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

Percentage Accurate: 87.9% → 99.0%

Time: 7.7s

Alternatives: 10

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: 87.9% 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: 99.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ t_1 := \frac{x + y}{t_0}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-229} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;\frac{y}{t_0} + \frac{x}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - \frac{x \cdot z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))) (t_1 (/ (+ x y) t_0)))
   (if (or (<= t_1 -2e-229) (not (<= t_1 0.0)))
     (+ (/ y t_0) (/ x t_0))
     (- (- z) (/ (* x z) y)))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double t_1 = (x + y) / t_0;
	double tmp;
	if ((t_1 <= -2e-229) || !(t_1 <= 0.0)) {
		tmp = (y / t_0) + (x / t_0);
	} else {
		tmp = -z - ((x * z) / 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) :: t_1
    real(8) :: tmp
    t_0 = 1.0d0 - (y / z)
    t_1 = (x + y) / t_0
    if ((t_1 <= (-2d-229)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = (y / t_0) + (x / t_0)
    else
        tmp = -z - ((x * z) / 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 t_1 = (x + y) / t_0;
	double tmp;
	if ((t_1 <= -2e-229) || !(t_1 <= 0.0)) {
		tmp = (y / t_0) + (x / t_0);
	} else {
		tmp = -z - ((x * z) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	t_1 = (x + y) / t_0
	tmp = 0
	if (t_1 <= -2e-229) or not (t_1 <= 0.0):
		tmp = (y / t_0) + (x / t_0)
	else:
		tmp = -z - ((x * z) / y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y / z))
	t_1 = Float64(Float64(x + y) / t_0)
	tmp = 0.0
	if ((t_1 <= -2e-229) || !(t_1 <= 0.0))
		tmp = Float64(Float64(y / t_0) + Float64(x / t_0));
	else
		tmp = Float64(Float64(-z) - Float64(Float64(x * z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y / z);
	t_1 = (x + y) / t_0;
	tmp = 0.0;
	if ((t_1 <= -2e-229) || ~((t_1 <= 0.0)))
		tmp = (y / t_0) + (x / t_0);
	else
		tmp = -z - ((x * z) / y);
	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[(N[(x + y), $MachinePrecision] / t$95$0), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-229], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(y / t$95$0), $MachinePrecision] + N[(x / t$95$0), $MachinePrecision]), $MachinePrecision], N[((-z) - N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < -2.00000000000000014e-229 or 0.0 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 99.9%

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

      1. +-commutative 99.9%

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

   4. Simplified 99.9%

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

   if -2.00000000000000014e-229 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < 0.0

   1. Initial program 6.1%

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

   2. Taylor expanded in z around 0 99.6%

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

      1. associate-/l* 99.9%

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

      2. associate-*r/ 99.9%

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

      3. associate-/r/ 16.7%

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

      4. mul-1-neg 16.7%

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

      5. +-commutative 16.7%

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

   4. Simplified 16.7%

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

   5. Taylor expanded in y around 0 100.0%

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

      1. associate-/l* 83.7%

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

      2. mul-1-neg 83.7%

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

      3. mul-1-neg 83.7%

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

      4. distribute-neg-out 83.7%

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

      5. associate-/r/ 99.9%

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

      6. distribute-rgt1-in 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in x around 0 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -2 \cdot 10^{-229} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}} + \frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - \frac{x \cdot z}{y}\\ \end{array} \]

Alternative 2: 99.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t_0 \leq -2 \cdot 10^{-229} \lor \neg \left(t_0 \leq 0\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - \frac{x \cdot z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -2e-229) (not (<= t_0 0.0))) t_0 (- (- z) (/ (* x z) y)))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -2e-229) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = -z - ((x * z) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x + y) / (1.0d0 - (y / z))
    if ((t_0 <= (-2d-229)) .or. (.not. (t_0 <= 0.0d0))) then
        tmp = t_0
    else
        tmp = -z - ((x * z) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -2e-229) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = -z - ((x * z) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -2e-229) or not (t_0 <= 0.0):
		tmp = t_0
	else:
		tmp = -z - ((x * z) / y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if ((t_0 <= -2e-229) || !(t_0 <= 0.0))
		tmp = t_0;
	else
		tmp = Float64(Float64(-z) - Float64(Float64(x * z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + y) / (1.0 - (y / z));
	tmp = 0.0;
	if ((t_0 <= -2e-229) || ~((t_0 <= 0.0)))
		tmp = t_0;
	else
		tmp = -z - ((x * z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -2e-229], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], t$95$0, N[((-z) - N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < -2.00000000000000014e-229 or 0.0 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

