Average Error: 0.0 → 0.0
Time: 2.7s
Precision: binary64
\[x \cdot y + \left(x - 1\right) \cdot z\]
↓
\[x \cdot y + \left(x \cdot z - z \cdot 1\right)\]
x \cdot y + \left(x - 1\right) \cdot z
↓
x \cdot y + \left(x \cdot z - z \cdot 1\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) (((double) (x * y)) + ((double) (((double) (x * z)) - ((double) (z * 1.0))))));
}

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 add-sqr-sqrt0.0

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

  4. Applied add-sqr-sqrt31.9

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

  5. Applied difference-of-squares31.9

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

  6. Applied associate-*l*31.9

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

  7. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{\left(x \cdot z + x \cdot y\right) - {\left(\sqrt{1}\right)}^{2} \cdot z}\]

  8. Simplified0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2020161 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))