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

Percentage Accurate: 88.7% → 99.8%

Time: 6.1s

Alternatives: 12

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{-281} \lor \neg \left(t\_0 \leq 0\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - \frac{z}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -2e-281) (not (<= t_0 0.0))) t_0 (- (- z) (/ z (/ y x))))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -2e-281) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = -z - (z / (y / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x + y) / (1.0d0 - (y / z))
    if ((t_0 <= (-2d-281)) .or. (.not. (t_0 <= 0.0d0))) then
        tmp = t_0
    else
        tmp = -z - (z / (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -2e-281) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = -z - (z / (y / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -2e-281) or not (t_0 <= 0.0):
		tmp = t_0
	else:
		tmp = -z - (z / (y / x))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if ((t_0 <= -2e-281) || !(t_0 <= 0.0))
		tmp = t_0;
	else
		tmp = Float64(Float64(-z) - Float64(z / Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + y) / (1.0 - (y / z));
	tmp = 0.0;
	if ((t_0 <= -2e-281) || ~((t_0 <= 0.0)))
		tmp = t_0;
	else
		tmp = -z - (z / (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -2e-281], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], t$95$0, N[((-z) - N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -2e-281 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 -2e-281 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -0.0

   1. Initial program 8.3%

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

   3. Taylor expanded in y around inf 8.3%

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

      1. neg-mul-1 8.3%

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

      2. distribute-neg-frac 8.3%

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

   5. Simplified 8.3%

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

   6. Taylor expanded in x around 0 99.9%

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

      1. mul-1-neg 99.9%

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

      2. unsub-neg 99.9%

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

      3. neg-mul-1 99.9%

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

      4. *-commutative 99.9%

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

      5. associate-/l* 99.9%

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

   8. Simplified 99.9%

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

      1. clear-num 99.9%

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

      2. un-div-inv 100.0%

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

   10. Applied egg-rr 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -2 \cdot 10^{-281} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - \frac{z}{\frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 73.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -9.6 \cdot 10^{+205}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{+86}:\\ \;\;\;\;y \cdot \frac{z}{z - y}\\ \mathbf{elif}\;y \leq -5.1 \cdot 10^{-11}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-55}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - \frac{z}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- -1.0 (/ x y)))))
   (if (<= y -9.6e+205)
     t_0
     (if (<= y -3.1e+86)
       (* y (/ z (- z y)))
       (if (<= y -5.1e-11)
         t_0
         (if (<= y 1.5e-55) (/ x (- 1.0 (/ y z))) (- (- z) (/ z (/ y x)))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (-1.0 - (x / y));
	double tmp;
	if (y <= -9.6e+205) {
		tmp = t_0;
	} else if (y <= -3.1e+86) {
		tmp = y * (z / (z - y));
	} else if (y <= -5.1e-11) {
		tmp = t_0;
	} else if (y <= 1.5e-55) {
		tmp = x / (1.0 - (y / z));
	} else {
		tmp = -z - (z / (y / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * ((-1.0d0) - (x / y))
    if (y <= (-9.6d+205)) then
        tmp = t_0
    else if (y <= (-3.1d+86)) then
        tmp = y * (z / (z - y))
    else if (y <= (-5.1d-11)) then
        tmp = t_0
    else if (y <= 1.5d-55) then
        tmp = x / (1.0d0 - (y / z))
    else
        tmp = -z - (z / (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (-1.0 - (x / y));
	double tmp;
	if (y <= -9.6e+205) {
		tmp = t_0;
	} else if (y <= -3.1e+86) {
		tmp = y * (z / (z - y));
	} else if (y <= -5.1e-11) {
		tmp = t_0;
	} else if (y <= 1.5e-55) {
		tmp = x / (1.0 - (y / z));
	} else {
		tmp = -z - (z / (y / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (-1.0 - (x / y))
	tmp = 0
	if y <= -9.6e+205:
		tmp = t_0
	elif y <= -3.1e+86:
		tmp = y * (z / (z - y))
	elif y <= -5.1e-11:
		tmp = t_0
	elif y <= 1.5e-55:
		tmp = x / (1.0 - (y / z))
	else:
		tmp = -z - (z / (y / x))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -9.6e+205)
		tmp = t_0;
	elseif (y <= -3.1e+86)
		tmp = Float64(y * Float64(z / Float64(z - y)));
	elseif (y <= -5.1e-11)
		tmp = t_0;
	elseif (y <= 1.5e-55)
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(Float64(-z) - Float64(z / Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (-1.0 - (x / y));
	tmp = 0.0;
	if (y <= -9.6e+205)
		tmp = t_0;
	elseif (y <= -3.1e+86)
		tmp = y * (z / (z - y));
	elseif (y <= -5.1e-11)
		tmp = t_0;
	elseif (y <= 1.5e-55)
		tmp = x / (1.0 - (y / z));
	else
		tmp = -z - (z / (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.6e+205], t$95$0, If[LessEqual[y, -3.1e+86], N[(y * N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.1e-11], t$95$0, If[LessEqual[y, 1.5e-55], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-z) - N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -9.59999999999999945e205 or -3.1000000000000002e86 < y < -5.09999999999999984e-11

