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

Percentage Accurate: 88.7% → 99.4%

Time: 5.5s

Alternatives: 12

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: 99.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t_0 \leq -1 \cdot 10^{-244} \lor \neg \left(t_0 \leq 0\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - \frac{z}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -1e-244) (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 <= -1e-244) || !(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 <= (-1d-244)) .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 <= -1e-244) || !(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 <= -1e-244) 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 <= -1e-244) || !(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 <= -1e-244) || ~((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, -1e-244], 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))) < -9.9999999999999993e-245 or 0.0 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

   1. Initial program 99.8%

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

   if -9.9999999999999993e-245 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < 0.0

   1. Initial program 19.3%

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

   2. Taylor expanded in z around 0 91.8%

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

      1. associate-*r/ 91.8%

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

      2. +-commutative 91.8%

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

      3. *-commutative 91.8%

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

      4. associate-*r* 91.8%

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

      5. mul-1-neg 91.8%

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

      6. +-commutative 91.8%

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

   4. Simplified 91.8%

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

   5. Taylor expanded in y around 0 99.6%

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

      1. mul-1-neg 99.6%

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

      2. unsub-neg 99.6%

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

      3. mul-1-neg 99.6%

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

      4. associate-/l* 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -1 \cdot 10^{-244} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - \frac{z}{\frac{y}{x}}\\ \end{array} \]

Alternative 2: 66.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+74}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-5}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-30}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+61}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.95e+74)
   (- z)
   (if (<= y -1.6e-5)
     (+ x y)
     (if (<= y -3.2e-30)
       (- z)
       (if (<= y 1.02e+61) (/ x (- 1.0 (/ y z))) (- z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.95e+74) {
		tmp = -z;
	} else if (y <= -1.6e-5) {
		tmp = x + y;
	} else if (y <= -3.2e-30) {
		tmp = -z;
	} else if (y <= 1.02e+61) {
		tmp = x / (1.0 - (y / z));
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.95d+74)) then
        tmp = -z
    else if (y <= (-1.6d-5)) then
        tmp = x + y
    else if (y <= (-3.2d-30)) then
        tmp = -z
    else if (y <= 1.02d+61) then
        tmp = x / (1.0d0 - (y / z))
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.95e+74) {
		tmp = -z;
	} else if (y <= -1.6e-5) {
		tmp = x + y;
	} else if (y <= -3.2e-30) {
		tmp = -z;
	} else if (y <= 1.02e+61) {
		tmp = x / (1.0 - (y / z));
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.95e+74:
		tmp = -z
	elif y <= -1.6e-5:
		tmp = x + y
	elif y <= -3.2e-30:
		tmp = -z
	elif y <= 1.02e+61:
		tmp = x / (1.0 - (y / z))
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.95e+74)
		tmp = Float64(-z);
	elseif (y <= -1.6e-5)
		tmp = Float64(x + y);
	elseif (y <= -3.2e-30)
		tmp = Float64(-z);
	elseif (y <= 1.02e+61)
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.95e+74)
		tmp = -z;
	elseif (y <= -1.6e-5)
		tmp = x + y;
	elseif (y <= -3.2e-30)
		tmp = -z;
	elseif (y <= 1.02e+61)
		tmp = x / (1.0 - (y / z));
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.95e+74], (-z), If[LessEqual[y, -1.6e-5], N[(x + y), $MachinePrecision], If[LessEqual[y, -3.2e-30], (-z), If[LessEqual[y, 1.02e+61], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], (-z)]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.95000000000000004e74 or -1.59999999999999993e-5 < y < -3.2e-30 or 1.01999999999999999e61 < y

