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

Percentage Accurate: 88.0% → 99.7%

Time: 7.2s

Alternatives: 9

Speedup: 0.5×

Specification

Math

\[\begin{array}{l} \\ \frac{x + y}{1 - \frac{y}{z}} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (+ x y) (- 1.0 (/ y z))))

C

double code(double x, double y, double z) {
	return (x + y) / (1.0 - (y / z));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + y) / (1.0d0 - (y / z))
end function

Java

public static double code(double x, double y, double z) {
	return (x + y) / (1.0 - (y / z));
}

Python

def code(x, y, z):
	return (x + y) / (1.0 - (y / z))

Julia

function code(x, y, z)
	return Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + y) / (1.0 - (y / z));
end

Wolfram

code[x_, y_, z_] := N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 88.0% 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: 99.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.25 \cdot 10^{+63} \lor \neg \left(y \leq 2 \cdot 10^{-23}\right):\\ \;\;\;\;z \cdot \frac{y + x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y + x}{1 - \frac{y}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.25e+63) (not (<= y 2e-23)))
   (* z (/ (+ y x) (- z y)))
   (/ (+ y x) (- 1.0 (/ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.25e+63) || !(y <= 2e-23)) {
		tmp = z * ((y + x) / (z - y));
	} else {
		tmp = (y + 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 <= (-3.25d+63)) .or. (.not. (y <= 2d-23))) then
        tmp = z * ((y + x) / (z - y))
    else
        tmp = (y + 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 <= -3.25e+63) || !(y <= 2e-23)) {
		tmp = z * ((y + x) / (z - y));
	} else {
		tmp = (y + x) / (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.25e+63) or not (y <= 2e-23):
		tmp = z * ((y + x) / (z - y))
	else:
		tmp = (y + x) / (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.25e+63) || !(y <= 2e-23))
		tmp = Float64(z * Float64(Float64(y + x) / Float64(z - y)));
	else
		tmp = Float64(Float64(y + x) / Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.25e+63) || ~((y <= 2e-23)))
		tmp = z * ((y + x) / (z - y));
	else
		tmp = (y + x) / (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.25e+63], N[Not[LessEqual[y, 2e-23]], $MachinePrecision]], N[(z * N[(N[(y + x), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y + x), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.24999999999999996e63 or 1.99999999999999992e-23 < y