   1. Initial program 99.9%

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

   if -2.00000000000000014e-229 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < 0.0

   1. Initial program 6.1%

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

   2. Taylor expanded in z around 0 99.6%

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

      1. associate-/l* 99.9%

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

      2. associate-*r/ 99.9%

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

      3. associate-/r/ 16.7%

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

      4. mul-1-neg 16.7%

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

      5. +-commutative 16.7%

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

   4. Simplified 16.7%

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

   5. Taylor expanded in y around 0 100.0%

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

      1. associate-/l* 83.7%

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

      2. mul-1-neg 83.7%

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

      3. mul-1-neg 83.7%

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

      4. distribute-neg-out 83.7%

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

      5. associate-/r/ 99.9%

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

      6. distribute-rgt1-in 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in x around 0 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -2 \cdot 10^{-229} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - \frac{x \cdot z}{y}\\ \end{array} \]

Alternative 3: 74.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+41}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -270000000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-12}:\\ \;\;\;\;\left(-z\right) - \frac{x \cdot z}{y}\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-245}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-82}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-51}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{y}{x + y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.7e+41)
   (* z (- -1.0 (/ x y)))
   (if (<= y -270000000000.0)
     (+ x y)
     (if (<= y -7e-12)
       (- (- z) (/ (* x z) y))
       (if (<= y -5e-245)
         (+ x y)
         (if (<= y 4.5e-82)
           (/ x (- 1.0 (/ y z)))
           (if (<= y 9.8e-51) (+ x y) (/ (- z) (/ y (+ x y))))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.7e+41) {
		tmp = z * (-1.0 - (x / y));
	} else if (y <= -270000000000.0) {
		tmp = x + y;
	} else if (y <= -7e-12) {
		tmp = -z - ((x * z) / y);
	} else if (y <= -5e-245) {
		tmp = x + y;
	} else if (y <= 4.5e-82) {
		tmp = x / (1.0 - (y / z));
	} else if (y <= 9.8e-51) {
		tmp = x + y;
	} else {
		tmp = -z / (y / (x + y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-2.7d+41)) then
        tmp = z * ((-1.0d0) - (x / y))
    else if (y <= (-270000000000.0d0)) then
        tmp = x + y
    else if (y <= (-7d-12)) then
        tmp = -z - ((x * z) / y)
    else if (y <= (-5d-245)) then
        tmp = x + y
    else if (y <= 4.5d-82) then
        tmp = x / (1.0d0 - (y / z))
    else if (y <= 9.8d-51) then
        tmp = x + y
    else
        tmp = -z / (y / (x + y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.7e+41) {
		tmp = z * (-1.0 - (x / y));
	} else if (y <= -270000000000.0) {
		tmp = x + y;
	} else if (y <= -7e-12) {
		tmp = -z - ((x * z) / y);
	} else if (y <= -5e-245) {
		tmp = x + y;
	} else if (y <= 4.5e-82) {
		tmp = x / (1.0 - (y / z));
	} else if (y <= 9.8e-51) {
		tmp = x + y;
	} else {
		tmp = -z / (y / (x + y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.7e+41:
		tmp = z * (-1.0 - (x / y))
	elif y <= -270000000000.0:
		tmp = x + y
	elif y <= -7e-12:
		tmp = -z - ((x * z) / y)
	elif y <= -5e-245:
		tmp = x + y
	elif y <= 4.5e-82:
		tmp = x / (1.0 - (y / z))
	elif y <= 9.8e-51:
		tmp = x + y
	else:
		tmp = -z / (y / (x + y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.7e+41)
		tmp = Float64(z * Float64(-1.0 - Float64(x / y)));
	elseif (y <= -270000000000.0)
		tmp = Float64(x + y);
	elseif (y <= -7e-12)
		tmp = Float64(Float64(-z) - Float64(Float64(x * z) / y));
	elseif (y <= -5e-245)
		tmp = Float64(x + y);
	elseif (y <= 4.5e-82)
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	elseif (y <= 9.8e-51)
		tmp = Float64(x + y);
	else
		tmp = Float64(Float64(-z) / Float64(y / Float64(x + y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.7e+41)
		tmp = z * (-1.0 - (x / y));
	elseif (y <= -270000000000.0)
		tmp = x + y;
	elseif (y <= -7e-12)
		tmp = -z - ((x * z) / y);
	elseif (y <= -5e-245)
		tmp = x + y;
	elseif (y <= 4.5e-82)
		tmp = x / (1.0 - (y / z));
	elseif (y <= 9.8e-51)
		tmp = x + y;
	else
		tmp = -z / (y / (x + y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.7e+41], N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -270000000000.0], N[(x + y), $MachinePrecision], If[LessEqual[y, -7e-12], N[((-z) - N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5e-245], N[(x + y), $MachinePrecision], If[LessEqual[y, 4.5e-82], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.8e-51], N[(x + y), $MachinePrecision], N[((-z) / N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.7e41

