Average Error: 0.0 → 0.0
Time: 4.4s
Precision: binary64
\[x \cdot y + \left(x - 1\right) \cdot z\]
↓
\[1 \cdot \left(x \cdot \left(y + z\right) - z\right)\]
x \cdot y + \left(x - 1\right) \cdot z
↓
1 \cdot \left(x \cdot \left(y + z\right) - z\right)
double code(double x, double y, double z) {
	return ((double) (((double) (x * y)) + ((double) (((double) (x - 1.0)) * z))));
}
↓
double code(double x, double y, double z) {
	return ((double) (1.0 * ((double) (((double) (x * ((double) (y + 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. Using strategy rm

  3. Applied flip3--12.4

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

  4. Applied associate-*l/14.6

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

  5. Simplified14.6

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

  7. Applied flip-+34.4

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

  8. Simplified36.2

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

  9. Simplified36.1

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

  10. Taylor expanded around 0 0.0

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

  11. Simplified0.0

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

  12. Final simplification0.0

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

Reproduce

herbie shell --seed 2020199 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))