   1. Initial program 71.3%

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

   3. Taylor expanded in z around 0 71.3%

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

      1. associate-/r/ 99.9%

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

   5. Applied egg-rr 99.9%

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

   if -3.24999999999999996e63 < y < 1.99999999999999992e-23

   1. Initial program 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.25 \cdot 10^{+63} \lor \neg \left(y \leq 2 \cdot 10^{-23}\right):\\ \;\;\;\;z \cdot \frac{y + x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y + x}{1 - \frac{y}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 74.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -4.7 \cdot 10^{+52}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-8}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-34}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-211}:\\ \;\;\;\;x \cdot \frac{z}{z - y}\\ \mathbf{elif}\;y \leq 0.0064:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- -1.0 (/ x y)))))
   (if (<= y -4.7e+52)
     t_0
     (if (<= y -4.4e-8)
       (+ y x)
       (if (<= y -2.2e-34)
         t_0
         (if (<= y 1.85e-211)
           (* x (/ z (- z y)))
           (if (<= y 0.0064) (+ y x) t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (-1.0 - (x / y));
	double tmp;
	if (y <= -4.7e+52) {
		tmp = t_0;
	} else if (y <= -4.4e-8) {
		tmp = y + x;
	} else if (y <= -2.2e-34) {
		tmp = t_0;
	} else if (y <= 1.85e-211) {
		tmp = x * (z / (z - y));
	} else if (y <= 0.0064) {
		tmp = y + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * ((-1.0d0) - (x / y))
    if (y <= (-4.7d+52)) then
        tmp = t_0
    else if (y <= (-4.4d-8)) then
        tmp = y + x
    else if (y <= (-2.2d-34)) then
        tmp = t_0
    else if (y <= 1.85d-211) then
        tmp = x * (z / (z - y))
    else if (y <= 0.0064d0) then
        tmp = y + x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (-1.0 - (x / y));
	double tmp;
	if (y <= -4.7e+52) {
		tmp = t_0;
	} else if (y <= -4.4e-8) {
		tmp = y + x;
	} else if (y <= -2.2e-34) {
		tmp = t_0;
	} else if (y <= 1.85e-211) {
		tmp = x * (z / (z - y));
	} else if (y <= 0.0064) {
		tmp = y + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (-1.0 - (x / y))
	tmp = 0
	if y <= -4.7e+52:
		tmp = t_0
	elif y <= -4.4e-8:
		tmp = y + x
	elif y <= -2.2e-34:
		tmp = t_0
	elif y <= 1.85e-211:
		tmp = x * (z / (z - y))
	elif y <= 0.0064:
		tmp = y + x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -4.7e+52)
		tmp = t_0;
	elseif (y <= -4.4e-8)
		tmp = Float64(y + x);
	elseif (y <= -2.2e-34)
		tmp = t_0;
	elseif (y <= 1.85e-211)
		tmp = Float64(x * Float64(z / Float64(z - y)));
	elseif (y <= 0.0064)
		tmp = Float64(y + x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (-1.0 - (x / y));
	tmp = 0.0;
	if (y <= -4.7e+52)
		tmp = t_0;
	elseif (y <= -4.4e-8)
		tmp = y + x;
	elseif (y <= -2.2e-34)
		tmp = t_0;
	elseif (y <= 1.85e-211)
		tmp = x * (z / (z - y));
	elseif (y <= 0.0064)
		tmp = y + x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.7e+52], t$95$0, If[LessEqual[y, -4.4e-8], N[(y + x), $MachinePrecision], If[LessEqual[y, -2.2e-34], t$95$0, If[LessEqual[y, 1.85e-211], N[(x * N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.0064], N[(y + x), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.7e52 or -4.3999999999999997e-8 < y < -2.1999999999999999e-34 or 0.00640000000000000031 < y

   1. Initial program 71.8%

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

   3. Taylor expanded in y around inf 66.7%

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

   5. Simplified 77.0%

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

   6. Taylor expanded in z around 0 81.6%

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

      1. sub-neg 81.6%

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

      2. metadata-eval 81.6%

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

      3. metadata-eval 81.6%

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

      4. distribute-lft-in 81.6%

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

      5. +-commutative 81.6%

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

      6. distribute-lft-in 81.6%

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

      7. metadata-eval 81.6%

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

      8. neg-mul-1 81.6%

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

      9. sub-neg 81.6%

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

   8. Simplified 81.6%

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

   if -4.7e52 < y < -4.3999999999999997e-8 or 1.8499999999999999e-211 < y < 0.00640000000000000031