   1. Initial program 71.1%

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

   2. Taylor expanded in z around 0 73.1%

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

      1. associate-/l* 80.9%

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

      2. associate-*r/ 80.9%

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

      3. associate-/r/ 55.0%

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

      4. mul-1-neg 55.0%

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

      5. +-commutative 55.0%

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

   4. Simplified 55.0%

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

   5. Taylor expanded in y around 0 77.8%

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

      1. associate-/l* 74.9%

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

      2. mul-1-neg 74.9%

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

      3. mul-1-neg 74.9%

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

      4. distribute-neg-out 74.9%

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

      5. associate-/r/ 80.9%

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

      6. distribute-rgt1-in 80.9%

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

   7. Simplified 80.9%

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

   if -2.7e41 < y < -2.7e11 or -7.0000000000000001e-12 < y < -4.9999999999999997e-245 or 4.4999999999999998e-82 < y < 9.79999999999999948e-51

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 83.6%

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

      1. +-commutative 83.6%

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

   4. Simplified 83.6%

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

   if -2.7e11 < y < -7.0000000000000001e-12

   1. Initial program 99.4%

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

   2. Taylor expanded in z around 0 99.7%

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

      1. associate-/l* 99.4%

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

      2. associate-*r/ 99.4%

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

      3. associate-/r/ 99.4%

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

      4. mul-1-neg 99.4%

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

      5. +-commutative 99.4%

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

   4. Simplified 99.4%

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

   5. Taylor expanded in y around 0 100.0%

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

      1. associate-/l* 100.0%

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

      2. mul-1-neg 100.0%

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

      3. mul-1-neg 100.0%

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

      4. distribute-neg-out 100.0%

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

      5. associate-/r/ 99.7%

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

      6. distribute-rgt1-in 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in x around 0 100.0%

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

   if -4.9999999999999997e-245 < y < 4.4999999999999998e-82

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 97.4%

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

   if 9.79999999999999948e-51 < y

   1. Initial program 77.6%

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

   2. Taylor expanded in z around 0 63.2%

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

      1. associate-/l* 76.5%

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

      2. associate-*r/ 76.5%

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

      3. mul-1-neg 76.5%

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

      4. +-commutative 76.5%

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

   4. Simplified 76.5%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+41}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -270000000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-12}:\\ \;\;\;\;\left(-z\right) - \frac{x \cdot z}{y}\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-245}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-82}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-51}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{y}{x + y}}\\ \end{array} \]

