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

Percentage Accurate: 77.4% → 99.7%

Time: 25.5s

Alternatives: 11

Speedup: 0.7×

• could not determine a ground truth

  1. x = 9.429174205771284e-145
  2. y = 1.1730846309764473e-229
  3. z = -6.994430973655785e+179

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: 77.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+27}:\\ \;\;\;\;\frac{y + x}{y} \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{+17}:\\ \;\;\;\;\frac{y + x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-z\right) - \frac{z}{\frac{y}{x}}\right) - \frac{z}{\frac{y}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.5e+27)
   (* (/ (+ y x) y) (- z))
   (if (<= y 2.65e+17)
     (/ (+ y x) (- 1.0 (/ y z)))
     (- (- (- z) (/ z (/ y x))) (/ z (/ y z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.5e+27) {
		tmp = ((y + x) / y) * -z;
	} else if (y <= 2.65e+17) {
		tmp = (y + x) / (1.0 - (y / z));
	} else {
		tmp = (-z - (z / (y / x))) - (z / (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-4.5d+27)) then
        tmp = ((y + x) / y) * -z
    else if (y <= 2.65d+17) then
        tmp = (y + x) / (1.0d0 - (y / z))
    else
        tmp = (-z - (z / (y / x))) - (z / (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.5e+27) {
		tmp = ((y + x) / y) * -z;
	} else if (y <= 2.65e+17) {
		tmp = (y + x) / (1.0 - (y / z));
	} else {
		tmp = (-z - (z / (y / x))) - (z / (y / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.5e+27:
		tmp = ((y + x) / y) * -z
	elif y <= 2.65e+17:
		tmp = (y + x) / (1.0 - (y / z))
	else:
		tmp = (-z - (z / (y / x))) - (z / (y / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.5e+27)
		tmp = Float64(Float64(Float64(y + x) / y) * Float64(-z));
	elseif (y <= 2.65e+17)
		tmp = Float64(Float64(y + x) / Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(Float64(Float64(-z) - Float64(z / Float64(y / x))) - Float64(z / Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4.5e+27)
		tmp = ((y + x) / y) * -z;
	elseif (y <= 2.65e+17)
		tmp = (y + x) / (1.0 - (y / z));
	else
		tmp = (-z - (z / (y / x))) - (z / (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.5e+27], N[(N[(N[(y + x), $MachinePrecision] / y), $MachinePrecision] * (-z)), $MachinePrecision], If[LessEqual[y, 2.65e+17], N[(N[(y + x), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[((-z) - N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.4999999999999999e27

   1. Initial program 49.1%

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

   2. Taylor expanded in z around 0 99.8%

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

      1. mul-1-neg 99.8%

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

      2. associate-/l* 49.1%

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

      3. +-commutative 49.1%

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

      4. associate-/r/ 100.0%

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

      5. distribute-rgt-neg-in 100.0%

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

      6. +-commutative 100.0%

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

   4. Simplified 100.0%

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

   if -4.4999999999999999e27 < y < 2.65e17

   1. Initial program 99.8%

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

   if 2.65e17 < y

   1. Initial program 50.8%

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

   2. Taylor expanded in y around inf 99.9%

      \[\leadsto \color{blue}{\left(-1 \cdot z + -1 \cdot \frac{z \cdot x}{y}\right) - \frac{{z}^{2}}{y}} \]
   3. Step-by-step derivation

      1. mul-1-neg 99.9%

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

      2. unsub-neg 99.9%

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

      3. mul-1-neg 99.9%

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

      4. associate-/l* 99.9%

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

      5. unpow2 99.9%

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

      6. associate-/l* 99.9%

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

   4. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+27}:\\ \;\;\;\;\frac{y + x}{y} \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{+17}:\\ \;\;\;\;\frac{y + x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-z\right) - \frac{z}{\frac{y}{x}}\right) - \frac{z}{\frac{y}{z}}\\ \end{array} \]

