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

Percentage Accurate: 87.5% → 99.1%

Time: 7.3s

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: 87.5% 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: 99.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{-236} \lor \neg \left(t\_0 \leq 0\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{y}{\left(-y\right) - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -1e-236) (not (<= t_0 0.0))) t_0 (/ z (/ y (- (- 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-236) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = z / (y / (-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-236)) .or. (.not. (t_0 <= 0.0d0))) then
        tmp = t_0
    else
        tmp = z / (y / (-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-236) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = z / (y / (-y - x));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -1e-236) or not (t_0 <= 0.0):
		tmp = t_0
	else:
		tmp = z / (y / (-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-236) || !(t_0 <= 0.0))
		tmp = t_0;
	else
		tmp = Float64(z / Float64(y / Float64(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-236) || ~((t_0 <= 0.0)))
		tmp = t_0;
	else
		tmp = z / (y / (-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-236], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], t$95$0, N[(z / N[(y / N[((-y) - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -1e-236 or -0.0 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z)))

   1. Initial program 99.9%

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

   if -1e-236 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -0.0

   1. Initial program 11.6%

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

   3. Taylor expanded in z around 0 95.0%

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

      1. mul-1-neg 95.0%

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

      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%

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

      1. associate-*r/ 95.0%

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

      2. distribute-frac-neg2 95.0%

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

      3. add-sqr-sqrt 43.3%

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

      4. sqrt-unprod 14.6%

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

      5. sqr-neg 14.6%

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

      6. sqrt-unprod 2.6%

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

      7. add-sqr-sqrt 4.7%

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

      8. associate-*r/ 4.7%

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

      9. clear-num 4.7%

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

      10. un-div-inv 4.7%

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

      11. add-sqr-sqrt 2.6%

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

      12. sqrt-unprod 16.7%

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

      13. sqr-neg 16.7%

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

      14. sqrt-unprod 45.4%

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

      15. add-sqr-sqrt 99.9%

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

   7. Applied egg-rr 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -1 \cdot 10^{-236} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{y}{\left(-y\right) - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 69.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{1 - \frac{y}{z}}\\ \mathbf{if}\;y \leq -4.1 \cdot 10^{+152}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{+101}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -3.65 \cdot 10^{+77}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1.32 \cdot 10^{-90}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-72}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+44}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ x (- 1.0 (/ y z)))))
   (if (<= y -4.1e+152)
     (- z)
     (if (<= y -1.02e+101)
       (+ x y)
       (if (<= y -3.65e+77)
         (- z)
         (if (<= y -1.32e-90)
           t_0
           (if (<= y 2.3e-72) (+ x y) (if (<= y 5e+44) t_0 (- z)))))))))

C

double code(double x, double y, double z) {
	double t_0 = x / (1.0 - (y / z));
	double tmp;
	if (y <= -4.1e+152) {
		tmp = -z;
	} else if (y <= -1.02e+101) {
		tmp = x + y;
	} else if (y <= -3.65e+77) {
		tmp = -z;
	} else if (y <= -1.32e-90) {
		tmp = t_0;
	} else if (y <= 2.3e-72) {
		tmp = x + y;
	} else if (y <= 5e+44) {
		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 / (1.0d0 - (y / z))
    if (y <= (-4.1d+152)) then
        tmp = -z
    else if (y <= (-1.02d+101)) then
        tmp = x + y
    else if (y <= (-3.65d+77)) then
        tmp = -z
    else if (y <= (-1.32d-90)) then
        tmp = t_0
    else if (y <= 2.3d-72) then
        tmp = x + y
    else if (y <= 5d+44) 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 / (1.0 - (y / z));
	double tmp;
	if (y <= -4.1e+152) {
		tmp = -z;
	} else if (y <= -1.02e+101) {
		tmp = x + y;
	} else if (y <= -3.65e+77) {
		tmp = -z;
	} else if (y <= -1.32e-90) {
		tmp = t_0;
	} else if (y <= 2.3e-72) {
		tmp = x + y;
	} else if (y <= 5e+44) {
		tmp = t_0;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x / (1.0 - (y / z))
	tmp = 0
	if y <= -4.1e+152:
		tmp = -z
	elif y <= -1.02e+101:
		tmp = x + y
	elif y <= -3.65e+77:
		tmp = -z
	elif y <= -1.32e-90:
		tmp = t_0
	elif y <= 2.3e-72:
		tmp = x + y
	elif y <= 5e+44:
		tmp = t_0
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x / Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (y <= -4.1e+152)
		tmp = Float64(-z);
	elseif (y <= -1.02e+101)
		tmp = Float64(x + y);
	elseif (y <= -3.65e+77)
		tmp = Float64(-z);
	elseif (y <= -1.32e-90)
		tmp = t_0;
	elseif (y <= 2.3e-72)
		tmp = Float64(x + y);
	elseif (y <= 5e+44)
		tmp = t_0;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x / (1.0 - (y / z));
	tmp = 0.0;
	if (y <= -4.1e+152)
		tmp = -z;
	elseif (y <= -1.02e+101)
		tmp = x + y;
	elseif (y <= -3.65e+77)
		tmp = -z;
	elseif (y <= -1.32e-90)
		tmp = t_0;
	elseif (y <= 2.3e-72)
		tmp = x + y;
	elseif (y <= 5e+44)
		tmp = t_0;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.1e+152], (-z), If[LessEqual[y, -1.02e+101], N[(x + y), $MachinePrecision], If[LessEqual[y, -3.65e+77], (-z), If[LessEqual[y, -1.32e-90], t$95$0, If[LessEqual[y, 2.3e-72], N[(x + y), $MachinePrecision], If[LessEqual[y, 5e+44], t$95$0, (-z)]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.0999999999999998e152 or -1.02000000000000002e101 < y < -3.65000000000000012e77 or 4.9999999999999996e44 < y

