Diagrams.Solve.Polynomial:quartForm from diagrams-solve-0.1, D

Percentage Accurate: 100.0% → 100.0%

Time: 7.2s

Alternatives: 5

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x \cdot y}{2} - \frac{z}{8} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (/ (* x y) 2.0) (/ z 8.0)))

C

double code(double x, double y, double z) {
	return ((x * y) / 2.0) - (z / 8.0);
}

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) / 2.0d0) - (z / 8.0d0)
end function

Java

public static double code(double x, double y, double z) {
	return ((x * y) / 2.0) - (z / 8.0);
}

Python

def code(x, y, z):
	return ((x * y) / 2.0) - (z / 8.0)

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x * y) / 2.0) - Float64(z / 8.0))
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x * y) / 2.0) - (z / 8.0);
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x * y), $MachinePrecision] / 2.0), $MachinePrecision] - N[(z / 8.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot y}{2} - \frac{z}{8} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (/ (* x y) 2.0) (/ z 8.0)))

C

double code(double x, double y, double z) {
	return ((x * y) / 2.0) - (z / 8.0);
}

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) / 2.0d0) - (z / 8.0d0)
end function

Java

public static double code(double x, double y, double z) {
	return ((x * y) / 2.0) - (z / 8.0);
}

Python

def code(x, y, z):
	return ((x * y) / 2.0) - (z / 8.0)

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x * y) / 2.0) - Float64(z / 8.0))
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x * y) / 2.0) - (z / 8.0);
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x * y), $MachinePrecision] / 2.0), $MachinePrecision] - N[(z / 8.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\frac{x}{2}, y, -0.125 \cdot z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma (/ x 2.0) y (* -0.125 z)))

C

double code(double x, double y, double z) {
	return fma((x / 2.0), y, (-0.125 * z));
}

Julia

function code(x, y, z)
	return fma(Float64(x / 2.0), y, Float64(-0.125 * z))
end

Wolfram

code[x_, y_, z_] := N[(N[(x / 2.0), $MachinePrecision] * y + N[(-0.125 * z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{x \cdot y}{2} - \frac{z}{8} \]
2. Step-by-step derivation

   1. associate-*l/ 100.0%

      \[\leadsto \color{blue}{\frac{x}{2} \cdot y} - \frac{z}{8} \]

   2. fma-neg 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{2}, y, -\frac{z}{8}\right)} \]

   3. distribute-frac-neg 100.0%

      \[\leadsto \mathsf{fma}\left(\frac{x}{2}, y, \color{blue}{\frac{-z}{8}}\right) \]

   4. neg-mul-1 100.0%

      \[\leadsto \mathsf{fma}\left(\frac{x}{2}, y, \frac{\color{blue}{-1 \cdot z}}{8}\right) \]

   5. associate-/l* 99.9%

      \[\leadsto \mathsf{fma}\left(\frac{x}{2}, y, \color{blue}{\frac{-1}{\frac{8}{z}}}\right) \]

   6. associate-/r/ 100.0%

      \[\leadsto \mathsf{fma}\left(\frac{x}{2}, y, \color{blue}{\frac{-1}{8} \cdot z}\right) \]

   7. metadata-eval 100.0%

      \[\leadsto \mathsf{fma}\left(\frac{x}{2}, y, \color{blue}{-0.125} \cdot z\right) \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{2}, y, -0.125 \cdot z\right)} \]

4. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(\frac{x}{2}, y, -0.125 \cdot z\right) \]