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 76.2%

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

      1. +-commutative 76.2%

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

   5. Simplified 76.2%

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

   if -2.1999999999999999e-34 < y < 1.8499999999999999e-211

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 99.8%

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

   4. Taylor expanded in x around inf 72.3%

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

      1. associate-/l* 86.7%

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

   6. Simplified 86.7%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+52}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-8}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-34}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-211}:\\ \;\;\;\;x \cdot \frac{z}{z - y}\\ \mathbf{elif}\;y \leq 0.0064:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -6 \cdot 10^{+52}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-6}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-35}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-210}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 0.68:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- -1.0 (/ x y)))))
   (if (<= y -6e+52)
     t_0
     (if (<= y -1.05e-6)
       (+ y x)
       (if (<= y -3.8e-35)
         t_0
         (if (<= y 2.1e-210)
           (/ x (- 1.0 (/ y z)))
           (if (<= y 0.68) (+ y x) t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (-1.0 - (x / y));
	double tmp;
	if (y <= -6e+52) {
		tmp = t_0;
	} else if (y <= -1.05e-6) {
		tmp = y + x;
	} else if (y <= -3.8e-35) {
		tmp = t_0;
	} else if (y <= 2.1e-210) {
		tmp = x / (1.0 - (y / z));
	} else if (y <= 0.68) {
		tmp = y + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * ((-1.0d0) - (x / y))
    if (y <= (-6d+52)) then
        tmp = t_0
    else if (y <= (-1.05d-6)) then
        tmp = y + x
    else if (y <= (-3.8d-35)) then
        tmp = t_0
    else if (y <= 2.1d-210) then
        tmp = x / (1.0d0 - (y / z))
    else if (y <= 0.68d0) then
        tmp = y + x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (-1.0 - (x / y));
	double tmp;
	if (y <= -6e+52) {
		tmp = t_0;
	} else if (y <= -1.05e-6) {
		tmp = y + x;
	} else if (y <= -3.8e-35) {
		tmp = t_0;
	} else if (y <= 2.1e-210) {
		tmp = x / (1.0 - (y / z));
	} else if (y <= 0.68) {
		tmp = y + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (-1.0 - (x / y))
	tmp = 0
	if y <= -6e+52:
		tmp = t_0
	elif y <= -1.05e-6:
		tmp = y + x
	elif y <= -3.8e-35:
		tmp = t_0
	elif y <= 2.1e-210:
		tmp = x / (1.0 - (y / z))
	elif y <= 0.68:
		tmp = y + x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -6e+52)
		tmp = t_0;
	elseif (y <= -1.05e-6)
		tmp = Float64(y + x);
	elseif (y <= -3.8e-35)
		tmp = t_0;
	elseif (y <= 2.1e-210)
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	elseif (y <= 0.68)
		tmp = Float64(y + x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (-1.0 - (x / y));
	tmp = 0.0;
	if (y <= -6e+52)
		tmp = t_0;
	elseif (y <= -1.05e-6)
		tmp = y + x;
	elseif (y <= -3.8e-35)
		tmp = t_0;
	elseif (y <= 2.1e-210)
		tmp = x / (1.0 - (y / z));
	elseif (y <= 0.68)
		tmp = y + x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6e+52], t$95$0, If[LessEqual[y, -1.05e-6], N[(y + x), $MachinePrecision], If[LessEqual[y, -3.8e-35], t$95$0, If[LessEqual[y, 2.1e-210], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.68], N[(y + x), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6e52 or -1.0499999999999999e-6 < y < -3.8000000000000001e-35 or 0.680000000000000049 < y

   1. Initial program 71.8%

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

   3. Taylor expanded in y around inf 66.7%

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

   5. Simplified 77.0%

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

   6. Taylor expanded in z around 0 81.6%

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

      1. sub-neg 81.6%

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

      2. metadata-eval 81.6%

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

      3. metadata-eval 81.6%

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

      4. distribute-lft-in 81.6%

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

      5. +-commutative 81.6%

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

      6. distribute-lft-in 81.6%

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

      7. metadata-eval 81.6%

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

      8. neg-mul-1 81.6%

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

      9. sub-neg 81.6%

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

   8. Simplified 81.6%

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

   if -6e52 < y < -1.0499999999999999e-6 or 2.10000000000000016e-210 < y < 0.680000000000000049