   1. Initial program 69.0%

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

   3. Taylor expanded in y around inf 60.3%

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

      1. neg-mul-1 60.3%

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

      2. distribute-neg-frac 60.3%

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

   5. Simplified 60.3%

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

   6. Taylor expanded in x around 0 87.8%

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

      1. mul-1-neg 87.8%

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

      2. unsub-neg 87.8%

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

      3. neg-mul-1 87.8%

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

      4. *-commutative 87.8%

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

      5. associate-/l* 91.1%

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

   8. Simplified 91.1%

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

   9. Taylor expanded in z around 0 91.2%

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

       1. mul-1-neg 91.2%

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

       2. distribute-rgt-neg-in 91.2%

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

       3. distribute-neg-in 91.2%

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

       4. metadata-eval 91.2%

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

       5. sub-neg 91.2%

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

   11. Simplified 91.2%

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

   if -9.59999999999999945e205 < y < -3.1000000000000002e86

   1. Initial program 84.2%

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

   3. Taylor expanded in z around 0 84.2%

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

   4. Taylor expanded in x around 0 61.6%

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

      1. associate-/l* 76.6%

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

   6. Simplified 76.6%

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

   if -5.09999999999999984e-11 < y < 1.50000000000000008e-55

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 83.2%

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

   if 1.50000000000000008e-55 < y

   1. Initial program 81.7%

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

   3. Taylor expanded in y around inf 56.4%

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

      1. neg-mul-1 56.4%

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

      2. distribute-neg-frac 56.4%

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

   5. Simplified 56.4%

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

   6. Taylor expanded in x around 0 73.1%

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

      1. mul-1-neg 73.1%

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

      2. unsub-neg 73.1%

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

      3. neg-mul-1 73.1%

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

      4. *-commutative 73.1%

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

      5. associate-/l* 74.5%

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

   8. Simplified 74.5%

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

      1. clear-num 74.4%

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

      2. un-div-inv 74.5%

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

   10. Applied egg-rr 74.5%

       \[\leadsto \left(-z\right) - \color{blue}{\frac{z}{\frac{y}{x}}} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 3: 73.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{+205}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{+86}:\\ \;\;\;\;y \cdot \frac{z}{z - y}\\ \mathbf{elif}\;y \leq -1.04 \cdot 10^{-19}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-55}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - z \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- -1.0 (/ x y)))))
   (if (<= y -9.5e+205)
     t_0
     (if (<= y -2.1e+86)
       (* y (/ z (- z y)))
       (if (<= y -1.04e-19)
         t_0
         (if (<= y 1.5e-55) (/ x (- 1.0 (/ y z))) (- (- z) (* z (/ x y)))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (-1.0 - (x / y));
	double tmp;
	if (y <= -9.5e+205) {
		tmp = t_0;
	} else if (y <= -2.1e+86) {
		tmp = y * (z / (z - y));
	} else if (y <= -1.04e-19) {
		tmp = t_0;
	} else if (y <= 1.5e-55) {
		tmp = x / (1.0 - (y / z));
	} else {
		tmp = -z - (z * (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 = z * ((-1.0d0) - (x / y))
    if (y <= (-9.5d+205)) then
        tmp = t_0
    else if (y <= (-2.1d+86)) then
        tmp = y * (z / (z - y))
    else if (y <= (-1.04d-19)) then
        tmp = t_0
    else if (y <= 1.5d-55) then
        tmp = x / (1.0d0 - (y / z))
    else
        tmp = -z - (z * (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (-1.0 - (x / y));
	double tmp;
	if (y <= -9.5e+205) {
		tmp = t_0;
	} else if (y <= -2.1e+86) {
		tmp = y * (z / (z - y));
	} else if (y <= -1.04e-19) {
		tmp = t_0;
	} else if (y <= 1.5e-55) {
		tmp = x / (1.0 - (y / z));
	} else {
		tmp = -z - (z * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (-1.0 - (x / y))
	tmp = 0
	if y <= -9.5e+205:
		tmp = t_0
	elif y <= -2.1e+86:
		tmp = y * (z / (z - y))
	elif y <= -1.04e-19:
		tmp = t_0
	elif y <= 1.5e-55:
		tmp = x / (1.0 - (y / z))
	else:
		tmp = -z - (z * (x / y))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -9.5e+205)
		tmp = t_0;
	elseif (y <= -2.1e+86)
		tmp = Float64(y * Float64(z / Float64(z - y)));
	elseif (y <= -1.04e-19)
		tmp = t_0;
	elseif (y <= 1.5e-55)
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(Float64(-z) - Float64(z * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (-1.0 - (x / y));
	tmp = 0.0;
	if (y <= -9.5e+205)
		tmp = t_0;
	elseif (y <= -2.1e+86)
		tmp = y * (z / (z - y));
	elseif (y <= -1.04e-19)
		tmp = t_0;
	elseif (y <= 1.5e-55)
		tmp = x / (1.0 - (y / z));
	else
		tmp = -z - (z * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.5e+205], t$95$0, If[LessEqual[y, -2.1e+86], N[(y * N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.04e-19], t$95$0, If[LessEqual[y, 1.5e-55], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-z) - N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -9.4999999999999997e205 or -2.0999999999999999e86 < y < -1.03999999999999998e-19