   1. Initial program 70.0%

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

   2. Taylor expanded in y around inf 78.5%

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

      1. mul-1-neg 78.5%

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

   4. Simplified 78.5%

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

   if -1.95000000000000004e74 < y < -1.59999999999999993e-5

   1. Initial program 82.6%

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

   2. Taylor expanded in z around inf 65.1%

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

   if -3.2e-30 < y < 1.01999999999999999e61

   1. Initial program 97.9%

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

   2. Taylor expanded in x around inf 75.4%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+74}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-5}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-30}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+61}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 3: 67.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ \mathbf{if}\;y \leq -8.5 \cdot 10^{+77}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-46}:\\ \;\;\;\;\frac{y}{t_0}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+61}:\\ \;\;\;\;\frac{x}{t_0}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))))
   (if (<= y -8.5e+77)
     (- z)
     (if (<= y -7.5e-46) (/ y t_0) (if (<= y 1.2e+61) (/ x t_0) (- z))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double tmp;
	if (y <= -8.5e+77) {
		tmp = -z;
	} else if (y <= -7.5e-46) {
		tmp = y / t_0;
	} else if (y <= 1.2e+61) {
		tmp = x / 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 = 1.0d0 - (y / z)
    if (y <= (-8.5d+77)) then
        tmp = -z
    else if (y <= (-7.5d-46)) then
        tmp = y / t_0
    else if (y <= 1.2d+61) then
        tmp = x / 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 = 1.0 - (y / z);
	double tmp;
	if (y <= -8.5e+77) {
		tmp = -z;
	} else if (y <= -7.5e-46) {
		tmp = y / t_0;
	} else if (y <= 1.2e+61) {
		tmp = x / t_0;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	tmp = 0
	if y <= -8.5e+77:
		tmp = -z
	elif y <= -7.5e-46:
		tmp = y / t_0
	elif y <= 1.2e+61:
		tmp = x / t_0
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y / z))
	tmp = 0.0
	if (y <= -8.5e+77)
		tmp = Float64(-z);
	elseif (y <= -7.5e-46)
		tmp = Float64(y / t_0);
	elseif (y <= 1.2e+61)
		tmp = Float64(x / t_0);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y / z);
	tmp = 0.0;
	if (y <= -8.5e+77)
		tmp = -z;
	elseif (y <= -7.5e-46)
		tmp = y / t_0;
	elseif (y <= 1.2e+61)
		tmp = x / t_0;
	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]}, If[LessEqual[y, -8.5e+77], (-z), If[LessEqual[y, -7.5e-46], N[(y / t$95$0), $MachinePrecision], If[LessEqual[y, 1.2e+61], N[(x / t$95$0), $MachinePrecision], (-z)]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.50000000000000018e77 or 1.1999999999999999e61 < y

   1. Initial program 66.9%

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

   2. Taylor expanded in y around inf 79.9%

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

      1. mul-1-neg 79.9%

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

   4. Simplified 79.9%

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

   if -8.50000000000000018e77 < y < -7.50000000000000027e-46

   1. Initial program 92.3%

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

   2. Taylor expanded in x around 0 61.0%

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

   if -7.50000000000000027e-46 < y < 1.1999999999999999e61

   1. Initial program 97.8%

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

   2. Taylor expanded in x around inf 76.1%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+77}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-46}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+61}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 4: 65.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.72 \cdot 10^{+73}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-67}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+29}:\\ \;\;\;\;-x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.72e+73)
   (- z)
   (if (<= y 3.1e-67) (+ x y) (if (<= y 3.1e+29) (- (* x (/ z y))) (- z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.72e+73) {
		tmp = -z;
	} else if (y <= 3.1e-67) {
		tmp = x + y;
	} else if (y <= 3.1e+29) {
		tmp = -(x * (z / y));
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-2.72d+73)) then
        tmp = -z
    else if (y <= 3.1d-67) then
        tmp = x + y
    else if (y <= 3.1d+29) then
        tmp = -(x * (z / y))
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.72e+73) {
		tmp = -z;
	} else if (y <= 3.1e-67) {
		tmp = x + y;
	} else if (y <= 3.1e+29) {
		tmp = -(x * (z / y));
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.72e+73:
		tmp = -z
	elif y <= 3.1e-67:
		tmp = x + y
	elif y <= 3.1e+29:
		tmp = -(x * (z / y))
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.72e+73)
		tmp = Float64(-z);
	elseif (y <= 3.1e-67)
		tmp = Float64(x + y);
	elseif (y <= 3.1e+29)
		tmp = Float64(-Float64(x * Float64(z / y)));
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.72e+73)
		tmp = -z;
	elseif (y <= 3.1e-67)
		tmp = x + y;
	elseif (y <= 3.1e+29)
		tmp = -(x * (z / y));
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.72e+73], (-z), If[LessEqual[y, 3.1e-67], N[(x + y), $MachinePrecision], If[LessEqual[y, 3.1e+29], (-N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), (-z)]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.7199999999999999e73 or 3.0999999999999999e29 < y

