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

Percentage Accurate: 88.7% → 98.7%

Time: 6.2s

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: 88.7% 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: 98.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ t_1 := \frac{x + y}{t_0}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{-207} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;\frac{y}{t_0} + \frac{x}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - \frac{z}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))) (t_1 (/ (+ x y) t_0)))
   (if (or (<= t_1 -4e-207) (not (<= t_1 0.0)))
     (+ (/ y t_0) (/ x t_0))
     (- (- z) (/ z (/ y x))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double t_1 = (x + y) / t_0;
	double tmp;
	if ((t_1 <= -4e-207) || !(t_1 <= 0.0)) {
		tmp = (y / t_0) + (x / t_0);
	} else {
		tmp = -z - (z / (y / 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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 1.0d0 - (y / z)
    t_1 = (x + y) / t_0
    if ((t_1 <= (-4d-207)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = (y / t_0) + (x / t_0)
    else
        tmp = -z - (z / (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double t_1 = (x + y) / t_0;
	double tmp;
	if ((t_1 <= -4e-207) || !(t_1 <= 0.0)) {
		tmp = (y / t_0) + (x / t_0);
	} else {
		tmp = -z - (z / (y / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	t_1 = (x + y) / t_0
	tmp = 0
	if (t_1 <= -4e-207) or not (t_1 <= 0.0):
		tmp = (y / t_0) + (x / t_0)
	else:
		tmp = -z - (z / (y / x))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y / z))
	t_1 = Float64(Float64(x + y) / t_0)
	tmp = 0.0
	if ((t_1 <= -4e-207) || !(t_1 <= 0.0))
		tmp = Float64(Float64(y / t_0) + Float64(x / t_0));
	else
		tmp = Float64(Float64(-z) - Float64(z / Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y / z);
	t_1 = (x + y) / t_0;
	tmp = 0.0;
	if ((t_1 <= -4e-207) || ~((t_1 <= 0.0)))
		tmp = (y / t_0) + (x / t_0);
	else
		tmp = -z - (z / (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] / t$95$0), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -4e-207], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(y / t$95$0), $MachinePrecision] + N[(x / t$95$0), $MachinePrecision]), $MachinePrecision], N[((-z) - N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < -3.9999999999999997e-207 or -0.0 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 100.0%

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

      1. +-commutative 100.0%

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

   4. Simplified 100.0%

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

   if -3.9999999999999997e-207 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < -0.0

   1. Initial program 13.7%

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

   2. Taylor expanded in z around 0 99.6%

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

      1. mul-1-neg 99.6%

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

      2. +-commutative 99.6%

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

      3. *-commutative 99.6%

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

      4. +-commutative 99.6%

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

   4. Simplified 99.6%

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

   5. Taylor expanded in y around 0 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-/l* 99.9%

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

   7. Simplified 99.9%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -4 \cdot 10^{-207} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}} + \frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - \frac{z}{\frac{y}{x}}\\ \end{array} \]

Alternative 2: 98.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t_0 \leq -4 \cdot 10^{-207} \lor \neg \left(t_0 \leq 0\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - \frac{z}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -4e-207) (not (<= t_0 0.0))) t_0 (- (- z) (/ z (/ y x))))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -4e-207) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = -z - (z / (y / 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) :: t_0
    real(8) :: tmp
    t_0 = (x + y) / (1.0d0 - (y / z))
    if ((t_0 <= (-4d-207)) .or. (.not. (t_0 <= 0.0d0))) then
        tmp = t_0
    else
        tmp = -z - (z / (y / x))
    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 <= -4e-207) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = -z - (z / (y / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -4e-207) or not (t_0 <= 0.0):
		tmp = t_0
	else:
		tmp = -z - (z / (y / x))
	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 <= -4e-207) || !(t_0 <= 0.0))
		tmp = t_0;
	else
		tmp = Float64(Float64(-z) - Float64(z / Float64(y / x)));
	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 <= -4e-207) || ~((t_0 <= 0.0)))
		tmp = t_0;
	else
		tmp = -z - (z / (y / x));
	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, -4e-207], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], t$95$0, N[((-z) - N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < -3.9999999999999997e-207 or -0.0 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

