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

Percentage Accurate: 87.6% → 99.6%

Time: 7.0s

Alternatives: 9

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 87.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{-284} \lor \neg \left(t\_0 \leq 10^{-268}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{\left(-y\right) - x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -1e-284) (not (<= t_0 1e-268)))
     t_0
     (* z (/ (- (- y) x) y)))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -1e-284) || !(t_0 <= 1e-268)) {
		tmp = t_0;
	} else {
		tmp = z * ((-y - x) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x + y) / (1.0d0 - (y / z))
    if ((t_0 <= (-1d-284)) .or. (.not. (t_0 <= 1d-268))) then
        tmp = t_0
    else
        tmp = z * ((-y - x) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -1e-284) || !(t_0 <= 1e-268)) {
		tmp = t_0;
	} else {
		tmp = z * ((-y - x) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -1e-284) or not (t_0 <= 1e-268):
		tmp = t_0
	else:
		tmp = z * ((-y - x) / y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if ((t_0 <= -1e-284) || !(t_0 <= 1e-268))
		tmp = t_0;
	else
		tmp = Float64(z * Float64(Float64(Float64(-y) - x) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + y) / (1.0 - (y / z));
	tmp = 0.0;
	if ((t_0 <= -1e-284) || ~((t_0 <= 1e-268)))
		tmp = t_0;
	else
		tmp = z * ((-y - x) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -1e-284], N[Not[LessEqual[t$95$0, 1e-268]], $MachinePrecision]], t$95$0, N[(z * N[(N[((-y) - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -1.00000000000000004e-284 or 9.99999999999999958e-269 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z)))

   1. Initial program 99.9%

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

   if -1.00000000000000004e-284 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < 9.99999999999999958e-269

   1. Initial program 23.6%

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

   3. Taylor expanded in z around 0 87.0%

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

      1. mul-1-neg 87.0%

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

      2. associate-/l* 99.9%

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

      3. distribute-rgt-neg-in 99.9%

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

      4. distribute-neg-frac2 99.9%

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

      5. +-commutative 99.9%

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

   5. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -1 \cdot 10^{-284} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 10^{-268}\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{\left(-y\right) - x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 68.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{+132}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-46}:\\ \;\;\;\;\frac{y}{t\_0}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-81}:\\ \;\;\;\;\frac{x}{t\_0}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+258}:\\ \;\;\;\;y \cdot \frac{z}{z - y}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))))
   (if (<= y -3.8e+132)
     (- z)
     (if (<= y -1e-46)
       (/ y t_0)
       (if (<= y 1.1e-81)
         (/ x t_0)
         (if (<= y 1.4e+258) (* y (/ z (- z y))) (- z)))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double tmp;
	if (y <= -3.8e+132) {
		tmp = -z;
	} else if (y <= -1e-46) {
		tmp = y / t_0;
	} else if (y <= 1.1e-81) {
		tmp = x / t_0;
	} else if (y <= 1.4e+258) {
		tmp = y * (z / (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) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 - (y / z)
    if (y <= (-3.8d+132)) then
        tmp = -z
    else if (y <= (-1d-46)) then
        tmp = y / t_0
    else if (y <= 1.1d-81) then
        tmp = x / t_0
    else if (y <= 1.4d+258) then
        tmp = y * (z / (z - y))
    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 <= -3.8e+132) {
		tmp = -z;
	} else if (y <= -1e-46) {
		tmp = y / t_0;
	} else if (y <= 1.1e-81) {
		tmp = x / t_0;
	} else if (y <= 1.4e+258) {
		tmp = y * (z / (z - y));
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	tmp = 0
	if y <= -3.8e+132:
		tmp = -z
	elif y <= -1e-46:
		tmp = y / t_0
	elif y <= 1.1e-81:
		tmp = x / t_0
	elif y <= 1.4e+258:
		tmp = y * (z / (z - y))
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y / z))
	tmp = 0.0
	if (y <= -3.8e+132)
		tmp = Float64(-z);
	elseif (y <= -1e-46)
		tmp = Float64(y / t_0);
	elseif (y <= 1.1e-81)
		tmp = Float64(x / t_0);
	elseif (y <= 1.4e+258)
		tmp = Float64(y * Float64(z / Float64(z - y)));
	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 <= -3.8e+132)
		tmp = -z;
	elseif (y <= -1e-46)
		tmp = y / t_0;
	elseif (y <= 1.1e-81)
		tmp = x / t_0;
	elseif (y <= 1.4e+258)
		tmp = y * (z / (z - y));
	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, -3.8e+132], (-z), If[LessEqual[y, -1e-46], N[(y / t$95$0), $MachinePrecision], If[LessEqual[y, 1.1e-81], N[(x / t$95$0), $MachinePrecision], If[LessEqual[y, 1.4e+258], N[(y * N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], (-z)]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.80000000000000006e132 or 1.39999999999999991e258 < y