   1. Initial program 72.4%

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

   3. Taylor expanded in y around inf 75.6%

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

      1. mul-1-neg 75.6%

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

   5. Simplified 75.6%

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

   if -4.0999999999999998e152 < y < -1.02000000000000002e101 or -1.32000000000000005e-90 < y < 2.29999999999999995e-72

   1. Initial program 99.1%

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

   3. Taylor expanded in z around inf 82.6%

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

      1. +-commutative 82.6%

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

   5. Simplified 82.6%

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

   if -3.65000000000000012e77 < y < -1.32000000000000005e-90 or 2.29999999999999995e-72 < y < 4.9999999999999996e44

   1. Initial program 97.3%

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

   3. Taylor expanded in x around inf 74.1%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+152}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{+101}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -3.65 \cdot 10^{+77}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1.32 \cdot 10^{-90}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-72}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+44}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ \mathbf{if}\;y \leq -1.02 \cdot 10^{+150}:\\ \;\;\;\;\frac{z}{\frac{y}{\left(-y\right) - x}}\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{+77}:\\ \;\;\;\;\frac{y}{t\_0}\\ \mathbf{elif}\;y \leq -5.3 \cdot 10^{-116}:\\ \;\;\;\;\frac{x}{t\_0}\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-57}:\\ \;\;\;\;\left(x + y\right) \cdot \left(1 + \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{-y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))))
   (if (<= y -1.02e+150)
     (/ z (/ y (- (- y) x)))
     (if (<= y -3.6e+77)
       (/ y t_0)
       (if (<= y -5.3e-116)
         (/ x t_0)
         (if (<= y 1.22e-57)
           (* (+ x y) (+ 1.0 (/ y z)))
           (* z (/ (+ x y) (- y)))))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double tmp;
	if (y <= -1.02e+150) {
		tmp = z / (y / (-y - x));
	} else if (y <= -3.6e+77) {
		tmp = y / t_0;
	} else if (y <= -5.3e-116) {
		tmp = x / t_0;
	} else if (y <= 1.22e-57) {
		tmp = (x + y) * (1.0 + (y / z));
	} else {
		tmp = z * ((x + y) / -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 = 1.0d0 - (y / z)
    if (y <= (-1.02d+150)) then
        tmp = z / (y / (-y - x))
    else if (y <= (-3.6d+77)) then
        tmp = y / t_0
    else if (y <= (-5.3d-116)) then
        tmp = x / t_0
    else if (y <= 1.22d-57) then
        tmp = (x + y) * (1.0d0 + (y / z))
    else
        tmp = z * ((x + y) / -y)
    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 <= -1.02e+150) {
		tmp = z / (y / (-y - x));
	} else if (y <= -3.6e+77) {
		tmp = y / t_0;
	} else if (y <= -5.3e-116) {
		tmp = x / t_0;
	} else if (y <= 1.22e-57) {
		tmp = (x + y) * (1.0 + (y / z));
	} else {
		tmp = z * ((x + y) / -y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	tmp = 0
	if y <= -1.02e+150:
		tmp = z / (y / (-y - x))
	elif y <= -3.6e+77:
		tmp = y / t_0
	elif y <= -5.3e-116:
		tmp = x / t_0
	elif y <= 1.22e-57:
		tmp = (x + y) * (1.0 + (y / z))
	else:
		tmp = z * ((x + y) / -y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y / z))
	tmp = 0.0
	if (y <= -1.02e+150)
		tmp = Float64(z / Float64(y / Float64(Float64(-y) - x)));
	elseif (y <= -3.6e+77)
		tmp = Float64(y / t_0);
	elseif (y <= -5.3e-116)
		tmp = Float64(x / t_0);
	elseif (y <= 1.22e-57)
		tmp = Float64(Float64(x + y) * Float64(1.0 + Float64(y / z)));
	else
		tmp = Float64(z * Float64(Float64(x + y) / Float64(-y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y / z);
	tmp = 0.0;
	if (y <= -1.02e+150)
		tmp = z / (y / (-y - x));
	elseif (y <= -3.6e+77)
		tmp = y / t_0;
	elseif (y <= -5.3e-116)
		tmp = x / t_0;
	elseif (y <= 1.22e-57)
		tmp = (x + y) * (1.0 + (y / z));
	else
		tmp = z * ((x + y) / -y);
	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, -1.02e+150], N[(z / N[(y / N[((-y) - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.6e+77], N[(y / t$95$0), $MachinePrecision], If[LessEqual[y, -5.3e-116], N[(x / t$95$0), $MachinePrecision], If[LessEqual[y, 1.22e-57], N[(N[(x + y), $MachinePrecision] * N[(1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(x + y), $MachinePrecision] / (-y)), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.0199999999999999e150