Alternative 4: 74.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{+41}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{+22}:\\ \;\;\;\;\left(x + y\right) \cdot \left(1 + \frac{y}{z}\right)\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-10}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-238}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-79}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-51}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{y}{x + y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- -1.0 (/ x y)))))
   (if (<= y -2.7e+41)
     t_0
     (if (<= y -6.2e+22)
       (* (+ x y) (+ 1.0 (/ y z)))
       (if (<= y -2.4e-10)
         t_0
         (if (<= y -6.2e-238)
           (+ x y)
           (if (<= y 2.65e-79)
             (/ x (- 1.0 (/ y z)))
             (if (<= y 9.8e-51) (+ x y) (/ (- z) (/ y (+ x y)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (-1.0 - (x / y));
	double tmp;
	if (y <= -2.7e+41) {
		tmp = t_0;
	} else if (y <= -6.2e+22) {
		tmp = (x + y) * (1.0 + (y / z));
	} else if (y <= -2.4e-10) {
		tmp = t_0;
	} else if (y <= -6.2e-238) {
		tmp = x + y;
	} else if (y <= 2.65e-79) {
		tmp = x / (1.0 - (y / z));
	} else if (y <= 9.8e-51) {
		tmp = x + y;
	} else {
		tmp = -z / (y / (x + y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * ((-1.0d0) - (x / y))
    if (y <= (-2.7d+41)) then
        tmp = t_0
    else if (y <= (-6.2d+22)) then
        tmp = (x + y) * (1.0d0 + (y / z))
    else if (y <= (-2.4d-10)) then
        tmp = t_0
    else if (y <= (-6.2d-238)) then
        tmp = x + y
    else if (y <= 2.65d-79) then
        tmp = x / (1.0d0 - (y / z))
    else if (y <= 9.8d-51) then
        tmp = x + y
    else
        tmp = -z / (y / (x + y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (-1.0 - (x / y));
	double tmp;
	if (y <= -2.7e+41) {
		tmp = t_0;
	} else if (y <= -6.2e+22) {
		tmp = (x + y) * (1.0 + (y / z));
	} else if (y <= -2.4e-10) {
		tmp = t_0;
	} else if (y <= -6.2e-238) {
		tmp = x + y;
	} else if (y <= 2.65e-79) {
		tmp = x / (1.0 - (y / z));
	} else if (y <= 9.8e-51) {
		tmp = x + y;
	} else {
		tmp = -z / (y / (x + y));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (-1.0 - (x / y))
	tmp = 0
	if y <= -2.7e+41:
		tmp = t_0
	elif y <= -6.2e+22:
		tmp = (x + y) * (1.0 + (y / z))
	elif y <= -2.4e-10:
		tmp = t_0
	elif y <= -6.2e-238:
		tmp = x + y
	elif y <= 2.65e-79:
		tmp = x / (1.0 - (y / z))
	elif y <= 9.8e-51:
		tmp = x + y
	else:
		tmp = -z / (y / (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 <= -2.7e+41)
		tmp = t_0;
	elseif (y <= -6.2e+22)
		tmp = Float64(Float64(x + y) * Float64(1.0 + Float64(y / z)));
	elseif (y <= -2.4e-10)
		tmp = t_0;
	elseif (y <= -6.2e-238)
		tmp = Float64(x + y);
	elseif (y <= 2.65e-79)
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	elseif (y <= 9.8e-51)
		tmp = Float64(x + y);
	else
		tmp = Float64(Float64(-z) / Float64(y / 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 <= -2.7e+41)
		tmp = t_0;
	elseif (y <= -6.2e+22)
		tmp = (x + y) * (1.0 + (y / z));
	elseif (y <= -2.4e-10)
		tmp = t_0;
	elseif (y <= -6.2e-238)
		tmp = x + y;
	elseif (y <= 2.65e-79)
		tmp = x / (1.0 - (y / z));
	elseif (y <= 9.8e-51)
		tmp = x + y;
	else
		tmp = -z / (y / (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, -2.7e+41], t$95$0, If[LessEqual[y, -6.2e+22], N[(N[(x + y), $MachinePrecision] * N[(1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.4e-10], t$95$0, If[LessEqual[y, -6.2e-238], N[(x + y), $MachinePrecision], If[LessEqual[y, 2.65e-79], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.8e-51], N[(x + y), $MachinePrecision], N[((-z) / N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.7e41 or -6.2000000000000004e22 < y < -2.4e-10

   1. Initial program 73.9%

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

   2. Taylor expanded in z around 0 74.4%

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

      1. associate-/l* 81.4%

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

      2. associate-*r/ 81.4%

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

      3. associate-/r/ 58.2%

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

      4. mul-1-neg 58.2%

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

      5. +-commutative 58.2%

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

   4. Simplified 58.2%

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

   5. Taylor expanded in y around 0 78.7%

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

      1. associate-/l* 76.1%

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

      2. mul-1-neg 76.1%

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

      3. mul-1-neg 76.1%

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

      4. distribute-neg-out 76.1%

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

      5. associate-/r/ 81.4%

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

      6. distribute-rgt1-in 81.4%

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

   7. Simplified 81.4%

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

   if -2.7e41 < y < -6.2000000000000004e22

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 100.0%

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

      1. associate-+r+ 100.0%

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

      2. *-rgt-identity 100.0%

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

      3. *-commutative 100.0%

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

      4. associate-*r/ 100.0%

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

      5. distribute-lft-in 99.7%

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

      6. +-commutative 99.7%

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

   4. Simplified 99.7%

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

   if -2.4e-10 < y < -6.2000000000000002e-238 or 2.6499999999999999e-79 < y < 9.79999999999999948e-51