   1. Initial program 53.5%

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

   3. Taylor expanded in y around inf 84.4%

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

      1. neg-mul-1 84.4%

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

   5. Simplified 84.4%

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

   if -3.80000000000000006e132 < y < -1.00000000000000002e-46

   1. Initial program 97.0%

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

   3. Taylor expanded in x around 0 66.1%

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

   if -1.00000000000000002e-46 < y < 1.1e-81

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 85.2%

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

   if 1.1e-81 < y < 1.39999999999999991e258

   1. Initial program 90.6%

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

   3. Taylor expanded in x around 0 69.2%

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

      1. clear-num 69.1%

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

      2. associate-/r/ 69.1%

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

      3. *-inverses 69.1%

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

      4. div-sub 69.1%

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

      5. clear-num 69.7%

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

   5. Applied egg-rr 69.7%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+132}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-46}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-81}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+258}:\\ \;\;\;\;y \cdot \frac{z}{z - y}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 68.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \frac{z}{z - y}\\ \mathbf{if}\;y \leq -8.6 \cdot 10^{+132}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-47}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-78}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+258}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (/ z (- z y)))))
   (if (<= y -8.6e+132)
     (- z)
     (if (<= y -7e-47)
       t_0
       (if (<= y 1.85e-78)
         (/ x (- 1.0 (/ y z)))
         (if (<= y 1.45e+258) t_0 (- z)))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (z / (z - y));
	double tmp;
	if (y <= -8.6e+132) {
		tmp = -z;
	} else if (y <= -7e-47) {
		tmp = t_0;
	} else if (y <= 1.85e-78) {
		tmp = x / (1.0 - (y / z));
	} else if (y <= 1.45e+258) {
		tmp = t_0;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * (z / (z - y))
    if (y <= (-8.6d+132)) then
        tmp = -z
    else if (y <= (-7d-47)) then
        tmp = t_0
    else if (y <= 1.85d-78) then
        tmp = x / (1.0d0 - (y / z))
    else if (y <= 1.45d+258) then
        tmp = t_0
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (z / (z - y));
	double tmp;
	if (y <= -8.6e+132) {
		tmp = -z;
	} else if (y <= -7e-47) {
		tmp = t_0;
	} else if (y <= 1.85e-78) {
		tmp = x / (1.0 - (y / z));
	} else if (y <= 1.45e+258) {
		tmp = t_0;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (z / (z - y))
	tmp = 0
	if y <= -8.6e+132:
		tmp = -z
	elif y <= -7e-47:
		tmp = t_0
	elif y <= 1.85e-78:
		tmp = x / (1.0 - (y / z))
	elif y <= 1.45e+258:
		tmp = t_0
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(z / Float64(z - y)))
	tmp = 0.0
	if (y <= -8.6e+132)
		tmp = Float64(-z);
	elseif (y <= -7e-47)
		tmp = t_0;
	elseif (y <= 1.85e-78)
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	elseif (y <= 1.45e+258)
		tmp = t_0;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (z / (z - y));
	tmp = 0.0;
	if (y <= -8.6e+132)
		tmp = -z;
	elseif (y <= -7e-47)
		tmp = t_0;
	elseif (y <= 1.85e-78)
		tmp = x / (1.0 - (y / z));
	elseif (y <= 1.45e+258)
		tmp = t_0;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.6e+132], (-z), If[LessEqual[y, -7e-47], t$95$0, If[LessEqual[y, 1.85e-78], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.45e+258], t$95$0, (-z)]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.59999999999999964e132 or 1.4500000000000001e258 < y