   1. Initial program 62.8%

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

   3. Taylor expanded in z around 0 71.9%

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

      1. mul-1-neg 71.9%

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

      2. associate-/l* 88.6%

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

      3. distribute-rgt-neg-in 88.6%

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

      4. distribute-neg-frac2 88.6%

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

      5. +-commutative 88.6%

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

   5. Simplified 88.6%

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

      1. associate-*r/ 71.9%

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

      2. distribute-frac-neg2 71.9%

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

      3. add-sqr-sqrt 0.0%

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

      4. sqrt-unprod 3.4%

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

      5. sqr-neg 3.4%

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

      6. sqrt-unprod 2.9%

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

      7. add-sqr-sqrt 2.9%

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

      8. associate-*r/ 3.0%

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

      9. clear-num 3.0%

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

      10. un-div-inv 3.0%

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

      11. add-sqr-sqrt 3.0%

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

      12. sqrt-unprod 3.9%

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

      13. sqr-neg 3.9%

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

      14. sqrt-unprod 0.0%

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

      15. add-sqr-sqrt 88.6%

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

   7. Applied egg-rr 88.6%

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

   if -1.0199999999999999e150 < y < -3.5999999999999998e77

   1. Initial program 89.3%

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

   3. Taylor expanded in x around 0 73.3%

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

   if -3.5999999999999998e77 < y < -5.3e-116

   1. Initial program 95.6%

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

   3. Taylor expanded in x around inf 78.1%

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

   if -5.3e-116 < y < 1.2200000000000001e-57

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 87.0%

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

      1. associate-+r+ 87.0%

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

      2. *-rgt-identity 87.0%

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

      3. *-commutative 87.0%

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

      4. associate-/l* 87.5%

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

      5. distribute-lft-in 87.5%

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

      6. +-commutative 87.5%

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

   5. Simplified 87.5%

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

   if 1.2200000000000001e-57 < y

   1. Initial program 82.9%

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

   3. Taylor expanded in z around 0 73.1%

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

      1. mul-1-neg 73.1%

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

      2. associate-/l* 83.0%

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

      3. distribute-rgt-neg-in 83.0%

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

      4. distribute-neg-frac2 83.0%

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

      5. +-commutative 83.0%

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

   5. Simplified 83.0%

      \[\leadsto \color{blue}{z \cdot \frac{y + x}{-y}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+150}:\\ \;\;\;\;\frac{z}{\frac{y}{\left(-y\right) - x}}\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{+77}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -5.3 \cdot 10^{-116}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-57}:\\ \;\;\;\;\left(x + y\right) \cdot \left(1 + \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{-y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ t_1 := \frac{z}{\frac{y}{\left(-y\right) - x}}\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{+149}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{+77}:\\ \;\;\;\;\frac{y}{t\_0}\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-89}:\\ \;\;\;\;\frac{x}{t\_0}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-56}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))) (t_1 (/ z (/ y (- (- y) x)))))
   (if (<= y -5.8e+149)
     t_1
     (if (<= y -3.7e+77)
       (/ y t_0)
       (if (<= y -1.95e-89) (/ x t_0) (if (<= y 1.7e-56) (+ x y) t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double t_1 = z / (y / (-y - x));
	double tmp;
	if (y <= -5.8e+149) {
		tmp = t_1;
	} else if (y <= -3.7e+77) {
		tmp = y / t_0;
	} else if (y <= -1.95e-89) {
		tmp = x / t_0;
	} else if (y <= 1.7e-56) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 1.0d0 - (y / z)
    t_1 = z / (y / (-y - x))
    if (y <= (-5.8d+149)) then
        tmp = t_1
    else if (y <= (-3.7d+77)) then
        tmp = y / t_0
    else if (y <= (-1.95d-89)) then
        tmp = x / t_0
    else if (y <= 1.7d-56) then
        tmp = x + y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double t_1 = z / (y / (-y - x));
	double tmp;
	if (y <= -5.8e+149) {
		tmp = t_1;
	} else if (y <= -3.7e+77) {
		tmp = y / t_0;
	} else if (y <= -1.95e-89) {
		tmp = x / t_0;
	} else if (y <= 1.7e-56) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	t_1 = z / (y / (-y - x))
	tmp = 0
	if y <= -5.8e+149:
		tmp = t_1
	elif y <= -3.7e+77:
		tmp = y / t_0
	elif y <= -1.95e-89:
		tmp = x / t_0
	elif y <= 1.7e-56:
		tmp = x + y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y / z))
	t_1 = Float64(z / Float64(y / Float64(Float64(-y) - x)))
	tmp = 0.0
	if (y <= -5.8e+149)
		tmp = t_1;
	elseif (y <= -3.7e+77)
		tmp = Float64(y / t_0);
	elseif (y <= -1.95e-89)
		tmp = Float64(x / t_0);
	elseif (y <= 1.7e-56)
		tmp = Float64(x + y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y / z);
	t_1 = z / (y / (-y - x));
	tmp = 0.0;
	if (y <= -5.8e+149)
		tmp = t_1;
	elseif (y <= -3.7e+77)
		tmp = y / t_0;
	elseif (y <= -1.95e-89)
		tmp = x / t_0;
	elseif (y <= 1.7e-56)
		tmp = x + y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z / N[(y / N[((-y) - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.8e+149], t$95$1, If[LessEqual[y, -3.7e+77], N[(y / t$95$0), $MachinePrecision], If[LessEqual[y, -1.95e-89], N[(x / t$95$0), $MachinePrecision], If[LessEqual[y, 1.7e-56], N[(x + y), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.8000000000000004e149 or 1.69999999999999991e-56 < y

