Average Error: 0.0 → 0.0
Time: 2.8s
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 flip3-+40.6

    \[\leadsto \color{blue}{\frac{{\left(x \cdot y\right)}^{3} + {\left(\left(x - 1\right) \cdot z\right)}^{3}}{\left(x \cdot y\right) \cdot \left(x \cdot y\right) + \left(\left(\left(x - 1\right) \cdot z\right) \cdot \left(\left(x - 1\right) \cdot z\right) - \left(x \cdot y\right) \cdot \left(\left(x - 1\right) \cdot z\right)\right)}}\]

  4. Simplified40.6

    \[\leadsto \frac{{\left(x \cdot y\right)}^{3} + {\left(\left(x - 1\right) \cdot z\right)}^{3}}{\color{blue}{\left(\left(x - 1\right) \cdot z\right) \cdot \left(\left(x - 1\right) \cdot z - x \cdot y\right) + \left(x \cdot y\right) \cdot \left(x \cdot y\right)}}\]

  5. Taylor expanded around 0 0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020103 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1) z)))