Average Error: 0.0 → 0.0
Time: 2.2s
Precision: 64
\[x \cdot y + \left(x - 1\right) \cdot z\]
↓
\[1 \cdot \left(x \cdot \left(z + y\right) - z\right)\]
x \cdot y + \left(x - 1\right) \cdot z
↓
1 \cdot \left(x \cdot \left(z + y\right) - z\right)
double code(double x, double y, double z) {
	return ((x * y) + ((x - 1.0) * z));
}
↓
double code(double x, double y, double z) {
	return (1.0 * ((x * (z + 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

    \[x \cdot y + \left(x - 1\right) \cdot z\]
  2. Using strategy rm

  3. Applied flip-+29.5

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

  4. Taylor expanded around 0 0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020053 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1) z)))