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 83.9%

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

      1. +-commutative 83.9%

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

   4. Simplified 83.9%

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

   if -6.2000000000000002e-238 < y < 2.6499999999999999e-79

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 97.4%

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

   if 9.79999999999999948e-51 < y

   1. Initial program 77.6%

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

   2. Taylor expanded in z around 0 63.2%

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

      1. associate-/l* 76.5%

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

      2. associate-*r/ 76.5%

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

      3. mul-1-neg 76.5%

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

      4. +-commutative 76.5%

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

   4. Simplified 76.5%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+41}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{+22}:\\ \;\;\;\;\left(x + y\right) \cdot \left(1 + \frac{y}{z}\right)\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-10}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-238}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-79}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-51}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{y}{x + y}}\\ \end{array} \]

Alternative 5: 74.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -2.55 \cdot 10^{+41}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -120000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-11}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-235}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-81}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 9.4 \cdot 10^{-51}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- -1.0 (/ x y)))))
   (if (<= y -2.55e+41)
     t_0
     (if (<= y -120000000.0)
       (+ x y)
       (if (<= y -4.5e-11)
         t_0
         (if (<= y -2.5e-235)
           (+ x y)
           (if (<= y 1.4e-81)
             (/ x (- 1.0 (/ y z)))
             (if (<= y 9.4e-51) (+ x y) t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (-1.0 - (x / y));
	double tmp;
	if (y <= -2.55e+41) {
		tmp = t_0;
	} else if (y <= -120000000.0) {
		tmp = x + y;
	} else if (y <= -4.5e-11) {
		tmp = t_0;
	} else if (y <= -2.5e-235) {
		tmp = x + y;
	} else if (y <= 1.4e-81) {
		tmp = x / (1.0 - (y / z));
	} else if (y <= 9.4e-51) {
		tmp = x + y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * ((-1.0d0) - (x / y))
    if (y <= (-2.55d+41)) then
        tmp = t_0
    else if (y <= (-120000000.0d0)) then
        tmp = x + y
    else if (y <= (-4.5d-11)) then
        tmp = t_0
    else if (y <= (-2.5d-235)) then
        tmp = x + y
    else if (y <= 1.4d-81) then
        tmp = x / (1.0d0 - (y / z))
    else if (y <= 9.4d-51) then
        tmp = x + y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (-1.0 - (x / y));
	double tmp;
	if (y <= -2.55e+41) {
		tmp = t_0;
	} else if (y <= -120000000.0) {
		tmp = x + y;
	} else if (y <= -4.5e-11) {
		tmp = t_0;
	} else if (y <= -2.5e-235) {
		tmp = x + y;
	} else if (y <= 1.4e-81) {
		tmp = x / (1.0 - (y / z));
	} else if (y <= 9.4e-51) {
		tmp = x + y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (-1.0 - (x / y))
	tmp = 0
	if y <= -2.55e+41:
		tmp = t_0
	elif y <= -120000000.0:
		tmp = x + y
	elif y <= -4.5e-11:
		tmp = t_0
	elif y <= -2.5e-235:
		tmp = x + y
	elif y <= 1.4e-81:
		tmp = x / (1.0 - (y / z))
	elif y <= 9.4e-51:
		tmp = x + y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -2.55e+41)
		tmp = t_0;
	elseif (y <= -120000000.0)
		tmp = Float64(x + y);
	elseif (y <= -4.5e-11)
		tmp = t_0;
	elseif (y <= -2.5e-235)
		tmp = Float64(x + y);
	elseif (y <= 1.4e-81)
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	elseif (y <= 9.4e-51)
		tmp = Float64(x + y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (-1.0 - (x / y));
	tmp = 0.0;
	if (y <= -2.55e+41)
		tmp = t_0;
	elseif (y <= -120000000.0)
		tmp = x + y;
	elseif (y <= -4.5e-11)
		tmp = t_0;
	elseif (y <= -2.5e-235)
		tmp = x + y;
	elseif (y <= 1.4e-81)
		tmp = x / (1.0 - (y / z));
	elseif (y <= 9.4e-51)
		tmp = x + y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.55e+41], t$95$0, If[LessEqual[y, -120000000.0], N[(x + y), $MachinePrecision], If[LessEqual[y, -4.5e-11], t$95$0, If[LessEqual[y, -2.5e-235], N[(x + y), $MachinePrecision], If[LessEqual[y, 1.4e-81], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.4e-51], N[(x + y), $MachinePrecision], t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.54999999999999989e41 or -1.2e8 < y < -4.5e-11 or 9.3999999999999995e-51 < y