   1. Initial program 69.0%

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

   3. Taylor expanded in y around inf 60.3%

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

      1. neg-mul-1 60.3%

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

      2. distribute-neg-frac 60.3%

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

   5. Simplified 60.3%

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

   6. Taylor expanded in x around 0 87.8%

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

      1. mul-1-neg 87.8%

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

      2. unsub-neg 87.8%

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

      3. neg-mul-1 87.8%

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

      4. *-commutative 87.8%

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

      5. associate-/l* 91.1%

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

   8. Simplified 91.1%

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

   9. Taylor expanded in z around 0 91.2%

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

       1. mul-1-neg 91.2%

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

       2. distribute-rgt-neg-in 91.2%

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

       3. distribute-neg-in 91.2%

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

       4. metadata-eval 91.2%

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

       5. sub-neg 91.2%

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

   11. Simplified 91.2%

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

   if -9.4999999999999997e205 < y < -2.0999999999999999e86

   1. Initial program 84.2%

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

   3. Taylor expanded in z around 0 84.2%

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

   4. Taylor expanded in x around 0 61.6%

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

      1. associate-/l* 76.6%

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

   6. Simplified 76.6%

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

   if -1.03999999999999998e-19 < y < 1.50000000000000008e-55

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 83.2%

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

   if 1.50000000000000008e-55 < y

   1. Initial program 81.7%

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

   3. Taylor expanded in y around inf 56.4%

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

      1. neg-mul-1 56.4%

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

      2. distribute-neg-frac 56.4%

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

   5. Simplified 56.4%

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

   6. Taylor expanded in x around 0 73.1%

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

      1. mul-1-neg 73.1%

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

      2. unsub-neg 73.1%

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

      3. neg-mul-1 73.1%

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

      4. *-commutative 73.1%

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

      5. associate-/l* 74.5%

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

   8. Simplified 74.5%

      \[\leadsto \color{blue}{\left(-z\right) - z \cdot \frac{x}{y}} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 4: 73.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{+205}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{+85}:\\ \;\;\;\;y \cdot \frac{z}{z - y}\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-14} \lor \neg \left(y \leq 1.5 \cdot 10^{-55}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- -1.0 (/ x y)))))
   (if (<= y -9.5e+205)
     t_0
     (if (<= y -8.2e+85)
       (* y (/ z (- z y)))
       (if (or (<= y -1.1e-14) (not (<= y 1.5e-55)))
         t_0
         (/ x (- 1.0 (/ y z))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (-1.0 - (x / y));
	double tmp;
	if (y <= -9.5e+205) {
		tmp = t_0;
	} else if (y <= -8.2e+85) {
		tmp = y * (z / (z - y));
	} else if ((y <= -1.1e-14) || !(y <= 1.5e-55)) {
		tmp = t_0;
	} else {
		tmp = x / (1.0 - (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * ((-1.0d0) - (x / y))
    if (y <= (-9.5d+205)) then
        tmp = t_0
    else if (y <= (-8.2d+85)) then
        tmp = y * (z / (z - y))
    else if ((y <= (-1.1d-14)) .or. (.not. (y <= 1.5d-55))) then
        tmp = t_0
    else
        tmp = x / (1.0d0 - (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (-1.0 - (x / y));
	double tmp;
	if (y <= -9.5e+205) {
		tmp = t_0;
	} else if (y <= -8.2e+85) {
		tmp = y * (z / (z - y));
	} else if ((y <= -1.1e-14) || !(y <= 1.5e-55)) {
		tmp = t_0;
	} else {
		tmp = x / (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (-1.0 - (x / y))
	tmp = 0
	if y <= -9.5e+205:
		tmp = t_0
	elif y <= -8.2e+85:
		tmp = y * (z / (z - y))
	elif (y <= -1.1e-14) or not (y <= 1.5e-55):
		tmp = t_0
	else:
		tmp = x / (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -9.5e+205)
		tmp = t_0;
	elseif (y <= -8.2e+85)
		tmp = Float64(y * Float64(z / Float64(z - y)));
	elseif ((y <= -1.1e-14) || !(y <= 1.5e-55))
		tmp = t_0;
	else
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (-1.0 - (x / y));
	tmp = 0.0;
	if (y <= -9.5e+205)
		tmp = t_0;
	elseif (y <= -8.2e+85)
		tmp = y * (z / (z - y));
	elseif ((y <= -1.1e-14) || ~((y <= 1.5e-55)))
		tmp = t_0;
	else
		tmp = x / (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.5e+205], t$95$0, If[LessEqual[y, -8.2e+85], N[(y * N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -1.1e-14], N[Not[LessEqual[y, 1.5e-55]], $MachinePrecision]], t$95$0, N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.4999999999999997e205 or -8.19999999999999957e85 < y < -1.1e-14 or 1.50000000000000008e-55 < y

