Average Error: 0.0 → 0.0
Time: 1.3s
Precision: binary64
\[x - \left(y \cdot 4\right) \cdot z \]
↓
\[x - 4 \cdot \left(y \cdot z\right) \]
x - \left(y \cdot 4\right) \cdot z
↓
x - 4 \cdot \left(y \cdot z\right)

(FPCore (x y z) :precision binary64 (- x (* (* y 4.0) z)))
↓
(FPCore (x y z) :precision binary64 (- x (* 4.0 (* y z))))
double code(double x, double y, double z) {
	return x - ((y * 4.0) * z);
}
↓
double code(double x, double y, double z) {
	return x - (4.0 * (y * z));
}

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

    \[x - \left(y \cdot 4\right) \cdot z \]
  2. Using strategy rm

  3. Applied pow1_binary640.0

    \[\leadsto x - \left(y \cdot 4\right) \cdot \color{blue}{{z}^{1}} \]

  4. Applied pow1_binary640.0

    \[\leadsto x - \left(y \cdot \color{blue}{{4}^{1}}\right) \cdot {z}^{1} \]

  5. Applied pow1_binary640.0

    \[\leadsto x - \left(\color{blue}{{y}^{1}} \cdot {4}^{1}\right) \cdot {z}^{1} \]

  6. Applied pow-prod-down_binary640.0

    \[\leadsto x - \color{blue}{{\left(y \cdot 4\right)}^{1}} \cdot {z}^{1} \]

  7. Applied pow-prod-down_binary640.0

    \[\leadsto x - \color{blue}{{\left(\left(y \cdot 4\right) \cdot z\right)}^{1}} \]

  8. Simplified0.0

    \[\leadsto x - {\color{blue}{\left(4 \cdot \left(y \cdot z\right)\right)}}^{1} \]

  9. Final simplification0.0

    \[\leadsto x - 4 \cdot \left(y \cdot z\right) \]

Reproduce

herbie shell --seed 2021204 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, A"
  :precision binary64
  (- x (* (* y 4.0) z)))