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

Percentage Accurate: 88.3% → 99.9%

Time: 7.3s

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: 88.3% 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: 99.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{-299}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_0 \leq 0:\\ \;\;\;\;z \cdot \frac{\left(-y\right) - x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{\frac{z - y}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (<= t_0 -2e-299)
     t_0
     (if (<= t_0 0.0) (* z (/ (- (- y) x) y)) (/ (+ x y) (/ (- 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 <= -2e-299) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = z * ((-y - x) / y);
	} else {
		tmp = (x + y) / ((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 <= (-2d-299)) then
        tmp = t_0
    else if (t_0 <= 0.0d0) then
        tmp = z * ((-y - x) / y)
    else
        tmp = (x + y) / ((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 <= -2e-299) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = z * ((-y - x) / y);
	} else {
		tmp = (x + y) / ((z - y) / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if t_0 <= -2e-299:
		tmp = t_0
	elif t_0 <= 0.0:
		tmp = z * ((-y - x) / y)
	else:
		tmp = (x + y) / ((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 <= -2e-299)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = Float64(z * Float64(Float64(Float64(-y) - x) / y));
	else
		tmp = Float64(Float64(x + y) / Float64(Float64(z - y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + y) / (1.0 - (y / z));
	tmp = 0.0;
	if (t_0 <= -2e-299)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = z * ((-y - x) / y);
	else
		tmp = (x + y) / ((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[LessEqual[t$95$0, -2e-299], t$95$0, If[LessEqual[t$95$0, 0.0], N[(z * N[(N[((-y) - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] / N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -1.99999999999999998e-299

   1. Initial program 99.8%

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

   if -1.99999999999999998e-299 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -0.0

   1. Initial program 5.8%

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

   3. Taylor expanded in z around 0 99.9%

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

      1. mul-1-neg 99.9%

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

      2. associate-/l* 99.9%

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

      3. distribute-rgt-neg-in 99.9%

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

      4. distribute-neg-frac2 99.9%

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

      5. +-commutative 99.9%

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

   5. Simplified 99.9%

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

   if -0.0 < (/.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. Taylor expanded in z around 0 99.9%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -2 \cdot 10^{-299}:\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;\frac{x + y}{1 - \frac{y}{z}} \leq 0:\\ \;\;\;\;z \cdot \frac{\left(-y\right) - x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{\frac{z - y}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{-299} \lor \neg \left(t\_0 \leq 0\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{\left(-y\right) - x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -2e-299) (not (<= t_0 0.0))) t_0 (* z (/ (- (- y) x) y)))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -2e-299) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = z * ((-y - x) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x + y) / (1.0d0 - (y / z))
    if ((t_0 <= (-2d-299)) .or. (.not. (t_0 <= 0.0d0))) then
        tmp = t_0
    else
        tmp = z * ((-y - x) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -2e-299) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = z * ((-y - x) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -2e-299) or not (t_0 <= 0.0):
		tmp = t_0
	else:
		tmp = z * ((-y - x) / y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if ((t_0 <= -2e-299) || !(t_0 <= 0.0))
		tmp = t_0;
	else
		tmp = Float64(z * Float64(Float64(Float64(-y) - 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 <= -2e-299) || ~((t_0 <= 0.0)))
		tmp = t_0;
	else
		tmp = z * ((-y - x) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -2e-299], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], t$95$0, N[(z * N[(N[((-y) - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -1.99999999999999998e-299 or -0.0 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z)))

   1. Initial program 99.8%

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

   if -1.99999999999999998e-299 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -0.0