   1. Initial program 76.6%

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

   3. Taylor expanded in z around 0 72.8%

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

      1. mul-1-neg 72.8%

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

      2. associate-/l* 84.7%

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

      3. distribute-rgt-neg-in 84.7%

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

      4. distribute-neg-frac2 84.7%

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

      5. +-commutative 84.7%

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

   5. Simplified 84.7%

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

      1. associate-*r/ 72.8%

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

      2. distribute-frac-neg2 72.8%

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

      3. add-sqr-sqrt 49.9%

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

      4. sqrt-unprod 34.4%

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

      5. sqr-neg 34.4%

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

      6. sqrt-unprod 0.9%

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

      7. add-sqr-sqrt 2.6%

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

      8. associate-*r/ 2.7%

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

      9. clear-num 2.7%

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

      10. un-div-inv 2.7%

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

      11. add-sqr-sqrt 0.9%

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

      12. sqrt-unprod 34.9%

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

      13. sqr-neg 34.9%

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

      14. sqrt-unprod 56.5%

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

      15. add-sqr-sqrt 84.7%

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

   7. Applied egg-rr 84.7%

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

   if -5.8000000000000004e149 < y < -3.69999999999999995e77

   1. Initial program 89.3%

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

   3. Taylor expanded in x around 0 73.3%

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

   if -3.69999999999999995e77 < y < -1.94999999999999989e-89

   1. Initial program 94.1%

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

   3. Taylor expanded in x around inf 82.0%

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

   if -1.94999999999999989e-89 < y < 1.69999999999999991e-56

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 85.6%

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

      1. +-commutative 85.6%

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

   5. Simplified 85.6%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+149}:\\ \;\;\;\;\frac{z}{\frac{y}{\left(-y\right) - x}}\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{+77}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-89}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-56}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{y}{\left(-y\right) - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ \mathbf{if}\;y \leq -1.75 \cdot 10^{+150}:\\ \;\;\;\;\frac{z}{\frac{y}{\left(-y\right) - x}}\\ \mathbf{elif}\;y \leq -7.3 \cdot 10^{+77}:\\ \;\;\;\;\frac{y}{t\_0}\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-92}:\\ \;\;\;\;\frac{x}{t\_0}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-59}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{-y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))))
   (if (<= y -1.75e+150)
     (/ z (/ y (- (- y) x)))
     (if (<= y -7.3e+77)
       (/ y t_0)
       (if (<= y -5e-92)
         (/ x t_0)
         (if (<= y 3.8e-59) (+ x y) (* z (/ (+ x y) (- y)))))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double tmp;
	if (y <= -1.75e+150) {
		tmp = z / (y / (-y - x));
	} else if (y <= -7.3e+77) {
		tmp = y / t_0;
	} else if (y <= -5e-92) {
		tmp = x / t_0;
	} else if (y <= 3.8e-59) {
		tmp = x + y;
	} else {
		tmp = z * ((x + y) / -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 = 1.0d0 - (y / z)
    if (y <= (-1.75d+150)) then
        tmp = z / (y / (-y - x))
    else if (y <= (-7.3d+77)) then
        tmp = y / t_0
    else if (y <= (-5d-92)) then
        tmp = x / t_0
    else if (y <= 3.8d-59) then
        tmp = x + y
    else
        tmp = z * ((x + y) / -y)
    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 <= -1.75e+150) {
		tmp = z / (y / (-y - x));
	} else if (y <= -7.3e+77) {
		tmp = y / t_0;
	} else if (y <= -5e-92) {
		tmp = x / t_0;
	} else if (y <= 3.8e-59) {
		tmp = x + y;
	} else {
		tmp = z * ((x + y) / -y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	tmp = 0
	if y <= -1.75e+150:
		tmp = z / (y / (-y - x))
	elif y <= -7.3e+77:
		tmp = y / t_0
	elif y <= -5e-92:
		tmp = x / t_0
	elif y <= 3.8e-59:
		tmp = x + y
	else:
		tmp = z * ((x + y) / -y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y / z))
	tmp = 0.0
	if (y <= -1.75e+150)
		tmp = Float64(z / Float64(y / Float64(Float64(-y) - x)));
	elseif (y <= -7.3e+77)
		tmp = Float64(y / t_0);
	elseif (y <= -5e-92)
		tmp = Float64(x / t_0);
	elseif (y <= 3.8e-59)
		tmp = Float64(x + y);
	else
		tmp = Float64(z * Float64(Float64(x + y) / Float64(-y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y / z);
	tmp = 0.0;
	if (y <= -1.75e+150)
		tmp = z / (y / (-y - x));
	elseif (y <= -7.3e+77)
		tmp = y / t_0;
	elseif (y <= -5e-92)
		tmp = x / t_0;
	elseif (y <= 3.8e-59)
		tmp = x + y;
	else
		tmp = z * ((x + y) / -y);
	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, -1.75e+150], N[(z / N[(y / N[((-y) - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7.3e+77], N[(y / t$95$0), $MachinePrecision], If[LessEqual[y, -5e-92], N[(x / t$95$0), $MachinePrecision], If[LessEqual[y, 3.8e-59], N[(x + y), $MachinePrecision], N[(z * N[(N[(x + y), $MachinePrecision] / (-y)), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.74999999999999992e150

