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

Percentage Accurate: 87.6% → 98.9%

Time: 8.1s

Alternatives: 10

Speedup: 0.5×

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: 87.6% 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: 98.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{-243}:\\ \;\;\;\;\frac{z}{z - y} \cdot \left(x + y\right)\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{-190}:\\ \;\;\;\;z \cdot \frac{x + y}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (<= t_0 -2e-243)
     (* (/ z (- z y)) (+ x y))
     (if (<= t_0 2e-190) (* z (/ (+ x y) (- z y))) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if (t_0 <= -2e-243) {
		tmp = (z / (z - y)) * (x + y);
	} else if (t_0 <= 2e-190) {
		tmp = z * ((x + y) / (z - y));
	} 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 = (x + y) / (1.0d0 - (y / z))
    if (t_0 <= (-2d-243)) then
        tmp = (z / (z - y)) * (x + y)
    else if (t_0 <= 2d-190) then
        tmp = z * ((x + y) / (z - y))
    else
        tmp = t_0
    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 <= -2e-243) {
		tmp = (z / (z - y)) * (x + y);
	} else if (t_0 <= 2e-190) {
		tmp = z * ((x + y) / (z - y));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if t_0 <= -2e-243:
		tmp = (z / (z - y)) * (x + y)
	elif t_0 <= 2e-190:
		tmp = z * ((x + y) / (z - y))
	else:
		tmp = t_0
	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 <= -2e-243)
		tmp = Float64(Float64(z / Float64(z - y)) * Float64(x + y));
	elseif (t_0 <= 2e-190)
		tmp = Float64(z * Float64(Float64(x + y) / Float64(z - y)));
	else
		tmp = t_0;
	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 <= -2e-243)
		tmp = (z / (z - y)) * (x + y);
	elseif (t_0 <= 2e-190)
		tmp = z * ((x + y) / (z - y));
	else
		tmp = t_0;
	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[LessEqual[t$95$0, -2e-243], N[(N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision] * N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 2e-190], N[(z * N[(N[(x + y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -1.99999999999999999e-243

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 99.9%

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

   4. Taylor expanded in x around 0 76.6%

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

      1. associate-*r/ 87.3%

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

      2. associate-/l* 99.9%

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

      3. distribute-rgt-in 99.9%

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

      4. +-commutative 99.9%

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

   6. Simplified 99.9%

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

   if -1.99999999999999999e-243 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < 2e-190

   1. Initial program 33.2%

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

   3. Taylor expanded in z around 0 33.2%

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

      1. associate-/r/ 99.9%

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

   5. Applied egg-rr 99.9%

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

   if 2e-190 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z)))

   1. Initial program 99.9%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing
3. Recombined 3 regimes into one program.

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -2 \cdot 10^{-243}:\\ \;\;\;\;\frac{z}{z - y} \cdot \left(x + y\right)\\ \mathbf{elif}\;\frac{x + y}{1 - \frac{y}{z}} \leq 2 \cdot 10^{-190}:\\ \;\;\;\;z \cdot \frac{x + y}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+63} \lor \neg \left(y \leq 4.8 \cdot 10^{-71}\right):\\ \;\;\;\;z \cdot \frac{x + y}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{z - y} \cdot \left(x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1e+63) (not (<= y 4.8e-71)))
   (* z (/ (+ x y) (- z y)))
   (* (/ z (- z y)) (+ x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1e+63) || !(y <= 4.8e-71)) {
		tmp = z * ((x + y) / (z - y));
	} else {
		tmp = (z / (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 ((y <= (-1d+63)) .or. (.not. (y <= 4.8d-71))) then
        tmp = z * ((x + y) / (z - y))
    else
        tmp = (z / (z - y)) * (x + y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1e+63) || !(y <= 4.8e-71)) {
		tmp = z * ((x + y) / (z - y));
	} else {
		tmp = (z / (z - y)) * (x + y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1e+63) or not (y <= 4.8e-71):
		tmp = z * ((x + y) / (z - y))
	else:
		tmp = (z / (z - y)) * (x + y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1e+63) || !(y <= 4.8e-71))
		tmp = Float64(z * Float64(Float64(x + y) / Float64(z - y)));
	else
		tmp = Float64(Float64(z / Float64(z - y)) * Float64(x + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1e+63) || ~((y <= 4.8e-71)))
		tmp = z * ((x + y) / (z - y));
	else
		tmp = (z / (z - y)) * (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1e+63], N[Not[LessEqual[y, 4.8e-71]], $MachinePrecision]], N[(z * N[(N[(x + y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision] * N[(x + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.00000000000000006e63 or 4.8e-71 < y