   1. Initial program 67.7%

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

   2. Taylor expanded in y around inf 75.6%

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

      1. mul-1-neg 75.6%

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

   4. Simplified 75.6%

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

   if -2.7199999999999999e73 < y < 3.1000000000000003e-67

   1. Initial program 98.4%

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

   2. Taylor expanded in z around inf 73.8%

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

   if 3.1000000000000003e-67 < y < 3.0999999999999999e29

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 69.6%

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

      1. associate-*r/ 69.6%

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

      2. +-commutative 69.6%

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

      3. *-commutative 69.6%

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

      4. associate-*r* 69.6%

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

      5. mul-1-neg 69.6%

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

      6. +-commutative 69.6%

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

   4. Simplified 69.6%

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

   5. Taylor expanded in y around 0 69.6%

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

      1. mul-1-neg 69.6%

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

      2. unsub-neg 69.6%

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

      3. mul-1-neg 69.6%

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

      4. associate-/l* 74.6%

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

   7. Simplified 74.6%

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

   8. Taylor expanded in y around 0 45.2%

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

      1. mul-1-neg 45.2%

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

      2. associate-*l/ 50.1%

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

      3. distribute-lft-neg-in 50.1%

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

      4. *-commutative 50.1%

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

      5. distribute-neg-frac 50.1%

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

   10. Simplified 50.1%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.72 \cdot 10^{+73}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-67}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+29}:\\ \;\;\;\;-x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 5: 64.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+73}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-66}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+53}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6.2e+73)
   (- z)
   (if (<= y 1.3e-66) (+ x y) (if (<= y 9.5e+53) (* z (/ (- x) y)) (- z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.2e+73) {
		tmp = -z;
	} else if (y <= 1.3e-66) {
		tmp = x + y;
	} else if (y <= 9.5e+53) {
		tmp = z * (-x / y);
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-6.2d+73)) then
        tmp = -z
    else if (y <= 1.3d-66) then
        tmp = x + y
    else if (y <= 9.5d+53) then
        tmp = z * (-x / y)
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.2e+73) {
		tmp = -z;
	} else if (y <= 1.3e-66) {
		tmp = x + y;
	} else if (y <= 9.5e+53) {
		tmp = z * (-x / y);
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -6.2e+73:
		tmp = -z
	elif y <= 1.3e-66:
		tmp = x + y
	elif y <= 9.5e+53:
		tmp = z * (-x / y)
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6.2e+73)
		tmp = Float64(-z);
	elseif (y <= 1.3e-66)
		tmp = Float64(x + y);
	elseif (y <= 9.5e+53)
		tmp = Float64(z * Float64(Float64(-x) / y));
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -6.2e+73)
		tmp = -z;
	elseif (y <= 1.3e-66)
		tmp = x + y;
	elseif (y <= 9.5e+53)
		tmp = z * (-x / y);
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6.2e+73], (-z), If[LessEqual[y, 1.3e-66], N[(x + y), $MachinePrecision], If[LessEqual[y, 9.5e+53], N[(z * N[((-x) / y), $MachinePrecision]), $MachinePrecision], (-z)]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.1999999999999999e73 or 9.5000000000000006e53 < y