   1. Initial program 62.8%

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

   3. Taylor expanded in z around 0 71.9%

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

      1. mul-1-neg 71.9%

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

      2. associate-/l* 88.6%

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

      3. distribute-rgt-neg-in 88.6%

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

      4. distribute-neg-frac2 88.6%

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

      5. +-commutative 88.6%

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

   5. Simplified 88.6%

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

      1. associate-*r/ 71.9%

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

      2. distribute-frac-neg2 71.9%

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

      3. add-sqr-sqrt 0.0%

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

      4. sqrt-unprod 3.4%

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

      5. sqr-neg 3.4%

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

      6. sqrt-unprod 2.9%

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

      7. add-sqr-sqrt 2.9%

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

      8. associate-*r/ 3.0%

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

      9. clear-num 3.0%

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

      10. un-div-inv 3.0%

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

      11. add-sqr-sqrt 3.0%

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

      12. sqrt-unprod 3.9%

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

      13. sqr-neg 3.9%

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

      14. sqrt-unprod 0.0%

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

      15. add-sqr-sqrt 88.6%

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

   7. Applied egg-rr 88.6%

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

   if -1.74999999999999992e150 < y < -7.30000000000000025e77

   1. Initial program 89.3%

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

   3. Taylor expanded in x around 0 73.3%

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

   if -7.30000000000000025e77 < y < -5.00000000000000011e-92

   1. Initial program 94.1%

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

   3. Taylor expanded in x around inf 82.0%

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

   if -5.00000000000000011e-92 < y < 3.79999999999999983e-59

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 85.6%

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

      1. +-commutative 85.6%

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

   5. Simplified 85.6%

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

   if 3.79999999999999983e-59 < y

   1. Initial program 82.9%

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

   3. Taylor expanded in z around 0 73.1%

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

      1. mul-1-neg 73.1%

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

      2. associate-/l* 83.0%

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

      3. distribute-rgt-neg-in 83.0%

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

      4. distribute-neg-frac2 83.0%

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

      5. +-commutative 83.0%

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

   5. Simplified 83.0%

      \[\leadsto \color{blue}{z \cdot \frac{y + x}{-y}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+150}:\\ \;\;\;\;\frac{z}{\frac{y}{\left(-y\right) - x}}\\ \mathbf{elif}\;y \leq -7.3 \cdot 10^{+77}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-92}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-59}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{-y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+152}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 0.19:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+35}:\\ \;\;\;\;\frac{z}{\frac{y}{-x}}\\ \mathbf{elif}\;y \leq 3.35 \cdot 10^{+44}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.2e+152)
   (- z)
   (if (<= y 0.19)
     (+ x y)
     (if (<= y 1.7e+35)
       (/ z (/ y (- x)))
       (if (<= y 3.35e+44) (+ x y) (- z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.2e+152) {
		tmp = -z;
	} else if (y <= 0.19) {
		tmp = x + y;
	} else if (y <= 1.7e+35) {
		tmp = z / (y / -x);
	} else if (y <= 3.35e+44) {
		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 <= (-4.2d+152)) then
        tmp = -z
    else if (y <= 0.19d0) then
        tmp = x + y
    else if (y <= 1.7d+35) then
        tmp = z / (y / -x)
    else if (y <= 3.35d+44) 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 <= -4.2e+152) {
		tmp = -z;
	} else if (y <= 0.19) {
		tmp = x + y;
	} else if (y <= 1.7e+35) {
		tmp = z / (y / -x);
	} else if (y <= 3.35e+44) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.2e+152:
		tmp = -z
	elif y <= 0.19:
		tmp = x + y
	elif y <= 1.7e+35:
		tmp = z / (y / -x)
	elif y <= 3.35e+44:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.2e+152)
		tmp = Float64(-z);
	elseif (y <= 0.19)
		tmp = Float64(x + y);
	elseif (y <= 1.7e+35)
		tmp = Float64(z / Float64(y / Float64(-x)));
	elseif (y <= 3.35e+44)
		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 <= -4.2e+152)
		tmp = -z;
	elseif (y <= 0.19)
		tmp = x + y;
	elseif (y <= 1.7e+35)