Alternative 2: 67.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{-z}{y}\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{+21}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-155}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{-148}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-8}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (/ (- z) y))))
   (if (<= y -5.5e+21)
     (- z)
     (if (<= y -2.7e-155)
       t_0
       (if (<= y 3.05e-148) (+ y x) (if (<= y 8e-8) t_0 (- z)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (-z / y);
	double tmp;
	if (y <= -5.5e+21) {
		tmp = -z;
	} else if (y <= -2.7e-155) {
		tmp = t_0;
	} else if (y <= 3.05e-148) {
		tmp = y + x;
	} else if (y <= 8e-8) {
		tmp = t_0;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (-z / y)
    if (y <= (-5.5d+21)) then
        tmp = -z
    else if (y <= (-2.7d-155)) then
        tmp = t_0
    else if (y <= 3.05d-148) then
        tmp = y + x
    else if (y <= 8d-8) then
        tmp = t_0
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (-z / y);
	double tmp;
	if (y <= -5.5e+21) {
		tmp = -z;
	} else if (y <= -2.7e-155) {
		tmp = t_0;
	} else if (y <= 3.05e-148) {
		tmp = y + x;
	} else if (y <= 8e-8) {
		tmp = t_0;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (-z / y)
	tmp = 0
	if y <= -5.5e+21:
		tmp = -z
	elif y <= -2.7e-155:
		tmp = t_0
	elif y <= 3.05e-148:
		tmp = y + x
	elif y <= 8e-8:
		tmp = t_0
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(Float64(-z) / y))
	tmp = 0.0
	if (y <= -5.5e+21)
		tmp = Float64(-z);
	elseif (y <= -2.7e-155)
		tmp = t_0;
	elseif (y <= 3.05e-148)
		tmp = Float64(y + x);
	elseif (y <= 8e-8)
		tmp = t_0;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (-z / y);
	tmp = 0.0;
	if (y <= -5.5e+21)
		tmp = -z;
	elseif (y <= -2.7e-155)
		tmp = t_0;
	elseif (y <= 3.05e-148)
		tmp = y + x;
	elseif (y <= 8e-8)
		tmp = t_0;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[((-z) / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.5e+21], (-z), If[LessEqual[y, -2.7e-155], t$95$0, If[LessEqual[y, 3.05e-148], N[(y + x), $MachinePrecision], If[LessEqual[y, 8e-8], t$95$0, (-z)]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.5e21 or 8.0000000000000002e-8 < y

   1. Initial program 52.5%

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

   2. Taylor expanded in y around inf 78.2%

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

      1. mul-1-neg 78.2%

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

   4. Simplified 78.2%

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

   if -5.5e21 < y < -2.69999999999999981e-155 or 3.04999999999999988e-148 < y < 8.0000000000000002e-8

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 70.2%

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

   3. Taylor expanded in y around inf 55.9%

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

      1. mul-1-neg 55.9%

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

      2. *-commutative 55.9%

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

      3. associate-*r/ 58.6%

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

      4. distribute-rgt-neg-in 58.6%

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

      5. distribute-frac-neg 58.6%

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

   5. Simplified 58.6%

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

   if -2.69999999999999981e-155 < y < 3.04999999999999988e-148

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 85.0%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+21}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-155}:\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{-148}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 3: 67.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{\frac{-y}{z}}\\ \mathbf{if}\;y \leq -3.9 \cdot 10^{+18}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-151}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-151}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-8}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ x (/ (- y) z))))
   (if (<= y -3.9e+18)
     (- z)
     (if (<= y -1.1e-151)
       t_0
       (if (<= y 5e-151) (+ y x) (if (<= y 7.5e-8) t_0 (- z)))))))