   1. Initial program 75.3%

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

   2. Taylor expanded in z around 0 69.3%

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

      1. associate-/l* 79.5%

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

      2. associate-*r/ 79.5%

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

      3. associate-/r/ 57.6%

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

      4. mul-1-neg 57.6%

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

      5. +-commutative 57.6%

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

   4. Simplified 57.6%

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

   5. Taylor expanded in y around 0 76.0%

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

      1. associate-/l* 75.2%

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

      2. mul-1-neg 75.2%

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

      3. mul-1-neg 75.2%

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

      4. distribute-neg-out 75.2%

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

      5. associate-/r/ 79.5%

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

      6. distribute-rgt1-in 79.5%

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

   7. Simplified 79.5%

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

   if -2.54999999999999989e41 < y < -1.2e8 or -4.5e-11 < y < -2.4999999999999999e-235 or 1.3999999999999999e-81 < y < 9.3999999999999995e-51

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 83.6%

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

      1. +-commutative 83.6%

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

   4. Simplified 83.6%

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

   if -2.4999999999999999e-235 < y < 1.3999999999999999e-81

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 97.4%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{+41}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -120000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-11}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-235}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-81}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 9.4 \cdot 10^{-51}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \]

Alternative 6: 74.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{+41}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -2150000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-11}:\\ \;\;\;\;\left(-z\right) - \frac{x \cdot z}{y}\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-235}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-78}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-51}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- -1.0 (/ x y)))))
   (if (<= y -2.3e+41)
     t_0
     (if (<= y -2150000000.0)
       (+ x y)
       (if (<= y -3.7e-11)
         (- (- z) (/ (* x z) y))
         (if (<= y -3.3e-235)
           (+ x y)
           (if (<= y 3e-78)
             (/ x (- 1.0 (/ y z)))
             (if (<= y 9.8e-51) (+ x y) t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (-1.0 - (x / y));
	double tmp;
	if (y <= -2.3e+41) {
		tmp = t_0;
	} else if (y <= -2150000000.0) {
		tmp = x + y;
	} else if (y <= -3.7e-11) {
		tmp = -z - ((x * z) / y);
	} else if (y <= -3.3e-235) {
		tmp = x + y;
	} else if (y <= 3e-78) {
		tmp = x / (1.0 - (y / z));
	} else if (y <= 9.8e-51) {
		tmp = x + y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * ((-1.0d0) - (x / y))
    if (y <= (-2.3d+41)) then
        tmp = t_0
    else if (y <= (-2150000000.0d0)) then
        tmp = x + y
    else if (y <= (-3.7d-11)) then
        tmp = -z - ((x * z) / y)
    else if (y <= (-3.3d-235)) then
        tmp = x + y
    else if (y <= 3d-78) then
        tmp = x / (1.0d0 - (y / z))
    else if (y <= 9.8d-51) then
        tmp = x + y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (-1.0 - (x / y));
	double tmp;
	if (y <= -2.3e+41) {
		tmp = t_0;
	} else if (y <= -2150000000.0) {
		tmp = x + y;
	} else if (y <= -3.7e-11) {
		tmp = -z - ((x * z) / y);
	} else if (y <= -3.3e-235) {
		tmp = x + y;
	} else if (y <= 3e-78) {
		tmp = x / (1.0 - (y / z));
	} else if (y <= 9.8e-51) {
		tmp = x + y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (-1.0 - (x / y))
	tmp = 0
	if y <= -2.3e+41:
		tmp = t_0
	elif y <= -2150000000.0:
		tmp = x + y
	elif y <= -3.7e-11:
		tmp = -z - ((x * z) / y)
	elif y <= -3.3e-235:
		tmp = x + y
	elif y <= 3e-78:
		tmp = x / (1.0 - (y / z))
	elif y <= 9.8e-51:
		tmp = x + y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -2.3e+41)
		tmp = t_0;
	elseif (y <= -2150000000.0)
		tmp = Float64(x + y);
	elseif (y <= -3.7e-11)
		tmp = Float64(Float64(-z) - Float64(Float64(x * z) / y));
	elseif (y <= -3.3e-235)
		tmp = Float64(x + y);
	elseif (y <= 3e-78)
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	elseif (y <= 9.8e-51)
		tmp = Float64(x + y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (-1.0 - (x / y));
	tmp = 0.0;
	if (y <= -2.3e+41)
		tmp = t_0;
	elseif (y <= -2150000000.0)
		tmp = x + y;
	elseif (y <= -3.7e-11)
		tmp = -z - ((x * z) / y);
	elseif (y <= -3.3e-235)
		tmp = x + y;
	elseif (y <= 3e-78)
		tmp = x / (1.0 - (y / z));
	elseif (y <= 9.8e-51)
		tmp = x + y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.3e+41], t$95$0, If[LessEqual[y, -2150000000.0], N[(x + y), $MachinePrecision], If[LessEqual[y, -3.7e-11], N[((-z) - N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.3e-235], N[(x + y), $MachinePrecision], If[LessEqual[y, 3e-78], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.8e-51], N[(x + y), $MachinePrecision], t$95$0]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.2999999999999998e41 or 9.79999999999999948e-51 < y