		tmp = z / (y / -x);
	elseif (y <= 3.35e+44)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.2e+152], (-z), If[LessEqual[y, 0.19], N[(x + y), $MachinePrecision], If[LessEqual[y, 1.7e+35], N[(z / N[(y / (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.35e+44], N[(x + y), $MachinePrecision], (-z)]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.2000000000000003e152 or 3.35000000000000018e44 < y

   1. Initial program 71.4%

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

   3. Taylor expanded in y around inf 76.8%

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

      1. mul-1-neg 76.8%

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

   5. Simplified 76.8%

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

   if -4.2000000000000003e152 < y < 0.19 or 1.7000000000000001e35 < y < 3.35000000000000018e44

   1. Initial program 98.0%

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

   3. Taylor expanded in z around inf 75.9%

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

      1. +-commutative 75.9%

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

   5. Simplified 75.9%

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

   if 0.19 < y < 1.7000000000000001e35

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0 93.0%

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

      1. mul-1-neg 93.0%

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

      2. associate-/l* 92.8%

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

      3. distribute-rgt-neg-in 92.8%

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

      4. distribute-neg-frac2 92.8%

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

      5. +-commutative 92.8%

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

   5. Simplified 92.8%

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

      1. associate-*r/ 93.0%

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

      2. distribute-frac-neg2 93.0%

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

      3. add-sqr-sqrt 92.6%

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

      4. sqrt-unprod 93.0%

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

      5. sqr-neg 93.0%

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

      6. sqrt-unprod 0.0%

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

      7. add-sqr-sqrt 1.4%

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

      8. associate-*r/ 1.4%

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

      9. clear-num 1.4%

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

      10. un-div-inv 1.4%

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

      11. add-sqr-sqrt 0.0%

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

      12. sqrt-unprod 93.2%

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

      13. sqr-neg 93.2%

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

      14. sqrt-unprod 92.4%

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

      15. add-sqr-sqrt 93.2%

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

   7. Applied egg-rr 93.2%

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

   8. Taylor expanded in y around 0 65.8%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+152}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 0.19:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+35}:\\ \;\;\;\;\frac{z}{\frac{y}{-x}}\\ \mathbf{elif}\;y \leq 3.35 \cdot 10^{+44}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+152}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 0.0035:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+35}:\\ \;\;\;\;x \cdot \frac{z}{-y}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+46}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.1e+152)
   (- z)
   (if (<= y 0.0035)
     (+ x y)
     (if (<= y 4e+35) (* x (/ z (- y))) (if (<= y 1.7e+46) (+ x y) (- z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.1e+152) {
		tmp = -z;
	} else if (y <= 0.0035) {
		tmp = x + y;
	} else if (y <= 4e+35) {
		tmp = x * (z / -y);
	} else if (y <= 1.7e+46) {
		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 <= (-4.1d+152)) then
        tmp = -z
    else if (y <= 0.0035d0) then
        tmp = x + y
    else if (y <= 4d+35) then
        tmp = x * (z / -y)
    else if (y <= 1.7d+46) 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 <= -4.1e+152) {
		tmp = -z;
	} else if (y <= 0.0035) {
		tmp = x + y;
	} else if (y <= 4e+35) {
		tmp = x * (z / -y);
	} else if (y <= 1.7e+46) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.1e+152:
		tmp = -z
	elif y <= 0.0035:
		tmp = x + y
	elif y <= 4e+35:
		tmp = x * (z / -y)
	elif y <= 1.7e+46:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.1e+152)
		tmp = Float64(-z);
	elseif (y <= 0.0035)
		tmp = Float64(x + y);
	elseif (y <= 4e+35)
		tmp = Float64(x * Float64(z / Float64(-y)));
	elseif (y <= 1.7e+46)
		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 <= -4.1e+152)
		tmp = -z;
	elseif (y <= 0.0035)
		tmp = x + y;
	elseif (y <= 4e+35)
		tmp = x * (z / -y);
	elseif (y <= 1.7e+46)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.1e+152], (-z), If[LessEqual[y, 0.0035], N[(x + y), $MachinePrecision], If[LessEqual[y, 4e+35], N[(x * N[(z / (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e+46], N[(x + y), $MachinePrecision], (-z)]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.0999999999999998e152 or 1.6999999999999999e46 < y