C

double code(double x, double y, double z) {
	double t_0 = x / (-y / z);
	double tmp;
	if (y <= -3.9e+18) {
		tmp = -z;
	} else if (y <= -1.1e-151) {
		tmp = t_0;
	} else if (y <= 5e-151) {
		tmp = y + x;
	} else if (y <= 7.5e-8) {
		tmp = t_0;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x / (-y / z)
    if (y <= (-3.9d+18)) then
        tmp = -z
    else if (y <= (-1.1d-151)) then
        tmp = t_0
    else if (y <= 5d-151) then
        tmp = y + x
    else if (y <= 7.5d-8) then
        tmp = t_0
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x / (-y / z);
	double tmp;
	if (y <= -3.9e+18) {
		tmp = -z;
	} else if (y <= -1.1e-151) {
		tmp = t_0;
	} else if (y <= 5e-151) {
		tmp = y + x;
	} else if (y <= 7.5e-8) {
		tmp = t_0;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x / (-y / z)
	tmp = 0
	if y <= -3.9e+18:
		tmp = -z
	elif y <= -1.1e-151:
		tmp = t_0
	elif y <= 5e-151:
		tmp = y + x
	elif y <= 7.5e-8:
		tmp = t_0
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x / Float64(Float64(-y) / z))
	tmp = 0.0
	if (y <= -3.9e+18)
		tmp = Float64(-z);
	elseif (y <= -1.1e-151)
		tmp = t_0;
	elseif (y <= 5e-151)
		tmp = Float64(y + x);
	elseif (y <= 7.5e-8)
		tmp = t_0;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x / (-y / z);
	tmp = 0.0;
	if (y <= -3.9e+18)
		tmp = -z;
	elseif (y <= -1.1e-151)
		tmp = t_0;
	elseif (y <= 5e-151)
		tmp = y + x;
	elseif (y <= 7.5e-8)
		tmp = t_0;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x / N[((-y) / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.9e+18], (-z), If[LessEqual[y, -1.1e-151], t$95$0, If[LessEqual[y, 5e-151], N[(y + x), $MachinePrecision], If[LessEqual[y, 7.5e-8], t$95$0, (-z)]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.9e18 or 7.4999999999999997e-8 < y

   1. Initial program 52.5%

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

   2. Taylor expanded in y around inf 78.2%

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

      1. mul-1-neg 78.2%

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

   4. Simplified 78.2%

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

   if -3.9e18 < y < -1.1e-151 or 5.00000000000000003e-151 < y < 7.4999999999999997e-8

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 70.2%

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

   3. Taylor expanded in y around inf 58.7%

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

      1. mul-1-neg 58.7%

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

      2. distribute-frac-neg 58.7%

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

   5. Simplified 58.7%

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

   if -1.1e-151 < y < 5.00000000000000003e-151

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 85.0%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+18}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-151}:\\ \;\;\;\;\frac{x}{\frac{-y}{z}}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-151}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-8}:\\ \;\;\;\;\frac{x}{\frac{-y}{z}}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 4: 99.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+28}:\\ \;\;\;\;\frac{y + x}{y} \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+14}:\\ \;\;\;\;\frac{y + x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y + x\right) \cdot \left(-z\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1e+28)
   (* (/ (+ y x) y) (- z))
   (if (<= y 1.45e+14) (/ (+ y x) (- 1.0 (/ y z))) (/ (* (+ y x) (- z)) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1e+28) {
		tmp = ((y + x) / y) * -z;
	} else if (y <= 1.45e+14) {
		tmp = (y + x) / (1.0 - (y / z));
	} else {
		tmp = ((y + 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) :: tmp
    if (y <= (-1d+28)) then
        tmp = ((y + x) / y) * -z
    else if (y <= 1.45d+14) then
        tmp = (y + x) / (1.0d0 - (y / z))
    else
        tmp = ((y + x) * -z) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1e+28) {
		tmp = ((y + x) / y) * -z;
	} else if (y <= 1.45e+14) {
		tmp = (y + x) / (1.0 - (y / z));
	} else {
		tmp = ((y + x) * -z) / y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1e+28:
		tmp = ((y + x) / y) * -z
	elif y <= 1.45e+14:
		tmp = (y + x) / (1.0 - (y / z))
	else:
		tmp = ((y + x) * -z) / y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1e+28)
		tmp = Float64(Float64(Float64(y + x) / y) * Float64(-z));
	elseif (y <= 1.45e+14)
		tmp = Float64(Float64(y + x) / Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(Float64(Float64(y + x) * Float64(-z)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1e+28)
		tmp = ((y + x) / y) * -z;
	elseif (y <= 1.45e+14)
		tmp = (y + x) / (1.0 - (y / z));
	else
		tmp = ((y + x) * -z) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1e+28], N[(N[(N[(y + x), $MachinePrecision] / y), $MachinePrecision] * (-z)), $MachinePrecision], If[LessEqual[y, 1.45e+14], N[(N[(y + x), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y + x), $MachinePrecision] * (-z)), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.99999999999999958e27