   1. Initial program 76.6%

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

   3. Taylor expanded in z around 0 76.6%

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

      1. associate-/r/ 99.8%

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

   5. Applied egg-rr 99.8%

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

   if -1.00000000000000006e63 < y < 4.8e-71

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 99.9%

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

   4. Taylor expanded in x around 0 84.1%

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

      1. associate-*r/ 96.2%

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

      2. associate-/l* 100.0%

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

      3. distribute-rgt-in 99.9%

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

      4. +-commutative 99.9%

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

   6. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+63} \lor \neg \left(y \leq 4.8 \cdot 10^{-71}\right):\\ \;\;\;\;z \cdot \frac{x + y}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{z - y} \cdot \left(x + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 92.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+66} \lor \neg \left(y \leq 2.9 \cdot 10^{+182}\right):\\ \;\;\;\;z \cdot \frac{y}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{z - y} \cdot \left(x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5e+66) (not (<= y 2.9e+182)))
   (* z (/ y (- z y)))
   (* (/ z (- z y)) (+ x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5e+66) || !(y <= 2.9e+182)) {
		tmp = z * (y / (z - y));
	} else {
		tmp = (z / (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 ((y <= (-5d+66)) .or. (.not. (y <= 2.9d+182))) then
        tmp = z * (y / (z - y))
    else
        tmp = (z / (z - y)) * (x + y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5e+66) || !(y <= 2.9e+182)) {
		tmp = z * (y / (z - y));
	} else {
		tmp = (z / (z - y)) * (x + y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5e+66) or not (y <= 2.9e+182):
		tmp = z * (y / (z - y))
	else:
		tmp = (z / (z - y)) * (x + y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5e+66) || !(y <= 2.9e+182))
		tmp = Float64(z * Float64(y / Float64(z - y)));
	else
		tmp = Float64(Float64(z / Float64(z - y)) * Float64(x + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -5e+66) || ~((y <= 2.9e+182)))
		tmp = z * (y / (z - y));
	else
		tmp = (z / (z - y)) * (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5e+66], N[Not[LessEqual[y, 2.9e+182]], $MachinePrecision]], N[(z * N[(y / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision] * N[(x + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.99999999999999991e66 or 2.8999999999999998e182 < y

   1. Initial program 66.1%

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

   3. Taylor expanded in z around 0 66.1%

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

      1. associate-/r/ 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in x around 0 91.4%

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

   if -4.99999999999999991e66 < y < 2.8999999999999998e182

   1. Initial program 97.3%

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

   3. Taylor expanded in z around 0 97.3%

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

   4. Taylor expanded in x around 0 82.6%

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

      1. associate-*r/ 93.9%

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

      2. associate-/l* 98.1%

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

      3. distribute-rgt-in 98.1%

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

      4. +-commutative 98.1%

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

   6. Simplified 98.1%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+66} \lor \neg \left(y \leq 2.9 \cdot 10^{+182}\right):\\ \;\;\;\;z \cdot \frac{y}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{z - y} \cdot \left(x + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 68.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+85}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-71}:\\ \;\;\;\;y \cdot \frac{z}{z - y}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+91}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.2e+85)
   (- z)
   (if (<= y -3e-71) (* y (/ z (- z y))) (if (<= y 3.6e+91) (+ x y) (- z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.2e+85) {
		tmp = -z;
	} else if (y <= -3e-71) {
		tmp = y * (z / (z - y));
	} else if (y <= 3.6e+91) {
		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 <= (-3.2d+85)) then
        tmp = -z
    else if (y <= (-3d-71)) then
        tmp = y * (z / (z - y))
    else if (y <= 3.6d+91) 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 <= -3.2e+85) {
		tmp = -z;
	} else if (y <= -3e-71) {
		tmp = y * (z / (z - y));
	} else if (y <= 3.6e+91) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.2e+85:
		tmp = -z
	elif y <= -3e-71:
		tmp = y * (z / (z - y))
	elif y <= 3.6e+91:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.2e+85)
		tmp = Float64(-z);
	elseif (y <= -3e-71)
		tmp = Float64(y * Float64(z / Float64(z - y)));
	elseif (y <= 3.6e+91)
		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 <= -3.2e+85)
		tmp = -z;
	elseif (y <= -3e-71)
		tmp = y * (z / (z - y));
	elseif (y <= 3.6e+91)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.2e+85], (-z), If[LessEqual[y, -3e-71], N[(y * N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6e+91], N[(x + y), $MachinePrecision], (-z)]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.20000000000000018e85 or 3.6e91 < y

