Float64(-z) * Float64(x + y)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.15e+24) || ~((z <= 6.2e-53)))
		tmp = x + y;
	else
		tmp = (-z * (x + y)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.15e+24], N[Not[LessEqual[z, 6.2e-53]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(N[((-z) * N[(x + y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.15e24 or 6.20000000000000031e-53 < z

   1. Initial program 99.2%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 78.4%

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

      1. +-commutative 78.4%

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

   5. Simplified 78.4%

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

   if -1.15e24 < z < 6.20000000000000031e-53

   1. Initial program 76.3%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. flip-- 49.8%

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

      2. associate-/r/ 47.6%

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

      3. metadata-eval 47.6%

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

      4. pow2 47.6%

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

   4. Applied egg-rr 47.6%

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

      1. unpow2 47.6%

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

      2. clear-num 47.5%

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

      3. un-div-inv 47.5%

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

   6. Applied egg-rr 47.5%

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

   7. Taylor expanded in z around 0 74.8%

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

      1. mul-1-neg 74.8%

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

      2. +-commutative 74.8%

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

   9. Simplified 74.8%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+24} \lor \neg \left(z \leq 6.2 \cdot 10^{-53}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-z\right) \cdot \left(x + y\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+23} \lor \neg \left(z \leq 6.2 \cdot 10^{-53}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{y}{x + y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.8e+23) (not (<= z 6.2e-53)))
   (+ x y)
   (/ (- z) (/ y (+ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.8e+23) || !(z <= 6.2e-53)) {
		tmp = x + y;
	} 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) :: tmp
    if ((z <= (-2.8d+23)) .or. (.not. (z <= 6.2d-53))) then
        tmp = x + y
    else
        tmp = -z / (y / (x + y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.8e+23) || !(z <= 6.2e-53)) {
		tmp = x + y;
	} else {
		tmp = -z / (y / (x + y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.8e+23) or not (z <= 6.2e-53):
		tmp = x + y
	else:
		tmp = -z / (y / (x + y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.8e+23) || !(z <= 6.2e-53))
		tmp = Float64(x + y);
	else
		tmp = Float64(Float64(-z) / Float64(y / Float64(x + y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.8e+23) || ~((z <= 6.2e-53)))
		tmp = x + y;
	else
		tmp = -z / (y / (x + y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.8e+23], N[Not[LessEqual[z, 6.2e-53]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[((-z) / N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.8e23 or 6.20000000000000031e-53 < z

   1. Initial program 99.2%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 78.4%

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

      1. +-commutative 78.4%

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

   5. Simplified 78.4%

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

   if -2.8e23 < z < 6.20000000000000031e-53

   1. Initial program 76.3%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 74.8%

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

      1. mul-1-neg 74.8%

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

      2. associate-/l* 76.9%

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

      3. distribute-neg-frac 76.9%

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

      4. +-commutative 76.9%

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

   5. Simplified 76.9%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+23} \lor \neg \left(z \leq 6.2 \cdot 10^{-53}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{y}{x + y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+24}:\\ \;\;\;\;\left(x + y\right) \cdot \left(1 + \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-53}:\\ \;\;\;\;\frac{-z}{\frac{y}{x + y}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5.2e+24)
   (* (+ x y) (+ 1.0 (/ y z)))
   (if (<= z 9.2e-53) (/ (- z) (/ y (+ x y))) (+ x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.2e+24) {
		tmp = (x + y) * (1.0 + (y / z));
	} else if (z <= 9.2e-53) {
		tmp = -z / (y / (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 (z <= (-5.2d+24)) then
        tmp = (x + y) * (1.0d0 + (y / z))
    else if (z <= 9.2d-53) then
        tmp = -z / (y / (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 (z <= -5.2e+24) {
		tmp = (x + y) * (1.0 + (y / z));
	} else if (z <= 9.2e-53) {
		tmp = -z / (y / (x + y));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5.2e+24:
		tmp = (x + y) * (1.0 + (y / z))
	elif z <= 9.2e-53:
		tmp = -z / (y / (x + y))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5.2e+24)
		tmp = Float64(Float64(x + y) * Float64(1.0 + Float64(y / z)));
	elseif (z <= 9.2e-53)
		tmp = Float64(Float64(-z) / Float64(y / Float64(x + y)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -5.2e+24)
		tmp = (x + y) * (1.0 + (y / z));
	elseif (z <= 9.2e-53)
		tmp = -z / (y / (x + y));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5.2e+24], N[(N[(x + y), $MachinePrecision] * N[(1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.2e-53], N[((-z) / N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.1999999999999997e24