   1. Initial program 53.5%

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

   3. Taylor expanded in y around inf 84.4%

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

      1. neg-mul-1 84.4%

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

   5. Simplified 84.4%

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

   if -8.59999999999999964e132 < y < -6.9999999999999996e-47 or 1.85000000000000003e-78 < y < 1.4500000000000001e258

   1. Initial program 92.6%

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

   3. Taylor expanded in x around 0 68.2%

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

      1. clear-num 68.1%

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

      2. associate-/r/ 68.1%

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

      3. *-inverses 68.1%

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

      4. div-sub 68.1%

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

      5. clear-num 68.6%

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

   5. Applied egg-rr 68.6%

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

   if -6.9999999999999996e-47 < y < 1.85000000000000003e-78

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 85.2%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.6 \cdot 10^{+132}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-47}:\\ \;\;\;\;y \cdot \frac{z}{z - y}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-78}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+258}:\\ \;\;\;\;y \cdot \frac{z}{z - y}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 68.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \frac{z}{z - y}\\ \mathbf{if}\;y \leq -2.9 \cdot 10^{+128}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-43}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+18}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+258}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (/ z (- z y)))))
   (if (<= y -2.9e+128)
     (- z)
     (if (<= y -3.4e-43)
       t_0
       (if (<= y 1.55e+18) (+ x y) (if (<= y 1.4e+258) t_0 (- z)))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (z / (z - y));
	double tmp;
	if (y <= -2.9e+128) {
		tmp = -z;
	} else if (y <= -3.4e-43) {
		tmp = t_0;
	} else if (y <= 1.55e+18) {
		tmp = x + y;
	} else if (y <= 1.4e+258) {
		tmp = t_0;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * (z / (z - y))
    if (y <= (-2.9d+128)) then
        tmp = -z
    else if (y <= (-3.4d-43)) then
        tmp = t_0
    else if (y <= 1.55d+18) then
        tmp = x + y
    else if (y <= 1.4d+258) then
        tmp = t_0
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (z / (z - y));
	double tmp;
	if (y <= -2.9e+128) {
		tmp = -z;
	} else if (y <= -3.4e-43) {
		tmp = t_0;
	} else if (y <= 1.55e+18) {
		tmp = x + y;
	} else if (y <= 1.4e+258) {
		tmp = t_0;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (z / (z - y))
	tmp = 0
	if y <= -2.9e+128:
		tmp = -z
	elif y <= -3.4e-43:
		tmp = t_0
	elif y <= 1.55e+18:
		tmp = x + y
	elif y <= 1.4e+258:
		tmp = t_0
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(z / Float64(z - y)))
	tmp = 0.0
	if (y <= -2.9e+128)
		tmp = Float64(-z);
	elseif (y <= -3.4e-43)
		tmp = t_0;
	elseif (y <= 1.55e+18)
		tmp = Float64(x + y);
	elseif (y <= 1.4e+258)
		tmp = t_0;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (z / (z - y));
	tmp = 0.0;
	if (y <= -2.9e+128)
		tmp = -z;
	elseif (y <= -3.4e-43)
		tmp = t_0;
	elseif (y <= 1.55e+18)
		tmp = x + y;
	elseif (y <= 1.4e+258)
		tmp = t_0;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.9e+128], (-z), If[LessEqual[y, -3.4e-43], t$95$0, If[LessEqual[y, 1.55e+18], N[(x + y), $MachinePrecision], If[LessEqual[y, 1.4e+258], t$95$0, (-z)]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.9e128 or 1.39999999999999991e258 < y

   1. Initial program 53.5%

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

   3. Taylor expanded in y around inf 84.4%

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

      1. neg-mul-1 84.4%

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

   5. Simplified 84.4%

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

   if -2.9e128 < y < -3.4000000000000001e-43 or 1.55e18 < y < 1.39999999999999991e258