   1. Initial program 74.3%

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

   2. Taylor expanded in z around 0 68.1%

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

      1. associate-/l* 78.7%

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

      2. associate-*r/ 78.7%

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

      3. associate-/r/ 55.9%

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

      4. mul-1-neg 55.9%

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

      5. +-commutative 55.9%

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

   4. Simplified 55.9%

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

   5. Taylor expanded in y around 0 75.1%

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

      1. associate-/l* 74.3%

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

      2. mul-1-neg 74.3%

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

      3. mul-1-neg 74.3%

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

      4. distribute-neg-out 74.3%

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

      5. associate-/r/ 78.7%

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

      6. distribute-rgt1-in 78.7%

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

   7. Simplified 78.7%

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

   if -2.2999999999999998e41 < y < -2.15e9 or -3.7000000000000001e-11 < y < -3.30000000000000028e-235 or 2.99999999999999988e-78 < y < 9.79999999999999948e-51

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 83.6%

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

      1. +-commutative 83.6%

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

   4. Simplified 83.6%

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

   if -2.15e9 < y < -3.7000000000000001e-11

   1. Initial program 99.4%

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

   2. Taylor expanded in z around 0 99.7%

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

      1. associate-/l* 99.4%

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

      2. associate-*r/ 99.4%

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

      3. associate-/r/ 99.4%

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

      4. mul-1-neg 99.4%

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

      5. +-commutative 99.4%

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

   4. Simplified 99.4%

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

   5. Taylor expanded in y around 0 100.0%

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

      1. associate-/l* 100.0%

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

      2. mul-1-neg 100.0%

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

      3. mul-1-neg 100.0%

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

      4. distribute-neg-out 100.0%

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

      5. associate-/r/ 99.7%

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

      6. distribute-rgt1-in 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in x around 0 100.0%

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

   if -3.30000000000000028e-235 < y < 2.99999999999999988e-78

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 97.4%

      \[\leadsto \color{blue}{\frac{x}{1 - \frac{y}{z}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+41}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -2150000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-11}:\\ \;\;\;\;\left(-z\right) - \frac{x \cdot z}{y}\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-235}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-78}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-51}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \]