Alternative 2: 78.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.6 \cdot 10^{+25} \lor \neg \left(x \cdot y \leq -2.6 \cdot 10^{-44} \lor \neg \left(x \cdot y \leq -2.1 \cdot 10^{-67}\right) \land x \cdot y \leq 1.05 \cdot 10^{+63}\right):\\ \;\;\;\;\left(x \cdot y\right) \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;-0.125 \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= (* x y) -1.6e+25)
         (not
          (or (<= (* x y) -2.6e-44)
              (and (not (<= (* x y) -2.1e-67)) (<= (* x y) 1.05e+63)))))
   (* (* x y) 0.5)
   (* -0.125 z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (((x * y) <= -1.6e+25) || !(((x * y) <= -2.6e-44) || (!((x * y) <= -2.1e-67) && ((x * y) <= 1.05e+63)))) {
		tmp = (x * y) * 0.5;
	} else {
		tmp = -0.125 * 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 (((x * y) <= (-1.6d+25)) .or. (.not. ((x * y) <= (-2.6d-44)) .or. (.not. ((x * y) <= (-2.1d-67))) .and. ((x * y) <= 1.05d+63))) then
        tmp = (x * y) * 0.5d0
    else
        tmp = (-0.125d0) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (((x * y) <= -1.6e+25) || !(((x * y) <= -2.6e-44) || (!((x * y) <= -2.1e-67) && ((x * y) <= 1.05e+63)))) {
		tmp = (x * y) * 0.5;
	} else {
		tmp = -0.125 * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((x * y) <= -1.6e+25) or not (((x * y) <= -2.6e-44) or (not ((x * y) <= -2.1e-67) and ((x * y) <= 1.05e+63))):
		tmp = (x * y) * 0.5
	else:
		tmp = -0.125 * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((Float64(x * y) <= -1.6e+25) || !((Float64(x * y) <= -2.6e-44) || (!(Float64(x * y) <= -2.1e-67) && (Float64(x * y) <= 1.05e+63))))
		tmp = Float64(Float64(x * y) * 0.5);
	else
		tmp = Float64(-0.125 * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((x * y) <= -1.6e+25) || ~((((x * y) <= -2.6e-44) || (~(((x * y) <= -2.1e-67)) && ((x * y) <= 1.05e+63)))))
		tmp = (x * y) * 0.5;
	else
		tmp = -0.125 * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -1.6e+25], N[Not[Or[LessEqual[N[(x * y), $MachinePrecision], -2.6e-44], And[N[Not[LessEqual[N[(x * y), $MachinePrecision], -2.1e-67]], $MachinePrecision], LessEqual[N[(x * y), $MachinePrecision], 1.05e+63]]]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] * 0.5), $MachinePrecision], N[(-0.125 * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.6e25 or -2.5999999999999998e-44 < (*.f64 x y) < -2.1000000000000002e-67 or 1.0500000000000001e63 < (*.f64 x y)

   1. Initial program 100.0%

      \[\frac{x \cdot y}{2} - \frac{z}{8} \]
   2. Step-by-step derivation

      1. associate-*l/ 100.0%

         \[\leadsto \color{blue}{\frac{x}{2} \cdot y} - \frac{z}{8} \]

      2. fma-neg 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{2}, y, -\frac{z}{8}\right)} \]

      3. distribute-frac-neg 100.0%

         \[\leadsto \mathsf{fma}\left(\frac{x}{2}, y, \color{blue}{\frac{-z}{8}}\right) \]

      4. neg-mul-1 100.0%

         \[\leadsto \mathsf{fma}\left(\frac{x}{2}, y, \frac{\color{blue}{-1 \cdot z}}{8}\right) \]

      5. associate-/l* 99.9%

         \[\leadsto \mathsf{fma}\left(\frac{x}{2}, y, \color{blue}{\frac{-1}{\frac{8}{z}}}\right) \]

      6. associate-/r/ 100.0%

         \[\leadsto \mathsf{fma}\left(\frac{x}{2}, y, \color{blue}{\frac{-1}{8} \cdot z}\right) \]

      7. metadata-eval 100.0%

         \[\leadsto \mathsf{fma}\left(\frac{x}{2}, y, \color{blue}{-0.125} \cdot z\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{2}, y, -0.125 \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto \mathsf{fma}\left(\frac{x}{2}, y, \color{blue}{z \cdot -0.125}\right) \]

