Average Error: 0.0 → 0.0
Time: 1.8s
Precision: binary64
\[x \cdot y + \left(x - 1\right) \cdot z\]
↓
\[\left(x \cdot y + x \cdot z\right) - z\]
x \cdot y + \left(x - 1\right) \cdot z
↓
\left(x \cdot y + x \cdot z\right) - z
(FPCore (x y z) :precision binary64 (+ (* x y) (* (- x 1.0) z)))
↓
(FPCore (x y z) :precision binary64 (- (+ (* x y) (* x z)) z))
double code(double x, double y, double z) {
	return (x * y) + ((x - 1.0) * z);
}
↓
double code(double x, double y, double z) {
	return ((x * y) + (x * z)) - 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

    \[x \cdot y + \left(x - 1\right) \cdot z\]

  2. Simplified0.0

    \[\leadsto \color{blue}{x \cdot \left(y + z\right) - z}\]
  3. Using strategy rm

  4. Applied distribute-rgt-in_binary640.0

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

  5. Simplified0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020232 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))