   1. Initial program 99.9%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 70.9%

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

      1. associate-+r+ 70.9%

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

      2. *-lft-identity 70.9%

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

      3. associate-/l* 84.5%

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

      4. associate-/r/ 84.5%

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

      5. distribute-rgt-in 84.5%

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

      6. +-commutative 84.5%

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

   5. Simplified 84.5%

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

   if -5.1999999999999997e24 < z < 9.2000000000000005e-53

   1. Initial program 76.3%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 74.8%

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

      1. mul-1-neg 74.8%

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

      2. associate-/l* 76.9%

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

      3. distribute-neg-frac 76.9%

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

      4. +-commutative 76.9%

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

   5. Simplified 76.9%

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

   if 9.2000000000000005e-53 < z

   1. Initial program 98.9%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 75.2%

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

      1. +-commutative 75.2%

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

   5. Simplified 75.2%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+24}:\\ \;\;\;\;\left(x + y\right) \cdot \left(1 + \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-53}:\\ \;\;\;\;\frac{-z}{\frac{y}{x + y}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 58.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-55} \lor \neg \left(y \leq 1.5 \cdot 10^{-24}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6.5e-55) (not (<= y 1.5e-24))) (- z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.5e-55) || !(y <= 1.5e-24)) {
		tmp = -z;
	} 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 <= (-6.5d-55)) .or. (.not. (y <= 1.5d-24))) then
        tmp = -z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.5e-55) || !(y <= 1.5e-24)) {
		tmp = -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6.5e-55) or not (y <= 1.5e-24):
		tmp = -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6.5e-55) || !(y <= 1.5e-24))
		tmp = Float64(-z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -6.5e-55) || ~((y <= 1.5e-24)))
		tmp = -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6.5e-55], N[Not[LessEqual[y, 1.5e-24]], $MachinePrecision]], (-z), x]

Derivation

1. Split input into 2 regimes

2. if y < -6.50000000000000006e-55 or 1.49999999999999998e-24 < y

   1. Initial program 80.1%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 56.4%

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

      1. mul-1-neg 56.4%

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

   5. Simplified 56.4%

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

   if -6.50000000000000006e-55 < y < 1.49999999999999998e-24

   1. Initial program 99.9%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 59.8%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-55} \lor \neg \left(y \leq 1.5 \cdot 10^{-24}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 38.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-61}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-74}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5.2e-61) y (if (<= y 1.55e-74) x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.2e-61) {
		tmp = y;
	} else if (y <= 1.55e-74) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-5.2d-61)) then
        tmp = y
    else if (y <= 1.55d-74) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.2e-61) {
		tmp = y;
	} else if (y <= 1.55e-74) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5.2e-61:
		tmp = y
	elif y <= 1.55e-74:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5.2e-61)
		tmp = y;
	elseif (y <= 1.55e-74)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -5.2e-61)
		tmp = y;
	elseif (y <= 1.55e-74)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5.2e-61], y, If[LessEqual[y, 1.55e-74], x, y]]

Derivation

1. Split input into 2 regimes

2. if y < -5.20000000000000021e-61 or 1.5500000000000001e-74 < y

   1. Initial program 81.7%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 65.5%

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

   4. Taylor expanded in y around 0 29.1%

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

   if -5.20000000000000021e-61 < y < 1.5500000000000001e-74

   1. Initial program 99.9%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 62.6%

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

4. Final simplification 42.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-61}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-74}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 35.0% 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 88.9%

   \[\frac{x + y}{1 - \frac{y}{z}} \]
2. Add Preprocessing

3. Taylor expanded in y around 0 30.7%

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

4. Final simplification 30.7%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 93.7% accurate, 0.5× 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 2024031 
(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))))