Average Error: 0.0 → 0.0
Time: 1.6s
Precision: binary64
\[\frac{x \cdot y}{2} - \frac{z}{8}\]
↓
\[x \cdot \frac{y}{2} - \frac{z}{8}\]
\frac{x \cdot y}{2} - \frac{z}{8}
↓
x \cdot \frac{y}{2} - \frac{z}{8}
(FPCore (x y z) :precision binary64 (- (/ (* x y) 2.0) (/ z 8.0)))
↓
(FPCore (x y z) :precision binary64 (- (* x (/ y 2.0)) (/ z 8.0)))
double code(double x, double y, double z) {
	return ((x * y) / 2.0) - (z / 8.0);
}
↓
double code(double x, double y, double z) {
	return (x * (y / 2.0)) - (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 0.0

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

  3. Applied *-un-lft-identity_binary640.0

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

  4. Applied times-frac_binary640.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020253 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, D"
  :precision binary64
  (- (/ (* x y) 2.0) (/ z 8.0)))