   1. Initial program 71.4%

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

   3. Taylor expanded in y around inf 76.8%

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

      1. mul-1-neg 76.8%

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

   5. Simplified 76.8%

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

   if -4.0999999999999998e152 < y < 0.00350000000000000007 or 3.9999999999999999e35 < y < 1.6999999999999999e46

   1. Initial program 98.0%

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

   3. Taylor expanded in z around inf 75.9%

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

      1. +-commutative 75.9%

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

   5. Simplified 75.9%

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

   if 0.00350000000000000007 < y < 3.9999999999999999e35

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0 93.0%

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

      1. mul-1-neg 93.0%

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

      2. associate-/l* 92.8%

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

      3. distribute-rgt-neg-in 92.8%

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

      4. distribute-neg-frac2 92.8%

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

      5. +-commutative 92.8%

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

   5. Simplified 92.8%

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

   6. Taylor expanded in y around 0 65.4%

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

      1. associate-*r/ 65.4%

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

      2. neg-mul-1 65.4%

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

   8. Simplified 65.4%

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

   9. Taylor expanded in z around 0 65.6%

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

       1. mul-1-neg 65.6%

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

       2. associate-*r/ 66.1%

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

       3. distribute-rgt-neg-in 66.1%

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

       4. distribute-frac-neg2 66.1%

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

   11. Simplified 66.1%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+152}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 0.0035:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+35}:\\ \;\;\;\;x \cdot \frac{z}{-y}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+46}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+130}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{+101}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{+77} \lor \neg \left(y \leq 2.02 \cdot 10^{-10}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.9e+130)
   (- z)
   (if (<= y -1.95e+101)
     y
     (if (or (<= y -3.6e+77) (not (<= y 2.02e-10))) (- z) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.9e+130) {
		tmp = -z;
	} else if (y <= -1.95e+101) {
		tmp = y;
	} else if ((y <= -3.6e+77) || !(y <= 2.02e-10)) {
		tmp = -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.9d+130)) then
        tmp = -z
    else if (y <= (-1.95d+101)) then
        tmp = y
    else if ((y <= (-3.6d+77)) .or. (.not. (y <= 2.02d-10))) then
        tmp = -z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.9e+130) {
		tmp = -z;
	} else if (y <= -1.95e+101) {
		tmp = y;
	} else if ((y <= -3.6e+77) || !(y <= 2.02e-10)) {
		tmp = -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.9e+130:
		tmp = -z
	elif y <= -1.95e+101:
		tmp = y
	elif (y <= -3.6e+77) or not (y <= 2.02e-10):
		tmp = -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.9e+130)
		tmp = Float64(-z);
	elseif (y <= -1.95e+101)
		tmp = y;
	elseif ((y <= -3.6e+77) || !(y <= 2.02e-10))
		tmp = Float64(-z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.9e+130)
		tmp = -z;
	elseif (y <= -1.95e+101)
		tmp = y;
	elseif ((y <= -3.6e+77) || ~((y <= 2.02e-10)))
		tmp = -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.9e+130], (-z), If[LessEqual[y, -1.95e+101], y, If[Or[LessEqual[y, -3.6e+77], N[Not[LessEqual[y, 2.02e-10]], $MachinePrecision]], (-z), x]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.9000000000000001e130 or -1.95e101 < y < -3.5999999999999998e77 or 2.02e-10 < y