   1. Initial program 72.1%

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

   3. Taylor expanded in y around inf 69.7%

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

      1. neg-mul-1 69.7%

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

   5. Simplified 69.7%

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

   if -3.20000000000000018e85 < y < -3.0000000000000001e-71

   1. Initial program 93.3%

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

   3. Taylor expanded in z around 0 93.3%

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

   4. Taylor expanded in x around 0 50.8%

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

      1. associate-/l* 53.4%

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

   6. Simplified 53.4%

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

   if -3.0000000000000001e-71 < y < 3.6e91

   1. Initial program 98.4%

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

   3. Taylor expanded in z around inf 73.2%

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

      1. +-commutative 73.2%

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

   5. Simplified 73.2%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+85}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-71}:\\ \;\;\;\;y \cdot \frac{z}{z - y}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+91}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 69.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+109} \lor \neg \left(x \leq 2.3 \cdot 10^{-18}\right):\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.1e+109) (not (<= x 2.3e-18)))
   (/ x (- 1.0 (/ y z)))
   (* z (/ y (- z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.1e+109) || !(x <= 2.3e-18)) {
		tmp = x / (1.0 - (y / z));
	} else {
		tmp = z * (y / (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-2.1d+109)) .or. (.not. (x <= 2.3d-18))) then
        tmp = x / (1.0d0 - (y / z))
    else
        tmp = z * (y / (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.1e+109) || !(x <= 2.3e-18)) {
		tmp = x / (1.0 - (y / z));
	} else {
		tmp = z * (y / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.1e+109) or not (x <= 2.3e-18):
		tmp = x / (1.0 - (y / z))
	else:
		tmp = z * (y / (z - y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.1e+109) || !(x <= 2.3e-18))
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(z * Float64(y / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.1e+109) || ~((x <= 2.3e-18)))
		tmp = x / (1.0 - (y / z));
	else
		tmp = z * (y / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.1e+109], N[Not[LessEqual[x, 2.3e-18]], $MachinePrecision]], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(y / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.1000000000000001e109 or 2.3000000000000001e-18 < x

   1. Initial program 94.7%

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

   3. Taylor expanded in x around inf 80.8%

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

   if -2.1000000000000001e109 < x < 2.3000000000000001e-18

   1. Initial program 82.7%

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

   3. Taylor expanded in z around 0 82.7%

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

      1. associate-/r/ 95.5%

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

   5. Applied egg-rr 95.5%

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

   6. Taylor expanded in x around 0 76.1%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+109} \lor \neg \left(x \leq 2.3 \cdot 10^{-18}\right):\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-71} \lor \neg \left(y \leq 8.8 \cdot 10^{+88}\right):\\ \;\;\;\;z \cdot \frac{y}{z - y}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.8e-71) (not (<= y 8.8e+88))) (* z (/ y (- z y))) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.8e-71) || !(y <= 8.8e+88)) {
		tmp = z * (y / (z - 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 <= (-3.8d-71)) .or. (.not. (y <= 8.8d+88))) then
        tmp = z * (y / (z - 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 <= -3.8e-71) || !(y <= 8.8e+88)) {
		tmp = z * (y / (z - y));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.8e-71) or not (y <= 8.8e+88):
		tmp = z * (y / (z - y))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.8e-71) || !(y <= 8.8e+88))
		tmp = Float64(z * Float64(y / Float64(z - y)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.8e-71) || ~((y <= 8.8e+88)))
		tmp = z * (y / (z - y));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.8e-71], N[Not[LessEqual[y, 8.8e+88]], $MachinePrecision]], N[(z * N[(y / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.79999999999999992e-71 or 8.80000000000000035e88 < y

   1. Initial program 78.5%

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

   3. Taylor expanded in z around 0 78.5%

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

      1. associate-/r/ 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in x around 0 75.3%