   1. Initial program 77.0%

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

   3. Taylor expanded in y around inf 57.8%

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

      1. neg-mul-1 57.8%

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

      2. distribute-neg-frac 57.8%

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

   5. Simplified 57.8%

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

   6. Taylor expanded in x around 0 78.5%

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

      1. mul-1-neg 78.5%

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

      2. unsub-neg 78.5%

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

      3. neg-mul-1 78.5%

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

      4. *-commutative 78.5%

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

      5. associate-/l* 80.6%

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

   8. Simplified 80.6%

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

   9. Taylor expanded in z around 0 80.6%

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

       1. mul-1-neg 80.6%

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

       2. distribute-rgt-neg-in 80.6%

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

       3. distribute-neg-in 80.6%

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

       4. metadata-eval 80.6%

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

       5. sub-neg 80.6%

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

   11. Simplified 80.6%

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

   if -9.4999999999999997e205 < y < -8.19999999999999957e85

   1. Initial program 84.2%

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

   3. Taylor expanded in z around 0 84.2%

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

   4. Taylor expanded in x around 0 61.6%

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

      1. associate-/l* 76.6%

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

   6. Simplified 76.6%

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

   if -1.1e-14 < y < 1.50000000000000008e-55

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 83.2%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+205}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{+85}:\\ \;\;\;\;y \cdot \frac{z}{z - y}\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-14} \lor \neg \left(y \leq 1.5 \cdot 10^{-55}\right):\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{+205}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{+86}:\\ \;\;\;\;y \cdot \frac{z}{z - y}\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-37} \lor \neg \left(y \leq 1.8 \cdot 10^{-51}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- -1.0 (/ x y)))))
   (if (<= y -9.5e+205)
     t_0
     (if (<= y -2.1e+86)
       (* y (/ z (- z y)))
       (if (or (<= y -1.05e-37) (not (<= y 1.8e-51))) t_0 (+ x y))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (-1.0 - (x / y));
	double tmp;
	if (y <= -9.5e+205) {
		tmp = t_0;
	} else if (y <= -2.1e+86) {
		tmp = y * (z / (z - y));
	} else if ((y <= -1.05e-37) || !(y <= 1.8e-51)) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = z * ((-1.0d0) - (x / y))
    if (y <= (-9.5d+205)) then
        tmp = t_0
    else if (y <= (-2.1d+86)) then
        tmp = y * (z / (z - y))
    else if ((y <= (-1.05d-37)) .or. (.not. (y <= 1.8d-51))) then
        tmp = t_0
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (-1.0 - (x / y));
	double tmp;
	if (y <= -9.5e+205) {
		tmp = t_0;
	} else if (y <= -2.1e+86) {
		tmp = y * (z / (z - y));
	} else if ((y <= -1.05e-37) || !(y <= 1.8e-51)) {
		tmp = t_0;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (-1.0 - (x / y))
	tmp = 0
	if y <= -9.5e+205:
		tmp = t_0
	elif y <= -2.1e+86:
		tmp = y * (z / (z - y))
	elif (y <= -1.05e-37) or not (y <= 1.8e-51):
		tmp = t_0
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -9.5e+205)
		tmp = t_0;
	elseif (y <= -2.1e+86)
		tmp = Float64(y * Float64(z / Float64(z - y)));
	elseif ((y <= -1.05e-37) || !(y <= 1.8e-51))
		tmp = t_0;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (-1.0 - (x / y));
	tmp = 0.0;
	if (y <= -9.5e+205)
		tmp = t_0;
	elseif (y <= -2.1e+86)
		tmp = y * (z / (z - y));
	elseif ((y <= -1.05e-37) || ~((y <= 1.8e-51)))
		tmp = t_0;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.5e+205], t$95$0, If[LessEqual[y, -2.1e+86], N[(y * N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -1.05e-37], N[Not[LessEqual[y, 1.8e-51]], $MachinePrecision]], t$95$0, N[(x + y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.4999999999999997e205 or -2.0999999999999999e86 < y < -1.05e-37 or 1.8e-51 < y