   1. Initial program 99.9%

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

   if -3.9999999999999997e-207 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < -0.0

   1. Initial program 13.7%

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

   2. Taylor expanded in z around 0 99.6%

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

      1. mul-1-neg 99.6%

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

      2. +-commutative 99.6%

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

      3. *-commutative 99.6%

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

      4. +-commutative 99.6%

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

   4. Simplified 99.6%

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

   5. Taylor expanded in y around 0 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-/l* 99.9%

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

   7. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -4 \cdot 10^{-207} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - \frac{z}{\frac{y}{x}}\\ \end{array} \]

Alternative 3: 67.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ t_1 := \frac{y}{t_0}\\ t_2 := \frac{x}{t_0}\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{+95}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{+32}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{-104}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.56 \cdot 10^{-75}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-26}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+212}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))) (t_1 (/ y t_0)) (t_2 (/ x t_0)))
   (if (<= y -3.8e+95)
     (- z)
     (if (<= y -1.85e+32)
       t_2
       (if (<= y -9.2e-104)
         t_1
         (if (<= y 1.56e-75)
           (+ x y)
           (if (<= y 7.4e-26) t_2 (if (<= y 1.02e+212) t_1 (- z)))))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double t_1 = y / t_0;
	double t_2 = x / t_0;
	double tmp;
	if (y <= -3.8e+95) {
		tmp = -z;
	} else if (y <= -1.85e+32) {
		tmp = t_2;
	} else if (y <= -9.2e-104) {
		tmp = t_1;
	} else if (y <= 1.56e-75) {
		tmp = x + y;
	} else if (y <= 7.4e-26) {
		tmp = t_2;
	} else if (y <= 1.02e+212) {
		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) :: t_2
    real(8) :: tmp
    t_0 = 1.0d0 - (y / z)
    t_1 = y / t_0
    t_2 = x / t_0
    if (y <= (-3.8d+95)) then
        tmp = -z
    else if (y <= (-1.85d+32)) then
        tmp = t_2
    else if (y <= (-9.2d-104)) then
        tmp = t_1
    else if (y <= 1.56d-75) then
        tmp = x + y
    else if (y <= 7.4d-26) then
        tmp = t_2
    else if (y <= 1.02d+212) 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 = 1.0 - (y / z);
	double t_1 = y / t_0;
	double t_2 = x / t_0;
	double tmp;
	if (y <= -3.8e+95) {
		tmp = -z;
	} else if (y <= -1.85e+32) {
		tmp = t_2;
	} else if (y <= -9.2e-104) {
		tmp = t_1;
	} else if (y <= 1.56e-75) {
		tmp = x + y;
	} else if (y <= 7.4e-26) {
		tmp = t_2;
	} else if (y <= 1.02e+212) {
		tmp = t_1;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	t_1 = y / t_0
	t_2 = x / t_0
	tmp = 0
	if y <= -3.8e+95:
		tmp = -z
	elif y <= -1.85e+32:
		tmp = t_2
	elif y <= -9.2e-104:
		tmp = t_1
	elif y <= 1.56e-75:
		tmp = x + y
	elif y <= 7.4e-26:
		tmp = t_2
	elif y <= 1.02e+212:
		tmp = t_1
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y / z))
	t_1 = Float64(y / t_0)
	t_2 = Float64(x / t_0)
	tmp = 0.0
	if (y <= -3.8e+95)
		tmp = Float64(-z);
	elseif (y <= -1.85e+32)
		tmp = t_2;
	elseif (y <= -9.2e-104)
		tmp = t_1;
	elseif (y <= 1.56e-75)
		tmp = Float64(x + y);
	elseif (y <= 7.4e-26)
		tmp = t_2;
	elseif (y <= 1.02e+212)
		tmp = t_1;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y / z);
	t_1 = y / t_0;
	t_2 = x / t_0;
	tmp = 0.0;
	if (y <= -3.8e+95)
		tmp = -z;
	elseif (y <= -1.85e+32)
		tmp = t_2;
	elseif (y <= -9.2e-104)
		tmp = t_1;
	elseif (y <= 1.56e-75)
		tmp = x + y;
	elseif (y <= 7.4e-26)
		tmp = t_2;
	elseif (y <= 1.02e+212)
		tmp = t_1;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(y / t$95$0), $MachinePrecision]}, Block[{t$95$2 = N[(x / t$95$0), $MachinePrecision]}, If[LessEqual[y, -3.8e+95], (-z), If[LessEqual[y, -1.85e+32], t$95$2, If[LessEqual[y, -9.2e-104], t$95$1, If[LessEqual[y, 1.56e-75], N[(x + y), $MachinePrecision], If[LessEqual[y, 7.4e-26], t$95$2, If[LessEqual[y, 1.02e+212], t$95$1, (-z)]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.7999999999999999e95 or 1.01999999999999992e212 < y

