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

Percentage Accurate: 88.2% → 99.7%

Time: 5.9s

Alternatives: 7

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.2% 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, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{-266} \lor \neg \left(t\_0 \leq 0\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -2e-266) (not (<= t_0 0.0))) t_0 (* z (- -1.0 (/ x y))))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -2e-266) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = z * (-1.0 - (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x + y) / (1.0d0 - (y / z))
    if ((t_0 <= (-2d-266)) .or. (.not. (t_0 <= 0.0d0))) then
        tmp = t_0
    else
        tmp = z * ((-1.0d0) - (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -2e-266) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = z * (-1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -2e-266) or not (t_0 <= 0.0):
		tmp = t_0
	else:
		tmp = z * (-1.0 - (x / y))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if ((t_0 <= -2e-266) || !(t_0 <= 0.0))
		tmp = t_0;
	else
		tmp = Float64(z * Float64(-1.0 - Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + y) / (1.0 - (y / z));
	tmp = 0.0;
	if ((t_0 <= -2e-266) || ~((t_0 <= 0.0)))
		tmp = t_0;
	else
		tmp = z * (-1.0 - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -2e-266], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], t$95$0, N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < -2e-266 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. Add Preprocessing

   if -2e-266 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < 0.0

   1. Initial program 10.9%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 10.8%

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

      2. associate-/r/ 10.8%

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

   4. Applied egg-rr 10.8%

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

   5. Taylor expanded in z around 0 95.6%

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

      1. associate-*r/ 95.6%

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

      2. +-commutative 95.6%

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

      3. neg-mul-1 95.6%

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

      4. distribute-rgt-neg-in 95.6%

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

      5. +-commutative 95.6%

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

   7. Simplified 95.6%

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

   8. Taylor expanded in z around 0 95.6%

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

      1. associate-/l* 99.9%

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

      2. +-commutative 99.9%

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

      3. *-commutative 99.9%

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

      4. *-lft-identity 99.9%

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

      5. associate-*l/ 99.7%

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

      6. +-commutative 99.7%

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

      7. distribute-rgt-in 99.7%

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

      8. associate-*r/ 99.7%

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

      9. *-rgt-identity 99.7%

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

      10. rgt-mult-inverse 99.9%

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

      11. distribute-rgt1-in 99.9%

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

      12. *-commutative 99.9%

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

      13. associate-*r/ 100.0%

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

      14. *-commutative 100.0%

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

      15. distribute-lft-out 100.0%

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

      16. *-commutative 100.0%

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

      17. associate-*r/ 84.2%

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

      18. associate-*r* 84.2%

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

      19. *-commutative 84.2%

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

   10. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -2 \cdot 10^{-266} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 72.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ \mathbf{if}\;z \leq -1.36 \cdot 10^{+107}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -1 \cdot 10^{+79}:\\ \;\;\;\;\frac{y}{t\_0}\\ \mathbf{elif}\;z \leq -1.76 \cdot 10^{-15}:\\ \;\;\;\;\frac{x}{t\_0}\\ \mathbf{elif}\;z \leq 5.25 \cdot 10^{-48}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))))
   (if (<= z -1.36e+107)
     (+ x y)
     (if (<= z -1e+79)
       (/ y t_0)
       (if (<= z -1.76e-15)
         (/ x t_0)
         (if (<= z 5.25e-48) (* z (- -1.0 (/ x y))) (+ x y)))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double tmp;
	if (z <= -1.36e+107) {
		tmp = x + y;
	} else if (z <= -1e+79) {
		tmp = y / t_0;
	} else if (z <= -1.76e-15) {
		tmp = x / t_0;
	} else if (z <= 5.25e-48) {
		tmp = z * (-1.0 - (x / y));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 - (y / z)
    if (z <= (-1.36d+107)) then
        tmp = x + y
    else if (z <= (-1d+79)) then
        tmp = y / t_0
    else if (z <= (-1.76d-15)) then
        tmp = x / t_0
    else if (z <= 5.25d-48) then
        tmp = z * ((-1.0d0) - (x / y))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double tmp;
	if (z <= -1.36e+107) {
		tmp = x + y;
	} else if (z <= -1e+79) {
		tmp = y / t_0;
	} else if (z <= -1.76e-15) {
		tmp = x / t_0;
	} else if (z <= 5.25e-48) {
		tmp = z * (-1.0 - (x / y));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	tmp = 0
	if z <= -1.36e+107:
		tmp = x + y
	elif z <= -1e+79:
		tmp = y / t_0
	elif z <= -1.76e-15:
		tmp = x / t_0
	elif z <= 5.25e-48:
		tmp = z * (-1.0 - (x / y))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y / z))
	tmp = 0.0
	if (z <= -1.36e+107)
		tmp = Float64(x + y);
	elseif (z <= -1e+79)
		tmp = Float64(y / t_0);
	elseif (z <= -1.76e-15)
		tmp = Float64(x / t_0);
	elseif (z <= 5.25e-48)
		tmp = Float64(z * Float64(-1.0 - Float64(x / y)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y / z);
	tmp = 0.0;
	if (z <= -1.36e+107)
		tmp = x + y;
	elseif (z <= -1e+79)
		tmp = y / t_0;
	elseif (z <= -1.76e-15)
		tmp = x / t_0;
	elseif (z <= 5.25e-48)
		tmp = z * (-1.0 - (x / y));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.36e+107], N[(x + y), $MachinePrecision], If[LessEqual[z, -1e+79], N[(y / t$95$0), $MachinePrecision], If[LessEqual[z, -1.76e-15], N[(x / t$95$0), $MachinePrecision], If[LessEqual[z, 5.25e-48], N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.35999999999999998e107 or 5.2500000000000002e-48 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 83.1%