   1. Initial program 5.8%

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

   3. Taylor expanded in z around 0 99.9%

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

      1. mul-1-neg 99.9%

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

      2. associate-/l* 99.9%

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

      3. distribute-rgt-neg-in 99.9%

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

      4. distribute-neg-frac2 99.9%

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

      5. +-commutative 99.9%

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

   5. Simplified 99.9%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -2 \cdot 10^{-299} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{\left(-y\right) - x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 68.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \frac{z}{z - y}\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{+33}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-7}:\\ \;\;\;\;x \cdot \frac{z}{-y}\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-63}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-5}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+170}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (/ z (- z y)))))
   (if (<= y -4.4e+33)
     (- z)
     (if (<= y -2.7e-7)
       (* x (/ z (- y)))
       (if (<= y -1.35e-63)
         t_0
         (if (<= y 1.15e-5) (+ x y) (if (<= y 2.7e+170) t_0 (- z))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (z / (z - y));
	double tmp;
	if (y <= -4.4e+33) {
		tmp = -z;
	} else if (y <= -2.7e-7) {
		tmp = x * (z / -y);
	} else if (y <= -1.35e-63) {
		tmp = t_0;
	} else if (y <= 1.15e-5) {
		tmp = x + y;
	} else if (y <= 2.7e+170) {
		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 * (z / (z - y))
    if (y <= (-4.4d+33)) then
        tmp = -z
    else if (y <= (-2.7d-7)) then
        tmp = x * (z / -y)
    else if (y <= (-1.35d-63)) then
        tmp = t_0
    else if (y <= 1.15d-5) then
        tmp = x + y
    else if (y <= 2.7d+170) 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 * (z / (z - y));
	double tmp;
	if (y <= -4.4e+33) {
		tmp = -z;
	} else if (y <= -2.7e-7) {
		tmp = x * (z / -y);
	} else if (y <= -1.35e-63) {
		tmp = t_0;
	} else if (y <= 1.15e-5) {
		tmp = x + y;
	} else if (y <= 2.7e+170) {
		tmp = t_0;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (z / (z - y))
	tmp = 0
	if y <= -4.4e+33:
		tmp = -z
	elif y <= -2.7e-7:
		tmp = x * (z / -y)
	elif y <= -1.35e-63:
		tmp = t_0
	elif y <= 1.15e-5:
		tmp = x + y
	elif y <= 2.7e+170:
		tmp = t_0
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(z / Float64(z - y)))
	tmp = 0.0
	if (y <= -4.4e+33)
		tmp = Float64(-z);
	elseif (y <= -2.7e-7)
		tmp = Float64(x * Float64(z / Float64(-y)));
	elseif (y <= -1.35e-63)
		tmp = t_0;
	elseif (y <= 1.15e-5)
		tmp = Float64(x + y);
	elseif (y <= 2.7e+170)
		tmp = t_0;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (z / (z - y));
	tmp = 0.0;
	if (y <= -4.4e+33)
		tmp = -z;
	elseif (y <= -2.7e-7)
		tmp = x * (z / -y);
	elseif (y <= -1.35e-63)
		tmp = t_0;
	elseif (y <= 1.15e-5)
		tmp = x + y;
	elseif (y <= 2.7e+170)
		tmp = t_0;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.4e+33], (-z), If[LessEqual[y, -2.7e-7], N[(x * N[(z / (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.35e-63], t$95$0, If[LessEqual[y, 1.15e-5], N[(x + y), $MachinePrecision], If[LessEqual[y, 2.7e+170], t$95$0, (-z)]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.39999999999999988e33 or 2.7000000000000002e170 < y

   1. Initial program 70.0%

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

   3. Taylor expanded in y around inf 70.5%

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

      1. neg-mul-1 70.5%

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

   5. Simplified 70.5%

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

   if -4.39999999999999988e33 < y < -2.70000000000000009e-7

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 73.9%

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

      1. associate-*r/ 73.9%

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

      2. *-commutative 73.9%

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

      3. associate-*r* 73.9%

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

      4. neg-mul-1 73.9%

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

      5. distribute-neg-in 73.9%

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

      6. unsub-neg 73.9%

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

   5. Simplified 73.9%

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

   6. Taylor expanded in x around inf 57.1%

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

      1. mul-1-neg 57.1%

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

      2. associate-/l* 57.4%

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

   8. Simplified 57.4%

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

   if -2.70000000000000009e-7 < y < -1.3500000000000001e-63 or 1.15e-5 < y < 2.7000000000000002e170