   1. Initial program 69.9%

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

   2. Taylor expanded in y around inf 71.8%

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

      1. mul-1-neg 71.8%

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

   4. Simplified 71.8%

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

   if -3.7999999999999999e95 < y < -1.85e32 or 1.5600000000000001e-75 < y < 7.3999999999999997e-26

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 66.8%

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

   if -1.85e32 < y < -9.1999999999999998e-104 or 7.3999999999999997e-26 < y < 1.01999999999999992e212

   1. Initial program 88.7%

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

   2. Taylor expanded in x around 0 65.7%

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

   if -9.1999999999999998e-104 < y < 1.5600000000000001e-75

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 88.1%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+95}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{+32}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{-104}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 1.56 \cdot 10^{-75}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-26}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+212}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 4: 73.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ t_1 := \left(-z\right) - \frac{z}{\frac{y}{x}}\\ \mathbf{if}\;y \leq -1.36 \cdot 10^{-42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-76}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-26}:\\ \;\;\;\;\frac{x}{t_0}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+118}:\\ \;\;\;\;\frac{y}{t_0}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))) (t_1 (- (- z) (/ z (/ y x)))))
   (if (<= y -1.36e-42)
     t_1
     (if (<= y 1.7e-76)
       (+ x y)
       (if (<= y 8.2e-26) (/ x t_0) (if (<= y 1.45e+118) (/ y t_0) t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double t_1 = -z - (z / (y / x));
	double tmp;
	if (y <= -1.36e-42) {
		tmp = t_1;
	} else if (y <= 1.7e-76) {
		tmp = x + y;
	} else if (y <= 8.2e-26) {
		tmp = x / t_0;
	} else if (y <= 1.45e+118) {
		tmp = y / t_0;
	} else {
		tmp = t_1;
	}
	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 = 1.0d0 - (y / z)
    t_1 = -z - (z / (y / x))
    if (y <= (-1.36d-42)) then
        tmp = t_1
    else if (y <= 1.7d-76) then
        tmp = x + y
    else if (y <= 8.2d-26) then
        tmp = x / t_0
    else if (y <= 1.45d+118) then
        tmp = y / t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double t_1 = -z - (z / (y / x));
	double tmp;
	if (y <= -1.36e-42) {
		tmp = t_1;
	} else if (y <= 1.7e-76) {
		tmp = x + y;
	} else if (y <= 8.2e-26) {
		tmp = x / t_0;
	} else if (y <= 1.45e+118) {
		tmp = y / t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	t_1 = -z - (z / (y / x))
	tmp = 0
	if y <= -1.36e-42:
		tmp = t_1
	elif y <= 1.7e-76:
		tmp = x + y
	elif y <= 8.2e-26:
		tmp = x / t_0
	elif y <= 1.45e+118:
		tmp = y / t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y / z))
	t_1 = Float64(Float64(-z) - Float64(z / Float64(y / x)))
	tmp = 0.0
	if (y <= -1.36e-42)
		tmp = t_1;
	elseif (y <= 1.7e-76)
		tmp = Float64(x + y);
	elseif (y <= 8.2e-26)
		tmp = Float64(x / t_0);
	elseif (y <= 1.45e+118)
		tmp = Float64(y / t_0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y / z);
	t_1 = -z - (z / (y / x));
	tmp = 0.0;
	if (y <= -1.36e-42)
		tmp = t_1;
	elseif (y <= 1.7e-76)
		tmp = x + y;
	elseif (y <= 8.2e-26)
		tmp = x / t_0;
	elseif (y <= 1.45e+118)
		tmp = y / t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[((-z) - N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.36e-42], t$95$1, If[LessEqual[y, 1.7e-76], N[(x + y), $MachinePrecision], If[LessEqual[y, 8.2e-26], N[(x / t$95$0), $MachinePrecision], If[LessEqual[y, 1.45e+118], N[(y / t$95$0), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.36e-42 or 1.45000000000000008e118 < y