   1. Initial program 49.1%

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

   2. Taylor expanded in z around 0 99.8%

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

      1. mul-1-neg 99.8%

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

      2. associate-/l* 49.1%

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

      3. +-commutative 49.1%

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

      4. associate-/r/ 100.0%

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

      5. distribute-rgt-neg-in 100.0%

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

      6. +-commutative 100.0%

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

   4. Simplified 100.0%

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

   if -9.99999999999999958e27 < y < 1.45e14

   1. Initial program 99.8%

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

   if 1.45e14 < y

   1. Initial program 50.8%

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

   2. Taylor expanded in z around 0 99.8%

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

      1. mul-1-neg 99.8%

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

      2. +-commutative 99.8%

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

      3. *-commutative 99.8%

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

      4. +-commutative 99.8%

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

   4. Simplified 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+28}:\\ \;\;\;\;\frac{y + x}{y} \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+14}:\\ \;\;\;\;\frac{y + x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y + x\right) \cdot \left(-z\right)}{y}\\ \end{array} \]

Alternative 5: 87.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-64} \lor \neg \left(y \leq 5.6 \cdot 10^{-123}\right):\\ \;\;\;\;\left(-z\right) - x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.1e-64) (not (<= y 5.6e-123)))
   (- (- z) (* x (/ z y)))
   (/ x (- 1.0 (/ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.1e-64) || !(y <= 5.6e-123)) {
		tmp = -z - (x * (z / y));
	} else {
		tmp = x / (1.0 - (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-2.1d-64)) .or. (.not. (y <= 5.6d-123))) then
        tmp = -z - (x * (z / y))
    else
        tmp = x / (1.0d0 - (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.1e-64) || !(y <= 5.6e-123)) {
		tmp = -z - (x * (z / y));
	} else {
		tmp = x / (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.1e-64) or not (y <= 5.6e-123):
		tmp = -z - (x * (z / y))
	else:
		tmp = x / (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.1e-64) || !(y <= 5.6e-123))
		tmp = Float64(Float64(-z) - Float64(x * Float64(z / y)));
	else
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.1e-64) || ~((y <= 5.6e-123)))
		tmp = -z - (x * (z / y));
	else
		tmp = x / (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.1e-64], N[Not[LessEqual[y, 5.6e-123]], $MachinePrecision]], N[((-z) - N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.10000000000000011e-64 or 5.5999999999999998e-123 < y

   1. Initial program 62.0%

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

   2. Taylor expanded in z around 0 94.3%

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

      1. mul-1-neg 94.3%

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

      2. +-commutative 94.3%

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

      3. *-commutative 94.3%

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

      4. +-commutative 94.3%

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

   4. Simplified 94.3%

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

   5. Taylor expanded in y around 0 95.4%

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

      1. associate-*r/ 94.8%

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

      2. +-commutative 94.8%

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

      3. *-commutative 94.8%

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

      4. associate-*l/ 95.4%

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

      5. associate-*r/ 91.7%

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

   7. Simplified 91.7%

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

   if -2.10000000000000011e-64 < y < 5.5999999999999998e-123

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 84.9%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-64} \lor \neg \left(y \leq 5.6 \cdot 10^{-123}\right):\\ \;\;\;\;\left(-z\right) - x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \end{array} \]