   1. Initial program 89.1%

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

   3. Taylor expanded in z around 0 89.1%

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

   4. Taylor expanded in x around 0 52.4%

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

      1. associate-/l* 56.3%

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

   6. Simplified 56.3%

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

   if -1.3500000000000001e-63 < y < 1.15e-5

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 78.8%

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

      1. +-commutative 78.8%

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

   5. Simplified 78.8%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+33}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-7}:\\ \;\;\;\;x \cdot \frac{z}{-y}\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-63}:\\ \;\;\;\;y \cdot \frac{z}{z - y}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-5}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+170}:\\ \;\;\;\;y \cdot \frac{z}{z - y}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \frac{\left(-y\right) - x}{y}\\ \mathbf{if}\;y \leq -5.1 \cdot 10^{-8}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-90}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-113}:\\ \;\;\;\;x \cdot \frac{z}{z - y}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-15}:\\ \;\;\;\;\left(x + y\right) \cdot \left(1 + \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (/ (- (- y) x) y))))
   (if (<= y -5.1e-8)
     t_0
     (if (<= y -5e-90)
       (/ y (- 1.0 (/ y z)))
       (if (<= y -4.1e-113)
         (* x (/ z (- z y)))
         (if (<= y 5.8e-15) (* (+ x y) (+ 1.0 (/ y z))) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * ((-y - x) / y);
	double tmp;
	if (y <= -5.1e-8) {
		tmp = t_0;
	} else if (y <= -5e-90) {
		tmp = y / (1.0 - (y / z));
	} else if (y <= -4.1e-113) {
		tmp = x * (z / (z - y));
	} else if (y <= 5.8e-15) {
		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 = z * ((-y - x) / y)
    if (y <= (-5.1d-8)) then
        tmp = t_0
    else if (y <= (-5d-90)) then
        tmp = y / (1.0d0 - (y / z))
    else if (y <= (-4.1d-113)) then
        tmp = x * (z / (z - y))
    else if (y <= 5.8d-15) 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 = z * ((-y - x) / y);
	double tmp;
	if (y <= -5.1e-8) {
		tmp = t_0;
	} else if (y <= -5e-90) {
		tmp = y / (1.0 - (y / z));
	} else if (y <= -4.1e-113) {
		tmp = x * (z / (z - y));
	} else if (y <= 5.8e-15) {
		tmp = (x + y) * (1.0 + (y / z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * ((-y - x) / y)
	tmp = 0
	if y <= -5.1e-8:
		tmp = t_0
	elif y <= -5e-90:
		tmp = y / (1.0 - (y / z))
	elif y <= -4.1e-113:
		tmp = x * (z / (z - y))
	elif y <= 5.8e-15:
		tmp = (x + y) * (1.0 + (y / z))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(Float64(Float64(-y) - x) / y))
	tmp = 0.0
	if (y <= -5.1e-8)
		tmp = t_0;
	elseif (y <= -5e-90)
		tmp = Float64(y / Float64(1.0 - Float64(y / z)));
	elseif (y <= -4.1e-113)
		tmp = Float64(x * Float64(z / Float64(z - y)));
	elseif (y <= 5.8e-15)
		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 = z * ((-y - x) / y);
	tmp = 0.0;
	if (y <= -5.1e-8)
		tmp = t_0;
	elseif (y <= -5e-90)
		tmp = y / (1.0 - (y / z));
	elseif (y <= -4.1e-113)
		tmp = x * (z / (z - y));
	elseif (y <= 5.8e-15)
		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[(z * N[(N[((-y) - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.1e-8], t$95$0, If[LessEqual[y, -5e-90], N[(y / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.1e-113], N[(x * N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.8e-15], N[(N[(x + y), $MachinePrecision] * N[(1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.10000000000000001e-8 or 5.80000000000000037e-15 < y