   1. Initial program 76.0%

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

   3. Taylor expanded in y around inf 70.1%

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

      1. mul-1-neg 70.1%

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

   5. Simplified 70.1%

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

   if -1.9000000000000001e130 < y < -1.95e101

   1. Initial program 88.2%

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

   3. Taylor expanded in x around 0 63.8%

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

   4. Taylor expanded in y around 0 64.3%

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

   if -3.5999999999999998e77 < y < 2.02e-10

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0 65.4%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+130}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{+101}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{+77} \lor \neg \left(y \leq 2.02 \cdot 10^{-10}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 69.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ \mathbf{if}\;y \leq -3.35 \cdot 10^{+159}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{+77}:\\ \;\;\;\;\frac{y}{t\_0}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+41}:\\ \;\;\;\;\frac{x}{t\_0}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))))
   (if (<= y -3.35e+159)
     (- z)
     (if (<= y -3.6e+77) (/ y t_0) (if (<= y 1.35e+41) (/ x t_0) (- z))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double tmp;
	if (y <= -3.35e+159) {
		tmp = -z;
	} else if (y <= -3.6e+77) {
		tmp = y / t_0;
	} else if (y <= 1.35e+41) {
		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 <= (-3.35d+159)) then
        tmp = -z
    else if (y <= (-3.6d+77)) then
        tmp = y / t_0
    else if (y <= 1.35d+41) 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 <= -3.35e+159) {
		tmp = -z;
	} else if (y <= -3.6e+77) {
		tmp = y / t_0;
	} else if (y <= 1.35e+41) {
		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 <= -3.35e+159:
		tmp = -z
	elif y <= -3.6e+77:
		tmp = y / t_0
	elif y <= 1.35e+41:
		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 <= -3.35e+159)
		tmp = Float64(-z);
	elseif (y <= -3.6e+77)
		tmp = Float64(y / t_0);
	elseif (y <= 1.35e+41)
		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 <= -3.35e+159)
		tmp = -z;
	elseif (y <= -3.6e+77)
		tmp = y / t_0;
	elseif (y <= 1.35e+41)
		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, -3.35e+159], (-z), If[LessEqual[y, -3.6e+77], N[(y / t$95$0), $MachinePrecision], If[LessEqual[y, 1.35e+41], N[(x / t$95$0), $MachinePrecision], (-z)]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.35000000000000009e159 or 1.35e41 < y

   1. Initial program 71.1%

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

   3. Taylor expanded in y around inf 76.6%

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

      1. mul-1-neg 76.6%

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

   5. Simplified 76.6%

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

   if -3.35000000000000009e159 < y < -3.5999999999999998e77

   1. Initial program 90.8%

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

   3. Taylor expanded in x around 0 72.4%

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

   if -3.5999999999999998e77 < y < 1.35e41

   1. Initial program 99.2%

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

   3. Taylor expanded in x around inf 78.7%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.35 \cdot 10^{+159}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{+77}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+41}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 68.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+152} \lor \neg \left(y \leq 1.66 \cdot 10^{+28}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.1e+152) (not (<= y 1.66e+28))) (- z) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.1e+152) || !(y <= 1.66e+28)) {
		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 <= (-4.1d+152)) .or. (.not. (y <= 1.66d+28))) 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 <= -4.1e+152) || !(y <= 1.66e+28)) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.1e+152) or not (y <= 1.66e+28):
		tmp = -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.1e+152) || !(y <= 1.66e+28))
		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 <= -4.1e+152) || ~((y <= 1.66e+28)))
		tmp = -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.1e+152], N[Not[LessEqual[y, 1.66e+28]], $MachinePrecision]], (-z), N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.0999999999999998e152 or 1.6599999999999999e28 < y

   1. Initial program 73.0%

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

   3. Taylor expanded in y around inf 74.5%

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

      1. mul-1-neg 74.5%

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

   5. Simplified 74.5%

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

   if -4.0999999999999998e152 < y < 1.6599999999999999e28

   1. Initial program 98.0%

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

   3. Taylor expanded in z around inf 74.3%

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

      1. +-commutative 74.3%

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

   5. Simplified 74.3%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+152} \lor \neg \left(y \leq 1.66 \cdot 10^{+28}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 41.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{-200}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-160}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.2e-200) x (if (<= x 1.9e-160) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.2e-200) {
		tmp = x;
	} else if (x <= 1.9e-160) {
		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 <= (-4.2d-200)) then
        tmp = x
    else if (x <= 1.9d-160) 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 <= -4.2e-200) {
		tmp = x;
	} else if (x <= 1.9e-160) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.2e-200:
		tmp = x
	elif x <= 1.9e-160:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.2e-200)
		tmp = x;
	elseif (x <= 1.9e-160)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -4.2e-200)
		tmp = x;
	elseif (x <= 1.9e-160)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.2e-200], x, If[LessEqual[x, 1.9e-160], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -4.1999999999999998e-200 or 1.8999999999999999e-160 < x

   1. Initial program 87.5%

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

   3. Taylor expanded in y around 0 42.7%

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

   if -4.1999999999999998e-200 < x < 1.8999999999999999e-160

   1. Initial program 88.8%

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

   3. Taylor expanded in x around 0 79.4%

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

   4. Taylor expanded in y around 0 41.7%

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

4. Final simplification 42.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{-200}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-160}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 35.5% 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 87.8%

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

3. Taylor expanded in y around 0 35.8%

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

4. Final simplification 35.8%

   \[\leadsto x \]
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 2024059 
(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))))