   1. Initial program 75.7%

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

   2. Taylor expanded in z around 0 60.4%

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

      1. mul-1-neg 60.4%

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

      2. +-commutative 60.4%

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

      3. *-commutative 60.4%

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

      4. +-commutative 60.4%

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

   4. Simplified 60.4%

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

   5. Taylor expanded in y around 0 71.3%

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

      1. +-commutative 71.3%

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

      2. associate-/l* 78.0%

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

   7. Simplified 78.0%

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

   if -1.36e-42 < y < 1.7e-76

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 85.7%

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

   if 1.7e-76 < y < 8.1999999999999997e-26

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 74.4%

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

   if 8.1999999999999997e-26 < y < 1.45000000000000008e118

   1. Initial program 96.9%

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

   2. Taylor expanded in x around 0 71.0%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.36 \cdot 10^{-42}:\\ \;\;\;\;\left(-z\right) - \frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-76}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-26}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+118}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - \frac{z}{\frac{y}{x}}\\ \end{array} \]

Alternative 5: 67.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+95}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-82}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-28}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+96}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -7.2e+95)
   (- z)
   (if (<= y 2.7e-82)
     (+ x y)
     (if (<= y 7.2e-28)
       (/ x (- 1.0 (/ y z)))
       (if (<= y 8e+96) (+ x y) (- z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -7.2e+95) {
		tmp = -z;
	} else if (y <= 2.7e-82) {
		tmp = x + y;
	} else if (y <= 7.2e-28) {
		tmp = x / (1.0 - (y / z));
	} else if (y <= 8e+96) {
		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 <= (-7.2d+95)) then
        tmp = -z
    else if (y <= 2.7d-82) then
        tmp = x + y
    else if (y <= 7.2d-28) then
        tmp = x / (1.0d0 - (y / z))
    else if (y <= 8d+96) 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 <= -7.2e+95) {
		tmp = -z;
	} else if (y <= 2.7e-82) {
		tmp = x + y;
	} else if (y <= 7.2e-28) {
		tmp = x / (1.0 - (y / z));
	} else if (y <= 8e+96) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -7.2e+95:
		tmp = -z
	elif y <= 2.7e-82:
		tmp = x + y
	elif y <= 7.2e-28:
		tmp = x / (1.0 - (y / z))
	elif y <= 8e+96:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -7.2e+95)
		tmp = Float64(-z);
	elseif (y <= 2.7e-82)
		tmp = Float64(x + y);
	elseif (y <= 7.2e-28)
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	elseif (y <= 8e+96)
		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 <= -7.2e+95)
		tmp = -z;
	elseif (y <= 2.7e-82)
		tmp = x + y;
	elseif (y <= 7.2e-28)
		tmp = x / (1.0 - (y / z));
	elseif (y <= 8e+96)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -7.2e+95], (-z), If[LessEqual[y, 2.7e-82], N[(x + y), $MachinePrecision], If[LessEqual[y, 7.2e-28], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8e+96], N[(x + y), $MachinePrecision], (-z)]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.19999999999999955e95 or 8.0000000000000004e96 < y

   1. Initial program 70.1%

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

   2. Taylor expanded in y around inf 67.0%

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

      1. mul-1-neg 67.0%

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

   4. Simplified 67.0%

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

   if -7.19999999999999955e95 < y < 2.7000000000000001e-82 or 7.1999999999999997e-28 < y < 8.0000000000000004e96