   1. Initial program 77.6%

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

   3. Taylor expanded in z around 0 70.5%

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

      1. mul-1-neg 70.5%

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

      2. associate-/l* 78.7%

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

      3. distribute-rgt-neg-in 78.7%

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

      4. distribute-neg-frac2 78.7%

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

      5. +-commutative 78.7%

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

   5. Simplified 78.7%

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

   if -5.10000000000000001e-8 < y < -5.00000000000000019e-90

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 89.0%

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

   if -5.00000000000000019e-90 < y < -4.1e-113

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 84.3%

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

      1. clear-num 84.0%

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

      2. associate-/r/ 84.3%

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

      3. *-inverses 84.3%

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

      4. div-sub 84.3%

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

      5. clear-num 84.5%

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

   5. Applied egg-rr 84.5%

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

   if -4.1e-113 < y < 5.80000000000000037e-15

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 81.1%

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

      1. associate-+r+ 81.1%

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

      2. *-rgt-identity 81.1%

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

      3. *-commutative 81.1%

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

      4. associate-/l* 81.3%

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

      5. distribute-lft-in 81.3%

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

      6. +-commutative 81.3%

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

   5. Simplified 81.3%

      \[\leadsto \color{blue}{\left(y + x\right) \cdot \left(1 + \frac{y}{z}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{-8}:\\ \;\;\;\;z \cdot \frac{\left(-y\right) - x}{y}\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-90}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-113}:\\ \;\;\;\;x \cdot \frac{z}{z - y}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-15}:\\ \;\;\;\;\left(x + y\right) \cdot \left(1 + \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{\left(-y\right) - x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \frac{\left(-y\right) - x}{y}\\ \mathbf{if}\;y \leq -1.85 \cdot 10^{-8}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -2.25 \cdot 10^{-88}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-111}:\\ \;\;\;\;x \cdot \frac{z}{z - y}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-15}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (/ (- (- y) x) y))))
   (if (<= y -1.85e-8)
     t_0
     (if (<= y -2.25e-88)
       (/ y (- 1.0 (/ y z)))
       (if (<= y -3.5e-111)
         (* x (/ z (- z y)))
         (if (<= y 2.6e-15) (+ x y) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * ((-y - x) / y);
	double tmp;
	if (y <= -1.85e-8) {
		tmp = t_0;
	} else if (y <= -2.25e-88) {
		tmp = y / (1.0 - (y / z));
	} else if (y <= -3.5e-111) {
		tmp = x * (z / (z - y));
	} else if (y <= 2.6e-15) {
		tmp = x + 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 = z * ((-y - x) / y)
    if (y <= (-1.85d-8)) then
        tmp = t_0
    else if (y <= (-2.25d-88)) then
        tmp = y / (1.0d0 - (y / z))
    else if (y <= (-3.5d-111)) then
        tmp = x * (z / (z - y))
    else if (y <= 2.6d-15) then
        tmp = x + 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 = z * ((-y - x) / y);
	double tmp;
	if (y <= -1.85e-8) {
		tmp = t_0;
	} else if (y <= -2.25e-88) {
		tmp = y / (1.0 - (y / z));
	} else if (y <= -3.5e-111) {
		tmp = x * (z / (z - y));
	} else if (y <= 2.6e-15) {
		tmp = x + y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * ((-y - x) / y)
	tmp = 0
	if y <= -1.85e-8:
		tmp = t_0
	elif y <= -2.25e-88:
		tmp = y / (1.0 - (y / z))
	elif y <= -3.5e-111:
		tmp = x * (z / (z - y))
	elif y <= 2.6e-15:
		tmp = x + y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(Float64(Float64(-y) - x) / y))
	tmp = 0.0
	if (y <= -1.85e-8)
		tmp = t_0;
	elseif (y <= -2.25e-88)
		tmp = Float64(y / Float64(1.0 - Float64(y / z)));
	elseif (y <= -3.5e-111)
		tmp = Float64(x * Float64(z / Float64(z - y)));
	elseif (y <= 2.6e-15)
		tmp = Float64(x + y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * ((-y - x) / y);
	tmp = 0.0;
	if (y <= -1.85e-8)
		tmp = t_0;
	elseif (y <= -2.25e-88)
		tmp = y / (1.0 - (y / z));
	elseif (y <= -3.5e-111)
		tmp = x * (z / (z - y));
	elseif (y <= 2.6e-15)
		tmp = x + y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(N[((-y) - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.85e-8], t$95$0, If[LessEqual[y, -2.25e-88], N[(y / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.5e-111], N[(x * N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.6e-15], N[(x + y), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.85e-8 or 2.60000000000000004e-15 < y