Alternative 6: 89.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-57} \lor \neg \left(y \leq 5.6 \cdot 10^{-123}\right):\\ \;\;\;\;\frac{\left(y + x\right) \cdot \left(-z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -7.5e-57) (not (<= y 5.6e-123)))
   (/ (* (+ y x) (- z)) y)
   (/ x (- 1.0 (/ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7.5e-57) || !(y <= 5.6e-123)) {
		tmp = ((y + x) * -z) / y;
	} else {
		tmp = x / (1.0 - (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-7.5d-57)) .or. (.not. (y <= 5.6d-123))) then
        tmp = ((y + x) * -z) / y
    else
        tmp = x / (1.0d0 - (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7.5e-57) || !(y <= 5.6e-123)) {
		tmp = ((y + x) * -z) / y;
	} else {
		tmp = x / (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -7.5e-57) or not (y <= 5.6e-123):
		tmp = ((y + x) * -z) / y
	else:
		tmp = x / (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -7.5e-57) || !(y <= 5.6e-123))
		tmp = Float64(Float64(Float64(y + x) * Float64(-z)) / y);
	else
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -7.5e-57) || ~((y <= 5.6e-123)))
		tmp = ((y + x) * -z) / y;
	else
		tmp = x / (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -7.5e-57], N[Not[LessEqual[y, 5.6e-123]], $MachinePrecision]], N[(N[(N[(y + x), $MachinePrecision] * (-z)), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.49999999999999973e-57 or 5.5999999999999998e-123 < y

   1. Initial program 62.0%

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

   2. Taylor expanded in z around 0 94.3%

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

      1. mul-1-neg 94.3%

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

      2. +-commutative 94.3%

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

      3. *-commutative 94.3%

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

      4. +-commutative 94.3%

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

   4. Simplified 94.3%

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

   if -7.49999999999999973e-57 < y < 5.5999999999999998e-123

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 84.9%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-57} \lor \neg \left(y \leq 5.6 \cdot 10^{-123}\right):\\ \;\;\;\;\frac{\left(y + x\right) \cdot \left(-z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \end{array} \]

Alternative 7: 89.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-58} \lor \neg \left(y \leq 5.6 \cdot 10^{-123}\right):\\ \;\;\;\;\frac{y + x}{y} \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6e-58) (not (<= y 5.6e-123)))
   (* (/ (+ y x) y) (- z))
   (/ x (- 1.0 (/ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6e-58) || !(y <= 5.6e-123)) {
		tmp = ((y + x) / y) * -z;
	} else {
		tmp = x / (1.0 - (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-6d-58)) .or. (.not. (y <= 5.6d-123))) then
        tmp = ((y + x) / y) * -z
    else
        tmp = x / (1.0d0 - (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6e-58) || !(y <= 5.6e-123)) {
		tmp = ((y + x) / y) * -z;
	} else {
		tmp = x / (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6e-58) or not (y <= 5.6e-123):
		tmp = ((y + x) / y) * -z
	else:
		tmp = x / (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6e-58) || !(y <= 5.6e-123))
		tmp = Float64(Float64(Float64(y + x) / y) * Float64(-z));
	else
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -6e-58) || ~((y <= 5.6e-123)))
		tmp = ((y + x) / y) * -z;
	else
		tmp = x / (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6e-58], N[Not[LessEqual[y, 5.6e-123]], $MachinePrecision]], N[(N[(N[(y + x), $MachinePrecision] / y), $MachinePrecision] * (-z)), $MachinePrecision], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.00000000000000015e-58 or 5.5999999999999998e-123 < y

   1. Initial program 62.0%

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

   2. Taylor expanded in z around 0 94.3%

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

      1. mul-1-neg 94.3%

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

      2. associate-/l* 58.1%

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

      3. +-commutative 58.1%

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

      4. associate-/r/ 94.8%

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

      5. distribute-rgt-neg-in 94.8%

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

      6. +-commutative 94.8%

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

   4. Simplified 94.8%

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

   if -6.00000000000000015e-58 < y < 5.5999999999999998e-123

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 84.9%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-58} \lor \neg \left(y \leq 5.6 \cdot 10^{-123}\right):\\ \;\;\;\;\frac{y + x}{y} \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \end{array} \]