   1. Initial program 67.5%

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

   2. Taylor expanded in y around inf 79.3%

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

      1. mul-1-neg 79.3%

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

   4. Simplified 79.3%

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

   if -6.1999999999999999e73 < y < 1.2999999999999999e-66

   1. Initial program 98.4%

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

   2. Taylor expanded in z around inf 73.8%

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

   if 1.2999999999999999e-66 < y < 9.5000000000000006e53

   1. Initial program 89.8%

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

   2. Taylor expanded in z around 0 72.3%

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

      1. associate-*r/ 72.3%

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

      2. +-commutative 72.3%

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

      3. *-commutative 72.3%

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

      4. associate-*r* 72.3%

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

      5. mul-1-neg 72.3%

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

      6. +-commutative 72.3%

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

   4. Simplified 72.3%

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

   5. Taylor expanded in y around 0 72.3%

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

      1. mul-1-neg 72.3%

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

      2. unsub-neg 72.3%

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

      3. mul-1-neg 72.3%

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

      4. associate-/l* 75.6%

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

   7. Simplified 75.6%

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

   8. Taylor expanded in y around 0 45.2%

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

      1. mul-1-neg 45.2%

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

      2. associate-*r/ 48.5%

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

      3. distribute-rgt-neg-out 48.5%

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

      4. distribute-neg-frac 48.5%

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

   10. Simplified 48.5%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+73}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-66}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+53}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 6: 65.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+75}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-66}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 7.1 \cdot 10^{+53}:\\ \;\;\;\;\frac{z}{-\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.3e+75)
   (- z)
   (if (<= y 1.3e-66) (+ x y) (if (<= y 7.1e+53) (/ z (- (/ y x))) (- z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.3e+75) {
		tmp = -z;
	} else if (y <= 1.3e-66) {
		tmp = x + y;
	} else if (y <= 7.1e+53) {
		tmp = z / -(y / 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 <= (-3.3d+75)) then
        tmp = -z
    else if (y <= 1.3d-66) then
        tmp = x + y
    else if (y <= 7.1d+53) then
        tmp = z / -(y / 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 <= -3.3e+75) {
		tmp = -z;
	} else if (y <= 1.3e-66) {
		tmp = x + y;
	} else if (y <= 7.1e+53) {
		tmp = z / -(y / x);
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.3e+75:
		tmp = -z
	elif y <= 1.3e-66:
		tmp = x + y
	elif y <= 7.1e+53:
		tmp = z / -(y / x)
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.3e+75)
		tmp = Float64(-z);
	elseif (y <= 1.3e-66)
		tmp = Float64(x + y);
	elseif (y <= 7.1e+53)
		tmp = Float64(z / Float64(-Float64(y / x)));
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.3e+75)
		tmp = -z;
	elseif (y <= 1.3e-66)
		tmp = x + y;
	elseif (y <= 7.1e+53)
		tmp = z / -(y / x);
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.3e+75], (-z), If[LessEqual[y, 1.3e-66], N[(x + y), $MachinePrecision], If[LessEqual[y, 7.1e+53], N[(z / (-N[(y / x), $MachinePrecision])), $MachinePrecision], (-z)]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.29999999999999998e75 or 7.09999999999999974e53 < y

   1. Initial program 67.5%

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

   2. Taylor expanded in y around inf 79.3%

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

      1. mul-1-neg 79.3%

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

   4. Simplified 79.3%

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

   if -3.29999999999999998e75 < y < 1.2999999999999999e-66

   1. Initial program 98.4%

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

   2. Taylor expanded in z around inf 73.8%

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

   if 1.2999999999999999e-66 < y < 7.09999999999999974e53

   1. Initial program 89.8%

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

   2. Taylor expanded in z around 0 72.3%

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

      1. associate-*r/ 72.3%

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

      2. +-commutative 72.3%

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

      3. *-commutative 72.3%

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

      4. associate-*r* 72.3%

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

      5. mul-1-neg 72.3%

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

      6. +-commutative 72.3%

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

   4. Simplified 72.3%

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

   5. Taylor expanded in y around 0 72.3%

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

      1. mul-1-neg 72.3%

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

      2. unsub-neg 72.3%

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

      3. mul-1-neg 72.3%

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

      4. associate-/l* 75.6%

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

   7. Simplified 75.6%

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

   8. Taylor expanded in y around 0 45.2%

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

      1. mul-1-neg 45.2%

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

      2. associate-*l/ 41.8%

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

      3. distribute-lft-neg-in 41.8%

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

      4. *-commutative 41.8%

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

      5. distribute-neg-frac 41.8%

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

   10. Simplified 41.8%

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

       1. *-commutative 41.8%

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

       2. frac-2neg 41.8%

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

       3. remove-double-neg 41.8%

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

       4. associate-*l/ 45.2%

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

   12. Applied egg-rr 45.2%

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

       1. associate-/l* 48.6%

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

   14. Simplified 48.6%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+75}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-66}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 7.1 \cdot 10^{+53}:\\ \;\;\;\;\frac{z}{-\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 7: 72.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{-69} \lor \neg \left(y \leq 1.05 \cdot 10^{-71}\right):\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.85e-69) (not (<= y 1.05e-71)))
   (* z (- -1.0 (/ x y)))
   (/ x (- 1.0 (/ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.85e-69) || !(y <= 1.05e-71)) {
		tmp = z * (-1.0 - (x / y));
	} else {
		tmp = x / (1.0 - (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) :: tmp
    if ((y <= (-1.85d-69)) .or. (.not. (y <= 1.05d-71))) then
        tmp = z * ((-1.0d0) - (x / y))
    else
        tmp = x / (1.0d0 - (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.85e-69) || !(y <= 1.05e-71)) {
		tmp = z * (-1.0 - (x / y));
	} else {
		tmp = x / (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.85e-69) or not (y <= 1.05e-71):
		tmp = z * (-1.0 - (x / y))
	else:
		tmp = x / (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.85e-69) || !(y <= 1.05e-71))
		tmp = Float64(z * Float64(-1.0 - Float64(x / y)));
	else
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.85e-69) || ~((y <= 1.05e-71)))
		tmp = z * (-1.0 - (x / y));
	else
		tmp = x / (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.85e-69], N[Not[LessEqual[y, 1.05e-71]], $MachinePrecision]], N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.8500000000000001e-69 or 1.0500000000000001e-71 < y