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 76.2%

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

      1. +-commutative 76.2%

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

   5. Simplified 76.2%

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

   if -3.8000000000000001e-35 < y < 2.10000000000000016e-210

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 86.8%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+52}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-6}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-35}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-210}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 0.68:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 68.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{z}{z - y}\\ \mathbf{if}\;y \leq -7.6 \cdot 10^{+52}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-211}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-87}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+54}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (/ z (- z y)))))
   (if (<= y -7.6e+52)
     (- z)
     (if (<= y 2.3e-211)
       t_0
       (if (<= y 3.3e-87) (+ y x) (if (<= y 1.9e+54) t_0 (- z)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z / (z - y));
	double tmp;
	if (y <= -7.6e+52) {
		tmp = -z;
	} else if (y <= 2.3e-211) {
		tmp = t_0;
	} else if (y <= 3.3e-87) {
		tmp = y + x;
	} else if (y <= 1.9e+54) {
		tmp = t_0;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (z / (z - y))
    if (y <= (-7.6d+52)) then
        tmp = -z
    else if (y <= 2.3d-211) then
        tmp = t_0
    else if (y <= 3.3d-87) then
        tmp = y + x
    else if (y <= 1.9d+54) then
        tmp = t_0
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (z / (z - y));
	double tmp;
	if (y <= -7.6e+52) {
		tmp = -z;
	} else if (y <= 2.3e-211) {
		tmp = t_0;
	} else if (y <= 3.3e-87) {
		tmp = y + x;
	} else if (y <= 1.9e+54) {
		tmp = t_0;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z / (z - y))
	tmp = 0
	if y <= -7.6e+52:
		tmp = -z
	elif y <= 2.3e-211:
		tmp = t_0
	elif y <= 3.3e-87:
		tmp = y + x
	elif y <= 1.9e+54:
		tmp = t_0
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z / Float64(z - y)))
	tmp = 0.0
	if (y <= -7.6e+52)
		tmp = Float64(-z);
	elseif (y <= 2.3e-211)
		tmp = t_0;
	elseif (y <= 3.3e-87)
		tmp = Float64(y + x);
	elseif (y <= 1.9e+54)
		tmp = t_0;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z / (z - y));
	tmp = 0.0;
	if (y <= -7.6e+52)
		tmp = -z;
	elseif (y <= 2.3e-211)
		tmp = t_0;
	elseif (y <= 3.3e-87)
		tmp = y + x;
	elseif (y <= 1.9e+54)
		tmp = t_0;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.6e+52], (-z), If[LessEqual[y, 2.3e-211], t$95$0, If[LessEqual[y, 3.3e-87], N[(y + x), $MachinePrecision], If[LessEqual[y, 1.9e+54], t$95$0, (-z)]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.5999999999999999e52 or 1.9000000000000001e54 < y

   1. Initial program 69.1%

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

   3. Taylor expanded in y around inf 68.8%

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

      1. mul-1-neg 68.8%

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

   5. Simplified 68.8%

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

   if -7.5999999999999999e52 < y < 2.29999999999999988e-211 or 3.3e-87 < y < 1.9000000000000001e54

   1. Initial program 99.2%

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

   3. Taylor expanded in z around 0 99.2%

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

   4. Taylor expanded in x around inf 62.5%

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

      1. associate-/l* 78.5%

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

   6. Simplified 78.5%

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

   if 2.29999999999999988e-211 < y < 3.3e-87

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 81.0%

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

      1. +-commutative 81.0%

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

   5. Simplified 81.0%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+52}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-211}:\\ \;\;\;\;x \cdot \frac{z}{z - y}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-87}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+54}:\\ \;\;\;\;x \cdot \frac{z}{z - y}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 94.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-126} \lor \neg \left(y \leq 5.4 \cdot 10^{-242}\right):\\ \;\;\;\;z \cdot \frac{y + x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1e-126) (not (<= y 5.4e-242)))
   (* z (/ (+ y x) (- z y)))
   (/ x (- 1.0 (/ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1e-126) || !(y <= 5.4e-242)) {
		tmp = z * ((y + x) / (z - 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 <= (-1d-126)) .or. (.not. (y <= 5.4d-242))) then
        tmp = z * ((y + x) / (z - 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 <= -1e-126) || !(y <= 5.4e-242)) {
		tmp = z * ((y + x) / (z - y));
	} else {
		tmp = x / (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1e-126) or not (y <= 5.4e-242):
		tmp = z * ((y + x) / (z - y))
	else:
		tmp = x / (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1e-126) || !(y <= 5.4e-242))
		tmp = Float64(z * Float64(Float64(y + x) / Float64(z - 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 <= -1e-126) || ~((y <= 5.4e-242)))
		tmp = z * ((y + x) / (z - y));
	else
		tmp = x / (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1e-126], N[Not[LessEqual[y, 5.4e-242]], $MachinePrecision]], N[(z * N[(N[(y + x), $MachinePrecision] / N[(z - 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 < -9.9999999999999995e-127 or 5.4e-242 < y