   1. Initial program 77.8%

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

   3. Taylor expanded in y around inf 57.6%

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

      1. neg-mul-1 57.6%

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

      2. distribute-neg-frac 57.6%

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

   5. Simplified 57.6%

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

   6. Taylor expanded in x around 0 77.5%

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

      1. mul-1-neg 77.5%

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

      2. unsub-neg 77.5%

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

      3. neg-mul-1 77.5%

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

      4. *-commutative 77.5%

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

      5. associate-/l* 79.6%

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

   8. Simplified 79.6%

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

   9. Taylor expanded in z around 0 79.6%

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

       1. mul-1-neg 79.6%

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

       2. distribute-rgt-neg-in 79.6%

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

       3. distribute-neg-in 79.6%

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

       4. metadata-eval 79.6%

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

       5. sub-neg 79.6%

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

   11. Simplified 79.6%

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

   if -9.4999999999999997e205 < y < -2.0999999999999999e86

   1. Initial program 84.2%

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

   3. Taylor expanded in z around 0 84.2%

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

   4. Taylor expanded in x around 0 61.6%

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

      1. associate-/l* 76.6%

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

   6. Simplified 76.6%

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

   if -1.05e-37 < y < 1.8e-51

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 75.8%

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

      1. +-commutative 75.8%

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

   5. Simplified 75.8%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+205}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{+86}:\\ \;\;\;\;y \cdot \frac{z}{z - y}\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-37} \lor \neg \left(y \leq 1.8 \cdot 10^{-51}\right):\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 69.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \frac{z}{z - y}\\ \mathbf{if}\;y \leq -1 \cdot 10^{+206}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-10}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-55}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+158}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (/ z (- z y)))))
   (if (<= y -1e+206)
     (- z)
     (if (<= y -7e-10)
       t_0
       (if (<= y 1.5e-55) (+ x y) (if (<= y 6.5e+158) t_0 (- z)))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (z / (z - y));
	double tmp;
	if (y <= -1e+206) {
		tmp = -z;
	} else if (y <= -7e-10) {
		tmp = t_0;
	} else if (y <= 1.5e-55) {
		tmp = x + y;
	} else if (y <= 6.5e+158) {
		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 <= (-1d+206)) then
        tmp = -z
    else if (y <= (-7d-10)) then
        tmp = t_0
    else if (y <= 1.5d-55) then
        tmp = x + y
    else if (y <= 6.5d+158) 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 <= -1e+206) {
		tmp = -z;
	} else if (y <= -7e-10) {
		tmp = t_0;
	} else if (y <= 1.5e-55) {
		tmp = x + y;
	} else if (y <= 6.5e+158) {
		tmp = t_0;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (z / (z - y))
	tmp = 0