      2. metadata-eval 100.0%

         \[\leadsto \mathsf{fma}\left(\frac{x}{2}, y, z \cdot \color{blue}{\left(-0.125\right)}\right) \]

      3. metadata-eval 100.0%

         \[\leadsto \mathsf{fma}\left(\frac{x}{2}, y, z \cdot \left(-\color{blue}{\frac{1}{8}}\right)\right) \]

      4. distribute-rgt-neg-in 100.0%

         \[\leadsto \mathsf{fma}\left(\frac{x}{2}, y, \color{blue}{-z \cdot \frac{1}{8}}\right) \]

      5. div-inv 100.0%

         \[\leadsto \mathsf{fma}\left(\frac{x}{2}, y, -\color{blue}{\frac{z}{8}}\right) \]

      6. fma-neg 100.0%

         \[\leadsto \color{blue}{\frac{x}{2} \cdot y - \frac{z}{8}} \]

      7. associate-/r/ 99.8%

         \[\leadsto \color{blue}{\frac{x}{\frac{2}{y}}} - \frac{z}{8} \]

      8. associate-/l* 100.0%

         \[\leadsto \color{blue}{\frac{x \cdot y}{2}} - \frac{z}{8} \]

      9. frac-2neg 100.0%

         \[\leadsto \color{blue}{\frac{-x \cdot y}{-2}} - \frac{z}{8} \]

      10. clear-num 99.9%

          \[\leadsto \frac{-x \cdot y}{-2} - \color{blue}{\frac{1}{\frac{8}{z}}} \]

      11. frac-sub 85.5%

          \[\leadsto \color{blue}{\frac{\left(-x \cdot y\right) \cdot \frac{8}{z} - \left(-2\right) \cdot 1}{\left(-2\right) \cdot \frac{8}{z}}} \]

      12. metadata-eval 85.5%

          \[\leadsto \frac{\left(-x \cdot y\right) \cdot \frac{8}{z} - \color{blue}{-2} \cdot 1}{\left(-2\right) \cdot \frac{8}{z}} \]

      13. metadata-eval 85.5%

          \[\leadsto \frac{\left(-x \cdot y\right) \cdot \frac{8}{z} - \color{blue}{-2}}{\left(-2\right) \cdot \frac{8}{z}} \]

      14. metadata-eval 85.5%

          \[\leadsto \frac{\left(-x \cdot y\right) \cdot \frac{8}{z} - \color{blue}{\left(-2\right)}}{\left(-2\right) \cdot \frac{8}{z}} \]

      15. div-sub 85.5%

          \[\leadsto \color{blue}{\frac{\left(-x \cdot y\right) \cdot \frac{8}{z}}{\left(-2\right) \cdot \frac{8}{z}} - \frac{-2}{\left(-2\right) \cdot \frac{8}{z}}} \]

   5. Applied egg-rr 81.5%

      \[\leadsto \color{blue}{\frac{x \cdot \left(\left(-y\right) \cdot \frac{8}{z}\right)}{\frac{-16}{z}} - \frac{-2}{\frac{-16}{z}}} \]
   6. Step-by-step derivation

      1. associate-*r* 85.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot \left(-y\right)\right) \cdot \frac{8}{z}}}{\frac{-16}{z}} - \frac{-2}{\frac{-16}{z}} \]

      2. div-inv 85.5%

         \[\leadsto \frac{\left(x \cdot \left(-y\right)\right) \cdot \color{blue}{\left(8 \cdot \frac{1}{z}\right)}}{\frac{-16}{z}} - \frac{-2}{\frac{-16}{z}} \]

      3. associate-*r* 84.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot \left(-y\right)\right) \cdot 8\right) \cdot \frac{1}{z}}}{\frac{-16}{z}} - \frac{-2}{\frac{-16}{z}} \]

      4. div-inv 84.9%

         \[\leadsto \frac{\left(\left(x \cdot \left(-y\right)\right) \cdot 8\right) \cdot \frac{1}{z}}{\color{blue}{-16 \cdot \frac{1}{z}}} - \frac{-2}{\frac{-16}{z}} \]

