Average Error: 0.1 → 0.2
Time: 3.9s
Precision: 64
\[\frac{x \cdot y}{2} - \frac{z}{8}\]
↓
\[\frac{1}{\frac{\frac{2}{x}}{y}} - \frac{z}{8}\]
\frac{x \cdot y}{2} - \frac{z}{8}
↓
\frac{1}{\frac{\frac{2}{x}}{y}} - \frac{z}{8}
double code(double x, double y, double z) {
	return ((double) (((double) (((double) (x * y)) / 2.0)) - ((double) (z / 8.0))));
}
↓
double code(double x, double y, double z) {
	return ((double) (((double) (1.0 / ((double) (((double) (2.0 / x)) / y)))) - ((double) (z / 8.0))));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\frac{x \cdot y}{2} - \frac{z}{8}\]
  2. Using strategy rm

  3. Applied *-commutative0.1

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

  4. Applied associate-/l*0.1

    \[\leadsto \color{blue}{\frac{y}{\frac{2}{x}}} - \frac{z}{8}\]
  5. Using strategy rm

  6. Applied clear-num0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2020114 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, D"
  :precision binary64
  (- (/ (* x y) 2) (/ z 8)))