   1. Initial program 77.6%

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

   3. Taylor expanded in z around 0 70.5%

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

      1. mul-1-neg 70.5%

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

      2. associate-/l* 78.7%

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

      3. distribute-rgt-neg-in 78.7%

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

      4. distribute-neg-frac2 78.7%

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

      5. +-commutative 78.7%

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

   5. Simplified 78.7%

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

   if -1.85e-8 < y < -2.24999999999999996e-88

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 89.0%

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

   if -2.24999999999999996e-88 < y < -3.5e-111

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 84.3%

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

      1. clear-num 84.0%

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

      2. associate-/r/ 84.3%

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

      3. *-inverses 84.3%

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

      4. div-sub 84.3%

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

      5. clear-num 84.5%

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

   5. Applied egg-rr 84.5%

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

   if -3.5e-111 < y < 2.60000000000000004e-15

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 81.2%

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

      1. +-commutative 81.2%

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

   5. Simplified 81.2%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{-8}:\\ \;\;\;\;z \cdot \frac{\left(-y\right) - x}{y}\\ \mathbf{elif}\;y \leq -2.25 \cdot 10^{-88}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-111}:\\ \;\;\;\;x \cdot \frac{z}{z - y}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-15}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{\left(-y\right) - x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{z}{z - y}\\ \mathbf{if}\;y \leq -5.3 \cdot 10^{+72}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-9}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-80}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+58}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (/ z (- z y)))))
   (if (<= y -5.3e+72)
     (- z)
     (if (<= y -7e-9)
       t_0
       (if (<= y -3.1e-80)
         (/ y (- 1.0 (/ y z)))
         (if (<= y 3.7e+58) t_0 (- z)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z / (z - y));
	double tmp;
	if (y <= -5.3e+72) {
		tmp = -z;
	} else if (y <= -7e-9) {
		tmp = t_0;
	} else if (y <= -3.1e-80) {
		tmp = y / (1.0 - (y / z));
	} else if (y <= 3.7e+58) {
		tmp = t_0;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (z / (z - y))
    if (y <= (-5.3d+72)) then
        tmp = -z
    else if (y <= (-7d-9)) then
        tmp = t_0
    else if (y <= (-3.1d-80)) then
        tmp = y / (1.0d0 - (y / z))
    else if (y <= 3.7d+58) then
        tmp = t_0
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (z / (z - y));
	double tmp;
	if (y <= -5.3e+72) {
		tmp = -z;
	} else if (y <= -7e-9) {
		tmp = t_0;
	} else if (y <= -3.1e-80) {
		tmp = y / (1.0 - (y / z));
	} else if (y <= 3.7e+58) {
		tmp = t_0;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z / (z - y))
	tmp = 0
	if y <= -5.3e+72:
		tmp = -z
	elif y <= -7e-9:
		tmp = t_0
	elif y <= -3.1e-80:
		tmp = y / (1.0 - (y / z))
	elif y <= 3.7e+58:
		tmp = t_0
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z / Float64(z - y)))
	tmp = 0.0
	if (y <= -5.3e+72)
		tmp = Float64(-z);
	elseif (y <= -7e-9)
		tmp = t_0;
	elseif (y <= -3.1e-80)
		tmp = Float64(y / Float64(1.0 - Float64(y / z)));
	elseif (y <= 3.7e+58)
		tmp = t_0;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z / (z - y));
	tmp = 0.0;
	if (y <= -5.3e+72)
		tmp = -z;
	elseif (y <= -7e-9)
		tmp = t_0;
	elseif (y <= -3.1e-80)
		tmp = y / (1.0 - (y / z));
	elseif (y <= 3.7e+58)
		tmp = t_0;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.3e+72], (-z), If[LessEqual[y, -7e-9], t$95$0, If[LessEqual[y, -3.1e-80], N[(y / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.7e+58], t$95$0, (-z)]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.3000000000000003e72 or 3.7000000000000002e58 < y

   1. Initial program 70.8%

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

   3. Taylor expanded in y around inf 67.8%

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

      1. neg-mul-1 67.8%

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

   5. Simplified 67.8%

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

   if -5.3000000000000003e72 < y < -6.9999999999999998e-9 or -3.10000000000000016e-80 < y < 3.7000000000000002e58