	if y <= -1e+206:
		tmp = -z
	elif y <= -7e-10:
		tmp = t_0
	elif y <= 1.5e-55:
		tmp = x + y
	elif y <= 6.5e+158:
		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 <= -1e+206)
		tmp = Float64(-z);
	elseif (y <= -7e-10)
		tmp = t_0;
	elseif (y <= 1.5e-55)
		tmp = Float64(x + y);
	elseif (y <= 6.5e+158)
		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 <= -1e+206)
		tmp = -z;
	elseif (y <= -7e-10)
		tmp = t_0;
	elseif (y <= 1.5e-55)
		tmp = x + y;
	elseif (y <= 6.5e+158)
		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, -1e+206], (-z), If[LessEqual[y, -7e-10], t$95$0, If[LessEqual[y, 1.5e-55], N[(x + y), $MachinePrecision], If[LessEqual[y, 6.5e+158], t$95$0, (-z)]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1e206 or 6.5000000000000001e158 < y

   1. Initial program 59.2%

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

   3. Taylor expanded in y around inf 88.1%

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

      1. mul-1-neg 88.1%

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

   5. Simplified 88.1%

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

   if -1e206 < y < -6.99999999999999961e-10 or 1.50000000000000008e-55 < y < 6.5000000000000001e158

   1. Initial program 89.1%

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

   3. Taylor expanded in z around 0 89.2%

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

   4. Taylor expanded in x around 0 52.7%

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

      1. associate-/l* 59.1%

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

   6. Simplified 59.1%

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

   if -6.99999999999999961e-10 < y < 1.50000000000000008e-55

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 73.9%

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

      1. +-commutative 73.9%

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

   5. Simplified 73.9%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+206}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-10}:\\ \;\;\;\;y \cdot \frac{z}{z - y}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-55}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+158}:\\ \;\;\;\;y \cdot \frac{z}{z - y}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+118}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-51}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+72}:\\ \;\;\;\;\frac{z}{y} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.9e+118)
   (- z)
   (if (<= y 1.8e-51) (+ x y) (if (<= y 2e+72) (* (/ z y) (- x)) (- z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.9e+118) {
		tmp = -z;
	} else if (y <= 1.8e-51) {
		tmp = x + y;
	} else if (y <= 2e+72) {
		tmp = (z / y) * -x;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.9d+118)) then
        tmp = -z
    else if (y <= 1.8d-51) then
        tmp = x + y
    else if (y <= 2d+72) then
        tmp = (z / y) * -x
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.9e+118) {
		tmp = -z;
	} else if (y <= 1.8e-51) {
		tmp = x + y;
	} else if (y <= 2e+72) {
		tmp = (z / y) * -x;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.9e+118:
		tmp = -z
	elif y <= 1.8e-51:
		tmp = x + y
	elif y <= 2e+72:
		tmp = (z / y) * -x
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.9e+118)
		tmp = Float64(-z);
	elseif (y <= 1.8e-51)
		tmp = Float64(x + y);
	elseif (y <= 2e+72)
		tmp = Float64(Float64(z / y) * Float64(-x));
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.9e+118)
		tmp = -z;
	elseif (y <= 1.8e-51)
		tmp = x + y;
	elseif (y <= 2e+72)
		tmp = (z / y) * -x;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.9e+118], (-z), If[LessEqual[y, 1.8e-51], N[(x + y), $MachinePrecision], If[LessEqual[y, 2e+72], N[(N[(z / y), $MachinePrecision] * (-x)), $MachinePrecision], (-z)]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.90000000000000008e118 or 1.99999999999999989e72 < y