   1. Initial program 76.7%

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

   2. Taylor expanded in z around 0 63.6%

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

      1. associate-*r/ 63.6%

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

      2. +-commutative 63.6%

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

      3. *-commutative 63.6%

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

      4. associate-*r* 63.6%

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

      5. mul-1-neg 63.6%

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

      6. +-commutative 63.6%

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

   4. Simplified 63.6%

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

   5. Taylor expanded in y around 0 74.4%

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

      1. mul-1-neg 74.4%

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

      2. unsub-neg 74.4%

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

      3. mul-1-neg 74.4%

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

      4. associate-/l* 79.0%

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

   7. Simplified 79.0%

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

   8. Taylor expanded in z around 0 79.0%

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

      1. mul-1-neg 79.0%

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

      2. *-commutative 79.0%

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

   10. Simplified 79.0%

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

   if -1.8500000000000001e-69 < y < 1.0500000000000001e-71

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 84.8%

      \[\leadsto \color{blue}{\frac{x}{1 - \frac{y}{z}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{-69} \lor \neg \left(y \leq 1.05 \cdot 10^{-71}\right):\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \end{array} \]

Alternative 8: 72.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{-69}:\\ \;\;\;\;\left(-z\right) - \frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-72}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.75e-69)
   (- (- z) (/ z (/ y x)))
   (if (<= y 1.02e-72) (/ x (- 1.0 (/ y z))) (* z (- -1.0 (/ x y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.75e-69) {
		tmp = -z - (z / (y / x));
	} else if (y <= 1.02e-72) {
		tmp = x / (1.0 - (y / z));
	} else {
		tmp = z * (-1.0 - (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.75d-69)) then
        tmp = -z - (z / (y / x))
    else if (y <= 1.02d-72) then
        tmp = x / (1.0d0 - (y / z))
    else
        tmp = z * ((-1.0d0) - (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.75e-69) {
		tmp = -z - (z / (y / x));
	} else if (y <= 1.02e-72) {
		tmp = x / (1.0 - (y / z));
	} else {
		tmp = z * (-1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.75e-69:
		tmp = -z - (z / (y / x))
	elif y <= 1.02e-72:
		tmp = x / (1.0 - (y / z))
	else:
		tmp = z * (-1.0 - (x / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.75e-69)
		tmp = Float64(Float64(-z) - Float64(z / Float64(y / x)));
	elseif (y <= 1.02e-72)
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(z * Float64(-1.0 - Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.75e-69)
		tmp = -z - (z / (y / x));
	elseif (y <= 1.02e-72)
		tmp = x / (1.0 - (y / z));
	else
		tmp = z * (-1.0 - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.75e-69], N[((-z) - N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.02e-72], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.7500000000000001e-69

   1. Initial program 80.7%

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

   2. Taylor expanded in z around 0 57.7%

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

      1. associate-*r/ 57.7%

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

      2. +-commutative 57.7%

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

      3. *-commutative 57.7%

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

      4. associate-*r* 57.7%

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

      5. mul-1-neg 57.7%

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

      6. +-commutative 57.7%

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

   4. Simplified 57.7%

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

   5. Taylor expanded in y around 0 68.4%

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

      1. mul-1-neg 68.4%

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

      2. unsub-neg 68.4%

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

      3. mul-1-neg 68.4%

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

      4. associate-/l* 73.9%

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

   7. Simplified 73.9%

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

   if -1.7500000000000001e-69 < y < 1.02e-72

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 84.8%

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

   if 1.02e-72 < y

   1. Initial program 72.8%

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

   2. Taylor expanded in z around 0 69.5%

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

      1. associate-*r/ 69.5%

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

      2. +-commutative 69.5%

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

      3. *-commutative 69.5%

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

      4. associate-*r* 69.5%

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

      5. mul-1-neg 69.5%

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

      6. +-commutative 69.5%

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

   4. Simplified 69.5%

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

   5. Taylor expanded in y around 0 80.3%

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

      1. mul-1-neg 80.3%

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

      2. unsub-neg 80.3%

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

      3. mul-1-neg 80.3%

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

      4. associate-/l* 84.0%

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

   7. Simplified 84.0%

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

   8. Taylor expanded in z around 0 84.0%

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

      1. mul-1-neg 84.0%

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

      2. *-commutative 84.0%

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

   10. Simplified 84.0%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{-69}:\\ \;\;\;\;\left(-z\right) - \frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-72}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \]