Alternative 8: 75.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+21}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-8}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.95e+21) (- z) (if (<= y 7.6e-8) (/ x (- 1.0 (/ y z))) (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.95e+21) {
		tmp = -z;
	} else if (y <= 7.6e-8) {
		tmp = x / (1.0 - (y / z));
	} 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 <= (-1.95d+21)) then
        tmp = -z
    else if (y <= 7.6d-8) then
        tmp = x / (1.0d0 - (y / z))
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.95e+21) {
		tmp = -z;
	} else if (y <= 7.6e-8) {
		tmp = x / (1.0 - (y / z));
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.95e+21:
		tmp = -z
	elif y <= 7.6e-8:
		tmp = x / (1.0 - (y / z))
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.95e+21)
		tmp = Float64(-z);
	elseif (y <= 7.6e-8)
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.95e+21)
		tmp = -z;
	elseif (y <= 7.6e-8)
		tmp = x / (1.0 - (y / z));
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.95e+21], (-z), If[LessEqual[y, 7.6e-8], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], (-z)]]

Derivation

1. Split input into 2 regimes

2. if y < -1.95e21 or 7.60000000000000056e-8 < y

   1. Initial program 52.5%

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

   2. Taylor expanded in y around inf 78.2%

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

      1. mul-1-neg 78.2%

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

   4. Simplified 78.2%

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

   if -1.95e21 < y < 7.60000000000000056e-8

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 78.6%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+21}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-8}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 9: 65.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-49}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-123}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.25e-49) (- z) (if (<= y 5.6e-123) (+ y x) (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.25e-49) {
		tmp = -z;
	} else if (y <= 5.6e-123) {
		tmp = 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 <= (-1.25d-49)) then
        tmp = -z
    else if (y <= 5.6d-123) then
        tmp = 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 <= -1.25e-49) {
		tmp = -z;
	} else if (y <= 5.6e-123) {
		tmp = y + x;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.25e-49:
		tmp = -z
	elif y <= 5.6e-123:
		tmp = y + x
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.25e-49)
		tmp = Float64(-z);
	elseif (y <= 5.6e-123)
		tmp = Float64(y + x);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.25e-49)
		tmp = -z;
	elseif (y <= 5.6e-123)
		tmp = y + x;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.25e-49], (-z), If[LessEqual[y, 5.6e-123], N[(y + x), $MachinePrecision], (-z)]]

Derivation

1. Split input into 2 regimes

2. if y < -1.25e-49 or 5.5999999999999998e-123 < y

   1. Initial program 62.0%

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

   2. Taylor expanded in y around inf 67.8%

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

      1. mul-1-neg 67.8%

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

   4. Simplified 67.8%

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

   if -1.25e-49 < y < 5.5999999999999998e-123

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 67.1%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-49}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-123}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 10: 62.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-56}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{-123}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -9.5e-56) (- z) (if (<= y 5.3e-123) x (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -9.5e-56) {
		tmp = -z;
	} else if (y <= 5.3e-123) {
		tmp = 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 <= (-9.5d-56)) then
        tmp = -z
    else if (y <= 5.3d-123) then
        tmp = 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 <= -9.5e-56) {
		tmp = -z;
	} else if (y <= 5.3e-123) {
		tmp = x;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -9.5e-56:
		tmp = -z
	elif y <= 5.3e-123:
		tmp = x
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -9.5e-56)
		tmp = Float64(-z);
	elseif (y <= 5.3e-123)
		tmp = x;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -9.5e-56)
		tmp = -z;
	elseif (y <= 5.3e-123)
		tmp = x;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -9.5e-56], (-z), If[LessEqual[y, 5.3e-123], x, (-z)]]

Derivation

1. Split input into 2 regimes

2. if y < -9.4999999999999991e-56 or 5.29999999999999971e-123 < y

   1. Initial program 62.0%

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

   2. Taylor expanded in y around inf 67.8%

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

      1. mul-1-neg 67.8%

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

   4. Simplified 67.8%

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

   if -9.4999999999999991e-56 < y < 5.29999999999999971e-123

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 58.0%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-56}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{-123}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 11: 24.1% 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 73.7%

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

2. Taylor expanded in y around 0 21.1%

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

3. Final simplification 21.1%

   \[\leadsto x \]

Developer target: 93.0% 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 2023278 
(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))))