   1. Initial program 99.2%

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

   3. Taylor expanded in x around inf 75.9%

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

      1. clear-num 75.7%

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

      2. associate-/r/ 75.9%

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

      3. *-inverses 75.9%

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

      4. div-sub 75.9%

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

      5. clear-num 75.9%

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

   5. Applied egg-rr 75.9%

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

   if -6.9999999999999998e-9 < y < -3.10000000000000016e-80

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 99.8%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{+72}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-9}:\\ \;\;\;\;x \cdot \frac{z}{z - y}\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-80}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+58}:\\ \;\;\;\;x \cdot \frac{z}{z - y}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{z}{z - y}\\ t_1 := x \cdot t\_0\\ \mathbf{if}\;y \leq -1.32 \cdot 10^{+79}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-80}:\\ \;\;\;\;y \cdot t\_0\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+57}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ z (- z y))) (t_1 (* x t_0)))
   (if (<= y -1.32e+79)
     (- z)
     (if (<= y -3e-9)
       t_1
       (if (<= y -1.4e-80) (* y t_0) (if (<= y 6e+57) t_1 (- z)))))))

C

double code(double x, double y, double z) {
	double t_0 = z / (z - y);
	double t_1 = x * t_0;
	double tmp;
	if (y <= -1.32e+79) {
		tmp = -z;
	} else if (y <= -3e-9) {
		tmp = t_1;
	} else if (y <= -1.4e-80) {
		tmp = y * t_0;
	} else if (y <= 6e+57) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = z / (z - y)
    t_1 = x * t_0
    if (y <= (-1.32d+79)) then
        tmp = -z
    else if (y <= (-3d-9)) then
        tmp = t_1
    else if (y <= (-1.4d-80)) then
        tmp = y * t_0
    else if (y <= 6d+57) then
        tmp = t_1
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z / (z - y);
	double t_1 = x * t_0;
	double tmp;
	if (y <= -1.32e+79) {
		tmp = -z;
	} else if (y <= -3e-9) {
		tmp = t_1;
	} else if (y <= -1.4e-80) {
		tmp = y * t_0;
	} else if (y <= 6e+57) {
		tmp = t_1;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z / (z - y)
	t_1 = x * t_0
	tmp = 0
	if y <= -1.32e+79:
		tmp = -z
	elif y <= -3e-9:
		tmp = t_1
	elif y <= -1.4e-80:
		tmp = y * t_0
	elif y <= 6e+57:
		tmp = t_1
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z / Float64(z - y))
	t_1 = Float64(x * t_0)
	tmp = 0.0
	if (y <= -1.32e+79)
		tmp = Float64(-z);
	elseif (y <= -3e-9)
		tmp = t_1;
	elseif (y <= -1.4e-80)
		tmp = Float64(y * t_0);
	elseif (y <= 6e+57)
		tmp = t_1;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z / (z - y);
	t_1 = x * t_0;
	tmp = 0.0;
	if (y <= -1.32e+79)
		tmp = -z;
	elseif (y <= -3e-9)
		tmp = t_1;
	elseif (y <= -1.4e-80)
		tmp = y * t_0;
	elseif (y <= 6e+57)
		tmp = t_1;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x * t$95$0), $MachinePrecision]}, If[LessEqual[y, -1.32e+79], (-z), If[LessEqual[y, -3e-9], t$95$1, If[LessEqual[y, -1.4e-80], N[(y * t$95$0), $MachinePrecision], If[LessEqual[y, 6e+57], t$95$1, (-z)]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.32e79 or 5.9999999999999999e57 < y

   1. Initial program 70.8%

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

   3. Taylor expanded in y around inf 67.8%

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

      1. neg-mul-1 67.8%

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

   5. Simplified 67.8%

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

   if -1.32e79 < y < -2.99999999999999998e-9 or -1.39999999999999995e-80 < y < 5.9999999999999999e57

