Average Error: 0.0 → 0.0
Time: 2.3s
Precision: binary64
\[x \cdot y + \left(x - 1\right) \cdot z\]
↓
\[x \cdot y + \left(x \cdot z - z\right)\]
x \cdot y + \left(x - 1\right) \cdot z
↓
x \cdot y + \left(x \cdot z - z\right)
(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. Using strategy rm

  3. Applied *-un-lft-identity_binary640.0

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

  4. Applied associate-*l*_binary640.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Alternatives

Reproduce

herbie shell --seed 2021118 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))