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

      1. +-commutative 83.1%

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

   5. Simplified 83.1%

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

   if -1.35999999999999998e107 < z < -9.99999999999999967e78

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 88.8%

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

   if -9.99999999999999967e78 < z < -1.76e-15

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 69.2%

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

   if -1.76e-15 < z < 5.2500000000000002e-48

   1. Initial program 66.2%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 66.1%

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

      2. associate-/r/ 66.2%

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

   4. Applied egg-rr 66.2%

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

   5. Taylor expanded in z around 0 77.0%

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

      1. associate-*r/ 77.0%

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

      2. +-commutative 77.0%

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

      3. neg-mul-1 77.0%

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

      4. distribute-rgt-neg-in 77.0%

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

      5. +-commutative 77.0%

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

   7. Simplified 77.0%

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

   8. Taylor expanded in z around 0 77.0%

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

      1. associate-/l* 81.9%

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

      2. +-commutative 81.9%

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

      3. *-commutative 81.9%

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

      4. *-lft-identity 81.9%

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

      5. associate-*l/ 81.8%

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

      6. +-commutative 81.8%

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

      7. distribute-rgt-in 81.8%

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

      8. associate-*r/ 81.9%

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

      9. *-rgt-identity 81.9%

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

      10. rgt-mult-inverse 82.0%

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

      11. distribute-rgt1-in 82.0%

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

      12. *-commutative 82.0%

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

      13. associate-*r/ 84.1%

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

      14. *-commutative 84.1%

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

      15. distribute-lft-out 84.1%

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

      16. *-commutative 84.1%

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

      17. associate-*r/ 78.5%

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

      18. associate-*r* 78.5%

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

      19. *-commutative 78.5%

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

   10. Simplified 82.0%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.36 \cdot 10^{+107}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -1 \cdot 10^{+79}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;z \leq -1.76 \cdot 10^{-15}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;z \leq 5.25 \cdot 10^{-48}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+20} \lor \neg \left(z \leq 1.45 \cdot 10^{-42}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4e+20) (not (<= z 1.45e-42))) (+ x y) (* z (- -1.0 (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4e+20) || !(z <= 1.45e-42)) {
		tmp = x + y;
	} else {
		tmp = z * (-1.0 - (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 ((z <= (-4d+20)) .or. (.not. (z <= 1.45d-42))) then
        tmp = x + y
    else
        tmp = z * ((-1.0d0) - (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4e+20) || !(z <= 1.45e-42)) {
		tmp = x + y;
	} else {
		tmp = z * (-1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4e+20) or not (z <= 1.45e-42):
		tmp = x + y
	else:
		tmp = z * (-1.0 - (x / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4e+20) || !(z <= 1.45e-42))
		tmp = Float64(x + y);
	else
		tmp = Float64(z * Float64(-1.0 - Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4e+20) || ~((z <= 1.45e-42)))
		tmp = x + y;
	else
		tmp = z * (-1.0 - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4e+20], N[Not[LessEqual[z, 1.45e-42]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4e20 or 1.4500000000000001e-42 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 78.9%