      5. times-frac 99.3%

         \[\leadsto \color{blue}{\frac{\left(x \cdot \left(-y\right)\right) \cdot 8}{-16} \cdot \frac{\frac{1}{z}}{\frac{1}{z}}} - \frac{-2}{\frac{-16}{z}} \]

      6. associate-*r* 99.3%

         \[\leadsto \frac{\color{blue}{x \cdot \left(\left(-y\right) \cdot 8\right)}}{-16} \cdot \frac{\frac{1}{z}}{\frac{1}{z}} - \frac{-2}{\frac{-16}{z}} \]

      7. neg-mul-1 99.3%

         \[\leadsto \frac{x \cdot \left(\color{blue}{\left(-1 \cdot y\right)} \cdot 8\right)}{-16} \cdot \frac{\frac{1}{z}}{\frac{1}{z}} - \frac{-2}{\frac{-16}{z}} \]

      8. *-commutative 99.3%

         \[\leadsto \frac{x \cdot \left(\color{blue}{\left(y \cdot -1\right)} \cdot 8\right)}{-16} \cdot \frac{\frac{1}{z}}{\frac{1}{z}} - \frac{-2}{\frac{-16}{z}} \]

      9. associate-*l* 99.3%

         \[\leadsto \frac{x \cdot \color{blue}{\left(y \cdot \left(-1 \cdot 8\right)\right)}}{-16} \cdot \frac{\frac{1}{z}}{\frac{1}{z}} - \frac{-2}{\frac{-16}{z}} \]

      10. metadata-eval 99.3%

          \[\leadsto \frac{x \cdot \left(y \cdot \color{blue}{-8}\right)}{-16} \cdot \frac{\frac{1}{z}}{\frac{1}{z}} - \frac{-2}{\frac{-16}{z}} \]

   7. Applied egg-rr 99.3%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y \cdot -8\right)}{-16} \cdot \frac{\frac{1}{z}}{\frac{1}{z}}} - \frac{-2}{\frac{-16}{z}} \]
   8. Step-by-step derivation

      1. *-inverses 99.3%

         \[\leadsto \frac{x \cdot \left(y \cdot -8\right)}{-16} \cdot \color{blue}{1} - \frac{-2}{\frac{-16}{z}} \]

      2. *-rgt-identity 99.3%

         \[\leadsto \color{blue}{\frac{x \cdot \left(y \cdot -8\right)}{-16}} - \frac{-2}{\frac{-16}{z}} \]

      3. associate-/l* 99.7%

         \[\leadsto \color{blue}{\frac{x}{\frac{-16}{y \cdot -8}}} - \frac{-2}{\frac{-16}{z}} \]

      4. *-commutative 99.7%

         \[\leadsto \frac{x}{\frac{-16}{\color{blue}{-8 \cdot y}}} - \frac{-2}{\frac{-16}{z}} \]

      5. associate-/r* 99.7%

         \[\leadsto \frac{x}{\color{blue}{\frac{\frac{-16}{-8}}{y}}} - \frac{-2}{\frac{-16}{z}} \]

      6. metadata-eval 99.7%

         \[\leadsto \frac{x}{\frac{\color{blue}{2}}{y}} - \frac{-2}{\frac{-16}{z}} \]

   9. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{x}{\frac{2}{y}}} - \frac{-2}{\frac{-16}{z}} \]

   10. Taylor expanded in x around inf 82.3%

       \[\leadsto \color{blue}{0.5 \cdot \left(x \cdot y\right)} \]

   if -1.6e25 < (*.f64 x y) < -2.5999999999999998e-44 or -2.1000000000000002e-67 < (*.f64 x y) < 1.0500000000000001e63

   1. Initial program 100.0%

      \[\frac{x \cdot y}{2} - \frac{z}{8} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

         \[\leadsto \color{blue}{\frac{x}{\frac{2}{y}}} - \frac{z}{8} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{x}{\frac{2}{y}} - \frac{z}{8}} \]