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 73.4%

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

   if 2.7000000000000001e-82 < y < 7.1999999999999997e-28

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 70.1%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+95}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-82}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-28}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+96}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 6: 56.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-77}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-111}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-26}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.8e-77)
   (- z)
   (if (<= y -2.2e-111) y (if (<= y 7.5e-26) x (- z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.8e-77) {
		tmp = -z;
	} else if (y <= -2.2e-111) {
		tmp = y;
	} else if (y <= 7.5e-26) {
		tmp = x;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-4.8d-77)) then
        tmp = -z
    else if (y <= (-2.2d-111)) then
        tmp = y
    else if (y <= 7.5d-26) then
        tmp = x
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.8e-77) {
		tmp = -z;
	} else if (y <= -2.2e-111) {
		tmp = y;
	} else if (y <= 7.5e-26) {
		tmp = x;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.8e-77:
		tmp = -z
	elif y <= -2.2e-111:
		tmp = y
	elif y <= 7.5e-26:
		tmp = x
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.8e-77)
		tmp = Float64(-z);
	elseif (y <= -2.2e-111)
		tmp = y;
	elseif (y <= 7.5e-26)
		tmp = x;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4.8e-77)
		tmp = -z;
	elseif (y <= -2.2e-111)
		tmp = y;
	elseif (y <= 7.5e-26)
		tmp = x;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.8e-77], (-z), If[LessEqual[y, -2.2e-111], y, If[LessEqual[y, 7.5e-26], x, (-z)]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.7999999999999998e-77 or 7.4999999999999994e-26 < y

   1. Initial program 80.2%

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

   2. Taylor expanded in y around inf 54.4%

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

      1. mul-1-neg 54.4%

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

   4. Simplified 54.4%

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

   if -4.7999999999999998e-77 < y < -2.2e-111

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 80.8%

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

   3. Taylor expanded in y around 0 72.3%

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

   if -2.2e-111 < y < 7.4999999999999994e-26

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 67.4%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-77}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-111}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-26}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 7: 67.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+95}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+99}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -7.2e+95) (- z) (if (<= y 2e+99) (+ x y) (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -7.2e+95) {
		tmp = -z;
	} else if (y <= 2e+99) {
		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 <= (-7.2d+95)) then
        tmp = -z
    else if (y <= 2d+99) 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 <= -7.2e+95) {
		tmp = -z;
	} else if (y <= 2e+99) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -7.2e+95:
		tmp = -z
	elif y <= 2e+99:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -7.2e+95)
		tmp = Float64(-z);
	elseif (y <= 2e+99)
		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 <= -7.2e+95)
		tmp = -z;
	elseif (y <= 2e+99)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -7.2e+95], (-z), If[LessEqual[y, 2e+99], N[(x + y), $MachinePrecision], (-z)]]

Derivation

1. Split input into 2 regimes

2. if y < -7.19999999999999955e95 or 1.9999999999999999e99 < y

   1. Initial program 70.1%

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

   2. Taylor expanded in y around inf 67.0%

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

      1. mul-1-neg 67.0%

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

   4. Simplified 67.0%

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

   if -7.19999999999999955e95 < y < 1.9999999999999999e99

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 70.4%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+95}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+99}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 8: 41.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{-84}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-59}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.3e-84) x (if (<= x 2.2e-59) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.3e-84) {
		tmp = x;
	} else if (x <= 2.2e-59) {
		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 <= (-3.3d-84)) then
        tmp = x
    else if (x <= 2.2d-59) 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 <= -3.3e-84) {
		tmp = x;
	} else if (x <= 2.2e-59) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.3e-84:
		tmp = x
	elif x <= 2.2e-59:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.3e-84)
		tmp = x;
	elseif (x <= 2.2e-59)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -3.3e-84)
		tmp = x;
	elseif (x <= 2.2e-59)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.3e-84], x, If[LessEqual[x, 2.2e-59], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -3.29999999999999984e-84 or 2.1999999999999999e-59 < x

   1. Initial program 85.0%

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

   2. Taylor expanded in y around 0 36.6%

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

   if -3.29999999999999984e-84 < x < 2.1999999999999999e-59

   1. Initial program 91.4%

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

   2. Taylor expanded in x around 0 75.7%

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

   3. Taylor expanded in y around 0 43.6%

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

4. Final simplification 39.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{-84}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-59}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 35.2% 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 87.5%

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

2. Taylor expanded in y around 0 29.3%

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

3. Final simplification 29.3%

   \[\leadsto x \]

Developer target: 94.1% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023268 
(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))))