Alternative 9: 65.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+74}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-71}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.15e+74) (- z) (if (<= y 2.7e-71) (+ x y) (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.15e+74) {
		tmp = -z;
	} else if (y <= 2.7e-71) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.15d+74)) then
        tmp = -z
    else if (y <= 2.7d-71) then
        tmp = x + y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.15e+74) {
		tmp = -z;
	} else if (y <= 2.7e-71) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.15e+74:
		tmp = -z
	elif y <= 2.7e-71:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.15e+74)
		tmp = Float64(-z);
	elseif (y <= 2.7e-71)
		tmp = Float64(x + y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.15e+74)
		tmp = -z;
	elseif (y <= 2.7e-71)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.15e+74], (-z), If[LessEqual[y, 2.7e-71], N[(x + y), $MachinePrecision], (-z)]]

Derivation

1. Split input into 2 regimes

2. if y < -1.1499999999999999e74 or 2.7000000000000001e-71 < y

   1. Initial program 72.9%

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

   2. Taylor expanded in y around inf 68.3%

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

      1. mul-1-neg 68.3%

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

   4. Simplified 68.3%

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

   if -1.1499999999999999e74 < y < 2.7000000000000001e-71

   1. Initial program 98.4%

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

   2. Taylor expanded in z around inf 74.2%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+74}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-71}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 10: 56.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{-46}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{-73}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.75e-46) (- z) (if (<= y 1.06e-73) x (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.75e-46) {
		tmp = -z;
	} else if (y <= 1.06e-73) {
		tmp = x;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.75d-46)) then
        tmp = -z
    else if (y <= 1.06d-73) then
        tmp = x
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.75e-46) {
		tmp = -z;
	} else if (y <= 1.06e-73) {
		tmp = x;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.75e-46:
		tmp = -z
	elif y <= 1.06e-73:
		tmp = x
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.75e-46)
		tmp = Float64(-z);
	elseif (y <= 1.06e-73)
		tmp = x;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.75e-46)
		tmp = -z;
	elseif (y <= 1.06e-73)
		tmp = x;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.75e-46], (-z), If[LessEqual[y, 1.06e-73], x, (-z)]]

Derivation

1. Split input into 2 regimes

2. if y < -1.7500000000000001e-46 or 1.05999999999999997e-73 < y

   1. Initial program 76.1%

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

   2. Taylor expanded in y around inf 63.0%

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

      1. mul-1-neg 63.0%

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

   4. Simplified 63.0%

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

   if -1.7500000000000001e-46 < y < 1.05999999999999997e-73

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 70.0%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{-46}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{-73}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 11: 40.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{-193}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-95}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -8.2e-193) x (if (<= x 2e-95) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -8.2e-193) {
		tmp = x;
	} else if (x <= 2e-95) {
		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 <= (-8.2d-193)) then
        tmp = x
    else if (x <= 2d-95) 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 <= -8.2e-193) {
		tmp = x;
	} else if (x <= 2e-95) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -8.2e-193:
		tmp = x
	elif x <= 2e-95:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -8.2e-193)
		tmp = x;
	elseif (x <= 2e-95)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -8.2e-193)
		tmp = x;
	elseif (x <= 2e-95)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -8.2e-193], x, If[LessEqual[x, 2e-95], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -8.20000000000000005e-193 or 1.99999999999999998e-95 < x

   1. Initial program 87.8%

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

   2. Taylor expanded in y around 0 45.4%

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

   if -8.20000000000000005e-193 < x < 1.99999999999999998e-95

   1. Initial program 80.9%

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

   2. Taylor expanded in x around 0 67.9%

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

   3. Taylor expanded in y around 0 31.9%

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

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{-193}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-95}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 34.4% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 x)

C

double code(double x, double y, double z) {
	return x;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

public static double code(double x, double y, double z) {
	return x;
}

Python

def code(x, y, z):
	return x

Julia

function code(x, y, z)
	return x
end

MATLAB

function tmp = code(x, y, z)
	tmp = x;
end

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 85.7%

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

2. Taylor expanded in y around 0 35.3%

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

3. Final simplification 35.3%

   \[\leadsto x \]

Developer target: 93.8% 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 2023242 
(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))))