   1. Initial program 70.6%

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

   3. Taylor expanded in y around inf 69.6%

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

      1. mul-1-neg 69.6%

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

   5. Simplified 69.6%

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

   if -1.90000000000000008e118 < y < 1.8e-51

   1. Initial program 99.2%

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

   3. Taylor expanded in z around inf 69.7%

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

      1. +-commutative 69.7%

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

   5. Simplified 69.7%

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

   if 1.8e-51 < y < 1.99999999999999989e72

   1. Initial program 95.8%

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

   3. Taylor expanded in y around inf 69.7%

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

      1. neg-mul-1 69.7%

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

      2. distribute-neg-frac 69.7%

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

   5. Simplified 69.7%

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

   6. Taylor expanded in x around inf 53.0%

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

      1. *-commutative 53.0%

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

      2. associate-*l/ 53.1%

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

      3. associate-*l* 53.1%

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

      4. *-commutative 53.1%

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

      5. associate-*l* 53.1%

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

      6. neg-mul-1 53.1%

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

   8. Simplified 53.1%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+118}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-51}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+72}:\\ \;\;\;\;\frac{z}{y} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+118}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{-50}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+70}:\\ \;\;\;\;\left(-z\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.35e+118)
   (- z)
   (if (<= y 3.05e-50) (+ x y) (if (<= y 2.8e+70) (* (- z) (/ x y)) (- z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.35e+118) {
		tmp = -z;
	} else if (y <= 3.05e-50) {
		tmp = x + y;
	} else if (y <= 2.8e+70) {
		tmp = -z * (x / y);
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.35d+118)) then
        tmp = -z
    else if (y <= 3.05d-50) then
        tmp = x + y
    else if (y <= 2.8d+70) then
        tmp = -z * (x / y)
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.35e+118) {
		tmp = -z;
	} else if (y <= 3.05e-50) {
		tmp = x + y;
	} else if (y <= 2.8e+70) {
		tmp = -z * (x / y);
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.35e+118:
		tmp = -z
	elif y <= 3.05e-50:
		tmp = x + y
	elif y <= 2.8e+70:
		tmp = -z * (x / y)
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.35e+118)
		tmp = Float64(-z);
	elseif (y <= 3.05e-50)
		tmp = Float64(x + y);
	elseif (y <= 2.8e+70)
		tmp = Float64(Float64(-z) * Float64(x / y));
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.35e+118)
		tmp = -z;
	elseif (y <= 3.05e-50)
		tmp = x + y;
	elseif (y <= 2.8e+70)
		tmp = -z * (x / y);
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.35e+118], (-z), If[LessEqual[y, 3.05e-50], N[(x + y), $MachinePrecision], If[LessEqual[y, 2.8e+70], N[((-z) * N[(x / y), $MachinePrecision]), $MachinePrecision], (-z)]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.35e118 or 2.7999999999999999e70 < y