   4. Taylor expanded in x around 0 77.8%

      \[\leadsto \color{blue}{-0.125 \cdot z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.6 \cdot 10^{+25} \lor \neg \left(x \cdot y \leq -2.6 \cdot 10^{-44} \lor \neg \left(x \cdot y \leq -2.1 \cdot 10^{-67}\right) \land x \cdot y \leq 1.05 \cdot 10^{+63}\right):\\ \;\;\;\;\left(x \cdot y\right) \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;-0.125 \cdot z\\ \end{array} \]

Alternative 3: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{\frac{2}{y}} - \frac{z}{8} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (/ x (/ 2.0 y)) (/ z 8.0)))

C

double code(double x, double y, double z) {
	return (x / (2.0 / y)) - (z / 8.0);
}

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 / (2.0d0 / y)) - (z / 8.0d0)
end function

Java

public static double code(double x, double y, double z) {
	return (x / (2.0 / y)) - (z / 8.0);
}

Python

def code(x, y, z):
	return (x / (2.0 / y)) - (z / 8.0)

Julia

function code(x, y, z)
	return Float64(Float64(x / Float64(2.0 / y)) - Float64(z / 8.0))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x / (2.0 / y)) - (z / 8.0);
end

Wolfram

code[x_, y_, z_] := N[(N[(x / N[(2.0 / y), $MachinePrecision]), $MachinePrecision] - N[(z / 8.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{x \cdot y}{2} - \frac{z}{8} \]
2. Step-by-step derivation

   1. associate-/l* 99.8%

      \[\leadsto \color{blue}{\frac{x}{\frac{2}{y}}} - \frac{z}{8} \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{\frac{x}{\frac{2}{y}} - \frac{z}{8}} \]

4. Final simplification 99.8%

   \[\leadsto \frac{x}{\frac{2}{y}} - \frac{z}{8} \]

Alternative 4: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot y}{2} - \frac{z}{8} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (/ (* x y) 2.0) (/ z 8.0)))

C

double code(double x, double y, double z) {
	return ((x * y) / 2.0) - (z / 8.0);
}

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) / 2.0d0) - (z / 8.0d0)
end function

Java

public static double code(double x, double y, double z) {
	return ((x * y) / 2.0) - (z / 8.0);
}

Python

def code(x, y, z):
	return ((x * y) / 2.0) - (z / 8.0)

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x * y) / 2.0) - Float64(z / 8.0))
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x * y) / 2.0) - (z / 8.0);
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x * y), $MachinePrecision] / 2.0), $MachinePrecision] - N[(z / 8.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{x \cdot y}{2} - \frac{z}{8} \]

2. Final simplification 100.0%

   \[\leadsto \frac{x \cdot y}{2} - \frac{z}{8} \]

Alternative 5: 51.6% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ -0.125 \cdot z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* -0.125 z))

C

double code(double x, double y, double z) {
	return -0.125 * 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 = (-0.125d0) * z
end function

Java

public static double code(double x, double y, double z) {
	return -0.125 * z;
}

Python

def code(x, y, z):
	return -0.125 * z

Julia

function code(x, y, z)
	return Float64(-0.125 * z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = -0.125 * z;
end

Wolfram

code[x_, y_, z_] := N[(-0.125 * z), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{x \cdot y}{2} - \frac{z}{8} \]
2. Step-by-step derivation

   1. associate-/l* 99.8%

      \[\leadsto \color{blue}{\frac{x}{\frac{2}{y}}} - \frac{z}{8} \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{\frac{x}{\frac{2}{y}} - \frac{z}{8}} \]

4. Taylor expanded in x around 0 49.2%

   \[\leadsto \color{blue}{-0.125 \cdot z} \]

5. Final simplification 49.2%

   \[\leadsto -0.125 \cdot z \]

Reproduce

herbie shell --seed 2023297 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, D"
  :precision binary64
  (- (/ (* x y) 2.0) (/ z 8.0)))