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

   if -3.79999999999999992e-71 < y < 8.80000000000000035e88

   1. Initial program 98.4%

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

   3. Taylor expanded in z around inf 73.2%

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

      1. +-commutative 73.2%

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

   5. Simplified 73.2%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-71} \lor \neg \left(y \leq 8.8 \cdot 10^{+88}\right):\\ \;\;\;\;z \cdot \frac{y}{z - y}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+49} \lor \neg \left(y \leq 2.35 \cdot 10^{+89}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.65e+49) (not (<= y 2.35e+89))) (- z) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.65e+49) || !(y <= 2.35e+89)) {
		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 <= (-1.65d+49)) .or. (.not. (y <= 2.35d+89))) 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 <= -1.65e+49) || !(y <= 2.35e+89)) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.65e+49) or not (y <= 2.35e+89):
		tmp = -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.65e+49) || !(y <= 2.35e+89))
		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 <= -1.65e+49) || ~((y <= 2.35e+89)))
		tmp = -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.65e+49], N[Not[LessEqual[y, 2.35e+89]], $MachinePrecision]], (-z), N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.6499999999999999e49 or 2.35000000000000011e89 < y

   1. Initial program 72.9%

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

   3. Taylor expanded in y around inf 66.2%

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

      1. neg-mul-1 66.2%

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

   5. Simplified 66.2%

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

   if -1.6499999999999999e49 < y < 2.35000000000000011e89

   1. Initial program 98.7%

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

   3. Taylor expanded in z around inf 67.2%

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

      1. +-commutative 67.2%

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

   5. Simplified 67.2%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+49} \lor \neg \left(y \leq 2.35 \cdot 10^{+89}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 58.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.46 \cdot 10^{-40} \lor \neg \left(y \leq 9.2 \cdot 10^{+88}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.46e-40) (not (<= y 9.2e+88))) (- z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.46e-40) || !(y <= 9.2e+88)) {
		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 <= (-1.46d-40)) .or. (.not. (y <= 9.2d+88))) 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 <= -1.46e-40) || !(y <= 9.2e+88)) {
		tmp = -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.46e-40) or not (y <= 9.2e+88):
		tmp = -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.46e-40) || !(y <= 9.2e+88))
		tmp = Float64(-z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.46e-40) || ~((y <= 9.2e+88)))
		tmp = -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.46e-40], N[Not[LessEqual[y, 9.2e+88]], $MachinePrecision]], (-z), x]

Derivation

1. Split input into 2 regimes

2. if y < -1.46000000000000005e-40 or 9.2000000000000007e88 < y

   1. Initial program 77.8%

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

   3. Taylor expanded in y around inf 59.8%

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

      1. neg-mul-1 59.8%

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

   5. Simplified 59.8%

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

   if -1.46000000000000005e-40 < y < 9.2000000000000007e88

   1. Initial program 98.4%

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

   3. Taylor expanded in y around 0 60.1%

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

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.46 \cdot 10^{-40} \lor \neg \left(y \leq 9.2 \cdot 10^{+88}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 40.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{-121}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-201}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.35e-121) x (if (<= x 2.4e-201) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.35e-121) {
		tmp = x;
	} else if (x <= 2.4e-201) {
		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 (x <= (-1.35d-121)) then
        tmp = x
    else if (x <= 2.4d-201) 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 (x <= -1.35e-121) {
		tmp = x;
	} else if (x <= 2.4e-201) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.35e-121:
		tmp = x
	elif x <= 2.4e-201:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.35e-121)
		tmp = x;
	elseif (x <= 2.4e-201)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.35e-121)
		tmp = x;
	elseif (x <= 2.4e-201)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.35e-121], x, If[LessEqual[x, 2.4e-201], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3500000000000001e-121 or 2.40000000000000009e-201 < x

   1. Initial program 89.2%

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

   3. Taylor expanded in y around 0 40.4%

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

   if -1.3500000000000001e-121 < x < 2.40000000000000009e-201

   1. Initial program 83.9%

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

   3. Taylor expanded in x around 0 73.7%

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

   4. Taylor expanded in y around 0 36.0%

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

Alternative 10: 34.7% 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 87.9%

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

3. Taylor expanded in y around 0 33.9%

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

Developer Target 1: 93.3% 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 2024116 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< y -3742931076268985600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (* (/ (+ y x) (- y)) z) (if (< y 3553466245608673400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (+ x y) (- 1 (/ y z))) (* (/ (+ y x) (- y)) z))))

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