   1. Initial program 83.4%

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

   3. Taylor expanded in z around 0 83.4%

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

      1. associate-/r/ 95.5%

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

   5. Applied egg-rr 95.5%

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

   if -9.9999999999999995e-127 < y < 5.4e-242

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 93.9%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-126} \lor \neg \left(y \leq 5.4 \cdot 10^{-242}\right):\\ \;\;\;\;z \cdot \frac{y + x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+55} \lor \neg \left(y \leq 2.1 \cdot 10^{+53}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.8e+55) (not (<= y 2.1e+53))) (- z) (+ y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.8e+55) || !(y <= 2.1e+53)) {
		tmp = -z;
	} else {
		tmp = 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) :: tmp
    if ((y <= (-1.8d+55)) .or. (.not. (y <= 2.1d+53))) then
        tmp = -z
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.8e+55) || !(y <= 2.1e+53)) {
		tmp = -z;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.8e+55) or not (y <= 2.1e+53):
		tmp = -z
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.8e+55) || !(y <= 2.1e+53))
		tmp = Float64(-z);
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.8e+55) || ~((y <= 2.1e+53)))
		tmp = -z;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.8e+55], N[Not[LessEqual[y, 2.1e+53]], $MachinePrecision]], (-z), N[(y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.79999999999999994e55 or 2.1000000000000002e53 < y

   1. Initial program 68.5%

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

   3. Taylor expanded in y around inf 68.2%

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

      1. mul-1-neg 68.2%

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

   5. Simplified 68.2%

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

   if -1.79999999999999994e55 < y < 2.1000000000000002e53

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 72.5%

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

      1. +-commutative 72.5%

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

   5. Simplified 72.5%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+55} \lor \neg \left(y \leq 2.1 \cdot 10^{+53}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 58.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+54} \lor \neg \left(y \leq 2.8 \cdot 10^{+53}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.9e+54) (not (<= y 2.8e+53))) (- z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.9e+54) || !(y <= 2.8e+53)) {
		tmp = -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-3.9d+54)) .or. (.not. (y <= 2.8d+53))) then
        tmp = -z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.9e+54) || !(y <= 2.8e+53)) {
		tmp = -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.9e+54) or not (y <= 2.8e+53):
		tmp = -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.9e+54) || !(y <= 2.8e+53))
		tmp = Float64(-z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.9e+54) || ~((y <= 2.8e+53)))
		tmp = -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.9e+54], N[Not[LessEqual[y, 2.8e+53]], $MachinePrecision]], (-z), x]

Derivation

1. Split input into 2 regimes

2. if y < -3.9000000000000003e54 or 2.8e53 < y

   1. Initial program 68.5%

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

   3. Taylor expanded in y around inf 68.2%

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

      1. mul-1-neg 68.2%

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

   5. Simplified 68.2%

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

   if -3.9000000000000003e54 < y < 2.8e53

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 57.8%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+54} \lor \neg \left(y \leq 2.8 \cdot 10^{+53}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 40.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.32 \cdot 10^{-211}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-113}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.32e-211) x (if (<= x 5e-113) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.32e-211) {
		tmp = x;
	} else if (x <= 5e-113) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.32d-211)) then
        tmp = x
    else if (x <= 5d-113) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.32e-211) {
		tmp = x;
	} else if (x <= 5e-113) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.32e-211:
		tmp = x
	elif x <= 5e-113:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.32e-211)
		tmp = x;
	elseif (x <= 5e-113)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.32e-211)
		tmp = x;
	elseif (x <= 5e-113)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.32e-211], x, If[LessEqual[x, 5e-113], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3200000000000001e-211 or 4.9999999999999997e-113 < x

   1. Initial program 86.8%

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

   3. Taylor expanded in y around 0 44.5%

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

   if -1.3200000000000001e-211 < x < 4.9999999999999997e-113

   1. Initial program 89.3%

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

   3. Taylor expanded in x around 0 75.4%

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

   4. Taylor expanded in y around 0 40.8%

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

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.32 \cdot 10^{-211}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-113}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 34.7% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 87.4%

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

3. Taylor expanded in y around 0 37.8%

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

4. Final simplification 37.8%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 93.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y + x}{-y} \cdot z\\ \mathbf{if}\;y < -3.7429310762689856 \cdot 10^{+171}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y < 3.5534662456086734 \cdot 10^{+168}:\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024077 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, A"
  :precision binary64

  :alt
  (if (< y -3.7429310762689856e+171) (* (/ (+ y x) (- y)) z) (if (< y 3.5534662456086734e+168) (/ (+ x y) (- 1.0 (/ y z))) (* (/ (+ y x) (- y)) z)))

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