   1. Initial program 99.2%

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

   3. Taylor expanded in x around inf 75.9%

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

      1. clear-num 75.7%

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

      2. associate-/r/ 75.9%

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

      3. *-inverses 75.9%

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

      4. div-sub 75.9%

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

      5. clear-num 75.9%

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

   5. Applied egg-rr 75.9%

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

   if -2.99999999999999998e-9 < y < -1.39999999999999995e-80

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 99.8%

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

   4. Taylor expanded in x around 0 87.6%

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

      1. associate-/l* 99.6%

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

   6. Simplified 99.6%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.32 \cdot 10^{+79}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-9}:\\ \;\;\;\;x \cdot \frac{z}{z - y}\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-80}:\\ \;\;\;\;y \cdot \frac{z}{z - y}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+57}:\\ \;\;\;\;x \cdot \frac{z}{z - y}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+76} \lor \neg \left(y \leq 7.5 \cdot 10^{-7}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.5e+76) (not (<= y 7.5e-7))) (- z) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.5e+76) || !(y <= 7.5e-7)) {
		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 <= (-1.5d+76)) .or. (.not. (y <= 7.5d-7))) 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 <= -1.5e+76) || !(y <= 7.5e-7)) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.5e+76) or not (y <= 7.5e-7):
		tmp = -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.5e+76) || !(y <= 7.5e-7))
		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 <= -1.5e+76) || ~((y <= 7.5e-7)))
		tmp = -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.5e+76], N[Not[LessEqual[y, 7.5e-7]], $MachinePrecision]], (-z), N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4999999999999999e76 or 7.5000000000000002e-7 < y

   1. Initial program 74.9%

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

   3. Taylor expanded in y around inf 62.7%

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

      1. neg-mul-1 62.7%

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

   5. Simplified 62.7%

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

   if -1.4999999999999999e76 < y < 7.5000000000000002e-7

   1. Initial program 99.2%

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

   3. Taylor expanded in z around inf 72.2%

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

      1. +-commutative 72.2%

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

   5. Simplified 72.2%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+76} \lor \neg \left(y \leq 7.5 \cdot 10^{-7}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-63} \lor \neg \left(y \leq 1.2 \cdot 10^{-7}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.35e-63) (not (<= y 1.2e-7))) (- z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.35e-63) || !(y <= 1.2e-7)) {
		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 <= (-1.35d-63)) .or. (.not. (y <= 1.2d-7))) 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 <= -1.35e-63) || !(y <= 1.2e-7)) {
		tmp = -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.35e-63) or not (y <= 1.2e-7):
		tmp = -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.35e-63) || !(y <= 1.2e-7))
		tmp = Float64(-z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.35e-63) || ~((y <= 1.2e-7)))
		tmp = -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.35e-63], N[Not[LessEqual[y, 1.2e-7]], $MachinePrecision]], (-z), x]

Derivation

1. Split input into 2 regimes

2. if y < -1.3500000000000001e-63 or 1.19999999999999989e-7 < y

   1. Initial program 78.2%

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

   3. Taylor expanded in y around inf 57.4%

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

      1. neg-mul-1 57.4%

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

   5. Simplified 57.4%

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

   if -1.3500000000000001e-63 < y < 1.19999999999999989e-7

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 63.3%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-63} \lor \neg \left(y \leq 1.2 \cdot 10^{-7}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 40.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-165}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-185}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.1e-165) x (if (<= x 8.5e-185) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.1e-165) {
		tmp = x;
	} else if (x <= 8.5e-185) {
		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 <= (-2.1d-165)) then
        tmp = x
    else if (x <= 8.5d-185) 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 <= -2.1e-165) {
		tmp = x;
	} else if (x <= 8.5e-185) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.1e-165:
		tmp = x
	elif x <= 8.5e-185:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.1e-165)
		tmp = x;
	elseif (x <= 8.5e-185)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.1e-165)
		tmp = x;
	elseif (x <= 8.5e-185)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.1e-165], x, If[LessEqual[x, 8.5e-185], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.09999999999999995e-165 or 8.5000000000000001e-185 < x

   1. Initial program 87.4%

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

   3. Taylor expanded in y around 0 40.2%

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

   if -2.09999999999999995e-165 < x < 8.5000000000000001e-185

   1. Initial program 89.0%

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

   3. Taylor expanded in z around 0 89.0%

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

   4. Taylor expanded in x around 0 81.8%

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

      1. associate-/l* 78.0%

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

   6. Simplified 78.0%

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

   7. Taylor expanded in y around 0 35.3%

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

Alternative 11: 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 87.7%

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

3. Taylor expanded in y around 0 34.6%

   \[\leadsto \color{blue}{x} \]
4. 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 2024111 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, A"
  :precision binary64

  :alt
  (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))))