   1. Initial program 90.9%

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

   3. Taylor expanded in x around 0 68.9%

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

      1. clear-num 68.8%

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

      2. associate-/r/ 68.8%

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

      3. *-inverses 68.8%

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

      4. div-sub 68.8%

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

      5. clear-num 69.3%

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

   5. Applied egg-rr 69.3%

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

   if -3.4000000000000001e-43 < y < 1.55e18

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 75.2%

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

      1. +-commutative 75.2%

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

   5. Simplified 75.2%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+128}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-43}:\\ \;\;\;\;y \cdot \frac{z}{z - y}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+18}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+258}:\\ \;\;\;\;y \cdot \frac{z}{z - y}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \frac{\left(-y\right) - x}{y}\\ \mathbf{if}\;y \leq -2.22 \cdot 10^{-41}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-79}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+39}:\\ \;\;\;\;y \cdot \frac{z}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (/ (- (- y) x) y))))
   (if (<= y -2.22e-41)
     t_0
     (if (<= y 8.6e-79)
       (/ x (- 1.0 (/ y z)))
       (if (<= y 7.8e+39) (* y (/ z (- z y))) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = z * ((-y - x) / y);
	double tmp;
	if (y <= -2.22e-41) {
		tmp = t_0;
	} else if (y <= 8.6e-79) {
		tmp = x / (1.0 - (y / z));
	} else if (y <= 7.8e+39) {
		tmp = y * (z / (z - y));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * ((-y - x) / y)
    if (y <= (-2.22d-41)) then
        tmp = t_0
    else if (y <= 8.6d-79) then
        tmp = x / (1.0d0 - (y / z))
    else if (y <= 7.8d+39) then
        tmp = y * (z / (z - y))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * ((-y - x) / y);
	double tmp;
	if (y <= -2.22e-41) {
		tmp = t_0;
	} else if (y <= 8.6e-79) {
		tmp = x / (1.0 - (y / z));
	} else if (y <= 7.8e+39) {
		tmp = y * (z / (z - y));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * ((-y - x) / y)
	tmp = 0
	if y <= -2.22e-41:
		tmp = t_0
	elif y <= 8.6e-79:
		tmp = x / (1.0 - (y / z))
	elif y <= 7.8e+39:
		tmp = y * (z / (z - y))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(Float64(Float64(-y) - x) / y))
	tmp = 0.0
	if (y <= -2.22e-41)
		tmp = t_0;
	elseif (y <= 8.6e-79)
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	elseif (y <= 7.8e+39)
		tmp = Float64(y * Float64(z / Float64(z - y)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * ((-y - x) / y);
	tmp = 0.0;
	if (y <= -2.22e-41)
		tmp = t_0;
	elseif (y <= 8.6e-79)
		tmp = x / (1.0 - (y / z));
	elseif (y <= 7.8e+39)
		tmp = y * (z / (z - y));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(N[((-y) - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.22e-41], t$95$0, If[LessEqual[y, 8.6e-79], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.8e+39], N[(y * N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.2200000000000001e-41 or 7.8000000000000002e39 < y