   1. Initial program 70.6%

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

   3. Taylor expanded in y around inf 69.6%

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

      1. mul-1-neg 69.6%

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

   5. Simplified 69.6%

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

   if -1.35e118 < y < 3.0499999999999998e-50

   1. Initial program 99.2%

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

   3. Taylor expanded in z around inf 69.7%

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

      1. +-commutative 69.7%

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

   5. Simplified 69.7%

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

   if 3.0499999999999998e-50 < y < 2.7999999999999999e70

   1. Initial program 95.8%

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

   3. Taylor expanded in x around inf 52.6%

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

   4. Taylor expanded in y around inf 53.0%

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

      1. mul-1-neg 53.0%

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

      2. associate-*r/ 53.1%

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

      3. *-commutative 53.1%

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

      4. associate-*l/ 53.0%

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

      5. distribute-frac-neg2 53.0%

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

      6. associate-/l* 52.9%

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

   6. Simplified 52.9%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+118}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{-50}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+70}:\\ \;\;\;\;\left(-z\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 57.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{-5}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-91}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+30}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.7e-5) (- z) (if (<= y 1.3e-91) x (if (<= y 6e+30) y (- z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.7e-5) {
		tmp = -z;
	} else if (y <= 1.3e-91) {
		tmp = x;
	} else if (y <= 6e+30) {
		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 <= (-3.7d-5)) then
        tmp = -z
    else if (y <= 1.3d-91) then
        tmp = x
    else if (y <= 6d+30) 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 <= -3.7e-5) {
		tmp = -z;
	} else if (y <= 1.3e-91) {
		tmp = x;
	} else if (y <= 6e+30) {
		tmp = y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.7e-5:
		tmp = -z
	elif y <= 1.3e-91:
		tmp = x
	elif y <= 6e+30:
		tmp = y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.7e-5)
		tmp = Float64(-z);
	elseif (y <= 1.3e-91)
		tmp = x;
	elseif (y <= 6e+30)
		tmp = y;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.7e-5)
		tmp = -z;
	elseif (y <= 1.3e-91)
		tmp = x;
	elseif (y <= 6e+30)
		tmp = y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.7e-5], (-z), If[LessEqual[y, 1.3e-91], x, If[LessEqual[y, 6e+30], y, (-z)]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.69999999999999981e-5 or 5.99999999999999956e30 < y

   1. Initial program 75.0%

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

   3. Taylor expanded in y around inf 61.8%

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

      1. mul-1-neg 61.8%

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

   5. Simplified 61.8%

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

   if -3.69999999999999981e-5 < y < 1.30000000000000007e-91

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 62.0%

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

   if 1.30000000000000007e-91 < y < 5.99999999999999956e30

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0 52.0%

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

   4. Taylor expanded in y around 0 39.2%

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

Alternative 10: 67.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+117} \lor \neg \left(y \leq 4.3 \cdot 10^{+105}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.6e+117) (not (<= y 4.3e+105))) (- z) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.6e+117) || !(y <= 4.3e+105)) {
		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 <= (-4.6d+117)) .or. (.not. (y <= 4.3d+105))) 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 <= -4.6e+117) || !(y <= 4.3e+105)) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.6e+117) or not (y <= 4.3e+105):
		tmp = -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.6e+117) || !(y <= 4.3e+105))
		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 <= -4.6e+117) || ~((y <= 4.3e+105)))
		tmp = -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.6e+117], N[Not[LessEqual[y, 4.3e+105]], $MachinePrecision]], (-z), N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.59999999999999976e117 or 4.3000000000000002e105 < y

   1. Initial program 67.9%

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

   3. Taylor expanded in y around inf 73.6%

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

      1. mul-1-neg 73.6%

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

   5. Simplified 73.6%

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

   if -4.59999999999999976e117 < y < 4.3000000000000002e105

   1. Initial program 98.3%

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

   3. Taylor expanded in z around inf 62.9%

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

      1. +-commutative 62.9%

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

   5. Simplified 62.9%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+117} \lor \neg \left(y \leq 4.3 \cdot 10^{+105}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 40.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-70}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-224}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.4e-70) x (if (<= x 6.8e-224) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.4e-70) {
		tmp = x;
	} else if (x <= 6.8e-224) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-3.4d-70)) then
        tmp = x
    else if (x <= 6.8d-224) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.4e-70) {
		tmp = x;
	} else if (x <= 6.8e-224) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.4e-70:
		tmp = x
	elif x <= 6.8e-224:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.4e-70)
		tmp = x;
	elseif (x <= 6.8e-224)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -3.4e-70)
		tmp = x;
	elseif (x <= 6.8e-224)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.4e-70], x, If[LessEqual[x, 6.8e-224], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -3.39999999999999995e-70 or 6.79999999999999984e-224 < x

   1. Initial program 88.0%

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

   3. Taylor expanded in y around 0 40.4%

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

   if -3.39999999999999995e-70 < x < 6.79999999999999984e-224

   1. Initial program 90.0%

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

   3. Taylor expanded in x around 0 85.0%

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

   4. Taylor expanded in y around 0 46.2%

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

Alternative 12: 35.0% 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 88.4%

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

3. Taylor expanded in y around 0 33.0%

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

Developer target: 93.9% 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 2024107 
(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))))