Alternative 7: 67.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+45}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-233}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-84}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-51}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5.8e+45)
   (- z)
   (if (<= y -5.6e-233)
     (+ x y)
     (if (<= y 4.5e-84)
       (/ x (- 1.0 (/ y z)))
       (if (<= y 9.8e-51) (+ x y) (- z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.8e+45) {
		tmp = -z;
	} else if (y <= -5.6e-233) {
		tmp = x + y;
	} else if (y <= 4.5e-84) {
		tmp = x / (1.0 - (y / z));
	} else if (y <= 9.8e-51) {
		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 <= (-5.8d+45)) then
        tmp = -z
    else if (y <= (-5.6d-233)) then
        tmp = x + y
    else if (y <= 4.5d-84) then
        tmp = x / (1.0d0 - (y / z))
    else if (y <= 9.8d-51) 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 <= -5.8e+45) {
		tmp = -z;
	} else if (y <= -5.6e-233) {
		tmp = x + y;
	} else if (y <= 4.5e-84) {
		tmp = x / (1.0 - (y / z));
	} else if (y <= 9.8e-51) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5.8e+45:
		tmp = -z
	elif y <= -5.6e-233:
		tmp = x + y
	elif y <= 4.5e-84:
		tmp = x / (1.0 - (y / z))
	elif y <= 9.8e-51:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5.8e+45)
		tmp = Float64(-z);
	elseif (y <= -5.6e-233)
		tmp = Float64(x + y);
	elseif (y <= 4.5e-84)
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	elseif (y <= 9.8e-51)
		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 <= -5.8e+45)
		tmp = -z;
	elseif (y <= -5.6e-233)
		tmp = x + y;
	elseif (y <= 4.5e-84)
		tmp = x / (1.0 - (y / z));
	elseif (y <= 9.8e-51)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5.8e+45], (-z), If[LessEqual[y, -5.6e-233], N[(x + y), $MachinePrecision], If[LessEqual[y, 4.5e-84], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.8e-51], N[(x + y), $MachinePrecision], (-z)]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.7999999999999994e45 or 9.79999999999999948e-51 < y

   1. Initial program 73.5%

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

   2. Taylor expanded in y around inf 64.8%

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

      1. mul-1-neg 64.8%

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

   4. Simplified 64.8%

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

   if -5.7999999999999994e45 < y < -5.6000000000000002e-233 or 4.50000000000000016e-84 < y < 9.79999999999999948e-51

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 76.4%

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

      1. +-commutative 76.4%

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

   4. Simplified 76.4%

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

   if -5.6000000000000002e-233 < y < 4.50000000000000016e-84

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 97.4%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+45}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-233}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-84}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-51}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 8: 66.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+45} \lor \neg \left(y \leq 9.8 \cdot 10^{-51}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.1e+45) (not (<= y 9.8e-51))) (- z) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.1e+45) || !(y <= 9.8e-51)) {
		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 <= (-2.1d+45)) .or. (.not. (y <= 9.8d-51))) 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 <= -2.1e+45) || !(y <= 9.8e-51)) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.1e+45) or not (y <= 9.8e-51):
		tmp = -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.1e+45) || !(y <= 9.8e-51))
		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 <= -2.1e+45) || ~((y <= 9.8e-51)))
		tmp = -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.1e+45], N[Not[LessEqual[y, 9.8e-51]], $MachinePrecision]], (-z), N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.09999999999999995e45 or 9.79999999999999948e-51 < y

   1. Initial program 73.5%

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

   2. Taylor expanded in y around inf 64.8%

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

      1. mul-1-neg 64.8%

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

   4. Simplified 64.8%

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

   if -2.09999999999999995e45 < y < 9.79999999999999948e-51

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 82.4%

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

      1. +-commutative 82.4%

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

   4. Simplified 82.4%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+45} \lor \neg \left(y \leq 9.8 \cdot 10^{-51}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 9: 59.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-42} \lor \neg \left(y \leq 9.8 \cdot 10^{-51}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6.5e-42) (not (<= y 9.8e-51))) (- z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.5e-42) || !(y <= 9.8e-51)) {
		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 <= (-6.5d-42)) .or. (.not. (y <= 9.8d-51))) 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 <= -6.5e-42) || !(y <= 9.8e-51)) {
		tmp = -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6.5e-42) or not (y <= 9.8e-51):
		tmp = -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6.5e-42) || !(y <= 9.8e-51))
		tmp = Float64(-z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -6.5e-42) || ~((y <= 9.8e-51)))
		tmp = -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6.5e-42], N[Not[LessEqual[y, 9.8e-51]], $MachinePrecision]], (-z), x]

Derivation

1. Split input into 2 regimes

2. if y < -6.4999999999999998e-42 or 9.79999999999999948e-51 < y

   1. Initial program 77.0%

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

   2. Taylor expanded in y around inf 59.0%

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

      1. mul-1-neg 59.0%

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

   4. Simplified 59.0%

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

   if -6.4999999999999998e-42 < y < 9.79999999999999948e-51

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 72.1%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-42} \lor \neg \left(y \leq 9.8 \cdot 10^{-51}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 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 87.4%

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

2. Taylor expanded in y around 0 39.0%

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

3. Final simplification 39.0%

   \[\leadsto x \]

Developer target: 93.9% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023301 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, A"
  :precision binary64

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

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