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

      1. +-commutative 78.9%

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

   5. Simplified 78.9%

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

   if -4e20 < z < 1.4500000000000001e-42

   1. Initial program 69.0%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 68.8%

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

      2. associate-/r/ 68.9%

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

   4. Applied egg-rr 68.9%

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

   5. Taylor expanded in z around 0 74.9%

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

      1. associate-*r/ 74.9%

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

      2. +-commutative 74.9%

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

      3. neg-mul-1 74.9%

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

      4. distribute-rgt-neg-in 74.9%

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

      5. +-commutative 74.9%

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

   7. Simplified 74.9%

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

   8. Taylor expanded in z around 0 74.9%

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

      1. associate-/l* 79.5%

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

      2. +-commutative 79.5%

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

      3. *-commutative 79.5%

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

      4. *-lft-identity 79.5%

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

      5. associate-*l/ 79.4%

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

      6. +-commutative 79.4%

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

      7. distribute-rgt-in 79.4%

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

      8. associate-*r/ 79.4%

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

      9. *-rgt-identity 79.4%

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

      10. rgt-mult-inverse 79.5%

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

      11. distribute-rgt1-in 79.5%

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

      12. *-commutative 79.5%

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

      13. associate-*r/ 81.5%

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

      14. *-commutative 81.5%

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

      15. distribute-lft-out 81.5%

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

      16. *-commutative 81.5%

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

      17. associate-*r/ 76.4%

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

      18. associate-*r* 76.4%

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

      19. *-commutative 76.4%

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

   10. Simplified 79.5%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+20} \lor \neg \left(z \leq 1.45 \cdot 10^{-42}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 68.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+97} \lor \neg \left(y \leq 1.8 \cdot 10^{+93}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3e+97) (not (<= y 1.8e+93))) (- z) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3e+97) || !(y <= 1.8e+93)) {
		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 <= (-3d+97)) .or. (.not. (y <= 1.8d+93))) 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 <= -3e+97) || !(y <= 1.8e+93)) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3e+97) or not (y <= 1.8e+93):
		tmp = -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3e+97) || !(y <= 1.8e+93))
		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 <= -3e+97) || ~((y <= 1.8e+93)))
		tmp = -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3e+97], N[Not[LessEqual[y, 1.8e+93]], $MachinePrecision]], (-z), N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.9999999999999998e97 or 1.8e93 < y

   1. Initial program 63.5%

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

   3. Taylor expanded in y around inf 69.1%

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

      1. mul-1-neg 69.1%

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

   5. Simplified 69.1%

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

   if -2.9999999999999998e97 < y < 1.8e93

   1. Initial program 97.6%

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

   3. Taylor expanded in z around inf 69.8%

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

      1. +-commutative 69.8%

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

   5. Simplified 69.8%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+97} \lor \neg \left(y \leq 1.8 \cdot 10^{+93}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 58.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-74} \lor \neg \left(y \leq 8.2 \cdot 10^{+29}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.15e-74) (not (<= y 8.2e+29))) (- z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.15e-74) || !(y <= 8.2e+29)) {
		tmp = -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1.15d-74)) .or. (.not. (y <= 8.2d+29))) then
        tmp = -z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.15e-74) || !(y <= 8.2e+29)) {
		tmp = -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.15e-74) or not (y <= 8.2e+29):
		tmp = -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.15e-74) || !(y <= 8.2e+29))
		tmp = Float64(-z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.15e-74) || ~((y <= 8.2e+29)))
		tmp = -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.15e-74], N[Not[LessEqual[y, 8.2e+29]], $MachinePrecision]], (-z), x]

Derivation

1. Split input into 2 regimes

2. if y < -1.1499999999999999e-74 or 8.2000000000000007e29 < y

   1. Initial program 73.6%

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

   3. Taylor expanded in y around inf 55.5%

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

      1. mul-1-neg 55.5%

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

   5. Simplified 55.5%

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

   if -1.1499999999999999e-74 < y < 8.2000000000000007e29

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 63.7%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-74} \lor \neg \left(y \leq 8.2 \cdot 10^{+29}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 41.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{-117}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-108}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.05e-117) x (if (<= x 7.2e-108) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.05e-117) {
		tmp = x;
	} else if (x <= 7.2e-108) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.05d-117)) then
        tmp = x
    else if (x <= 7.2d-108) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.05e-117) {
		tmp = x;
	} else if (x <= 7.2e-108) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.05e-117:
		tmp = x
	elif x <= 7.2e-108:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.05e-117)
		tmp = x;
	elseif (x <= 7.2e-108)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.05e-117)
		tmp = x;
	elseif (x <= 7.2e-108)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.05e-117], x, If[LessEqual[x, 7.2e-108], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.05e-117 or 7.2000000000000001e-108 < x

   1. Initial program 84.5%

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

   3. Taylor expanded in y around 0 43.8%

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

   if -1.05e-117 < x < 7.2000000000000001e-108

   1. Initial program 85.9%

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

   3. Taylor expanded in x around 0 74.7%

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

   4. Taylor expanded in y around 0 37.1%

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

4. Final simplification 41.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{-117}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-108}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 35.7% 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 84.9%

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

3. Taylor expanded in y around 0 34.7%

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

4. Final simplification 34.7%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 93.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y + x}{-y} \cdot z\\ \mathbf{if}\;y < -3.7429310762689856 \cdot 10^{+171}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y < 3.5534662456086734 \cdot 10^{+168}:\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024054 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, A"
  :precision binary64

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

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