   1. Initial program 75.2%

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

   3. Taylor expanded in z around 0 63.7%

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

      1. mul-1-neg 63.7%

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

      2. associate-/l* 78.0%

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

      3. distribute-rgt-neg-in 78.0%

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

      4. distribute-neg-frac2 78.0%

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

      5. +-commutative 78.0%

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

   5. Simplified 78.0%

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

   if -2.2200000000000001e-41 < y < 8.59999999999999963e-79

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 84.3%

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

   if 8.59999999999999963e-79 < y < 7.8000000000000002e39

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 73.5%

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

      1. clear-num 73.6%

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

      2. associate-/r/ 73.4%

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

      3. *-inverses 73.4%

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

      4. div-sub 73.4%

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

      5. clear-num 73.6%

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

   5. Applied egg-rr 73.6%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.22 \cdot 10^{-41}:\\ \;\;\;\;z \cdot \frac{\left(-y\right) - x}{y}\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-79}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+39}:\\ \;\;\;\;y \cdot \frac{z}{z - y}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{\left(-y\right) - x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 57.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.85 \cdot 10^{-41}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-31}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 10000:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.85e-41) (- z) (if (<= y 6e-31) x (if (<= y 10000.0) y (- z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.85e-41) {
		tmp = -z;
	} else if (y <= 6e-31) {
		tmp = x;
	} else if (y <= 10000.0) {
		tmp = 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 <= (-2.85d-41)) then
        tmp = -z
    else if (y <= 6d-31) then
        tmp = x
    else if (y <= 10000.0d0) then
        tmp = 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 <= -2.85e-41) {
		tmp = -z;
	} else if (y <= 6e-31) {
		tmp = x;
	} else if (y <= 10000.0) {
		tmp = y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.85e-41:
		tmp = -z
	elif y <= 6e-31:
		tmp = x
	elif y <= 10000.0:
		tmp = y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.85e-41)
		tmp = Float64(-z);
	elseif (y <= 6e-31)
		tmp = x;
	elseif (y <= 10000.0)
		tmp = y;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.85e-41)
		tmp = -z;
	elseif (y <= 6e-31)
		tmp = x;
	elseif (y <= 10000.0)
		tmp = y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.85e-41], (-z), If[LessEqual[y, 6e-31], x, If[LessEqual[y, 10000.0], y, (-z)]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.85000000000000023e-41 or 1e4 < y

   1. Initial program 76.6%

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

   3. Taylor expanded in y around inf 63.4%

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

      1. neg-mul-1 63.4%

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

   5. Simplified 63.4%

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

   if -2.85000000000000023e-41 < y < 5.99999999999999962e-31

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 65.4%

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

   if 5.99999999999999962e-31 < y < 1e4

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 83.8%

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

      1. +-commutative 83.8%

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

   5. Simplified 83.8%

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

   6. Taylor expanded in y around inf 68.0%

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

Alternative 7: 67.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+76} \lor \neg \left(y \leq 1.5 \cdot 10^{+18}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1e+76) (not (<= y 1.5e+18))) (- z) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1e+76) || !(y <= 1.5e+18)) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1d+76)) .or. (.not. (y <= 1.5d+18))) then
        tmp = -z
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1e+76) || !(y <= 1.5e+18)) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1e+76) or not (y <= 1.5e+18):
		tmp = -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1e+76) || !(y <= 1.5e+18))
		tmp = Float64(-z);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1e+76) || ~((y <= 1.5e+18)))
		tmp = -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1e+76], N[Not[LessEqual[y, 1.5e+18]], $MachinePrecision]], (-z), N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1e76 or 1.5e18 < y

   1. Initial program 73.1%

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

   3. Taylor expanded in y around inf 67.2%

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

      1. neg-mul-1 67.2%

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

   5. Simplified 67.2%

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

   if -1e76 < y < 1.5e18

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 71.8%

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

      1. +-commutative 71.8%

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

   5. Simplified 71.8%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+76} \lor \neg \left(y \leq 1.5 \cdot 10^{+18}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 41.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{-137}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-144}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.5e-137) x (if (<= x 5.8e-144) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.5e-137) {
		tmp = x;
	} else if (x <= 5.8e-144) {
		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 <= (-1.5d-137)) then
        tmp = x
    else if (x <= 5.8d-144) 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 <= -1.5e-137) {
		tmp = x;
	} else if (x <= 5.8e-144) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.5e-137:
		tmp = x
	elif x <= 5.8e-144:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.5e-137)
		tmp = x;
	elseif (x <= 5.8e-144)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.5e-137)
		tmp = x;
	elseif (x <= 5.8e-144)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.5e-137], x, If[LessEqual[x, 5.8e-144], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.4999999999999999e-137 or 5.8000000000000004e-144 < x

   1. Initial program 87.5%

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

   3. Taylor expanded in y around 0 46.6%

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

   if -1.4999999999999999e-137 < x < 5.8000000000000004e-144

   1. Initial program 87.1%

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

   3. Taylor expanded in z around inf 43.2%

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

      1. +-commutative 43.2%

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

   5. Simplified 43.2%

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

   6. Taylor expanded in y around inf 38.3%

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

Alternative 9: 34.5% 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 34.6%

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

Developer Target 1: 93.5% 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 2024137 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, A"
  :precision binary64

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

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