Average Error: 0.0 → 0.0
Time: 1.4s
Precision: binary64
\[x - \left(y \cdot 4\right) \cdot z\]
↓
\[x - y \cdot \left(4 \cdot z\right)\]
x - \left(y \cdot 4\right) \cdot z
↓
x - y \cdot \left(4 \cdot z\right)
(FPCore (x y z) :precision binary64 (- x (* (* y 4.0) z)))
↓
(FPCore (x y z) :precision binary64 (- x (* y (* 4.0 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 - (y * (4.0 * 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 associate-*l*_binary640.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020224 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, A"
  :precision binary64
  (- x (* (* y 4.0) z)))