Average Error: 0.0 → 0.0
Time: 1.2s
Precision: binary64
\[\left(x + y\right) \cdot \left(z + 1\right)\]
↓
\[y + \left(x + \left(x + y\right) \cdot z\right)\]
\left(x + y\right) \cdot \left(z + 1\right)
↓
y + \left(x + \left(x + y\right) \cdot z\right)
(FPCore (x y z) :precision binary64 (* (+ x y) (+ z 1.0)))
↓
(FPCore (x y z) :precision binary64 (+ y (+ x (* (+ x y) z))))
double code(double x, double y, double z) {
	return (x + y) * (z + 1.0);
}
↓
double code(double x, double y, double z) {
	return y + (x + ((x + 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

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

  3. Applied distribute-rgt-in_binary640.0

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

  4. Simplified0.0

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

  5. Simplified0.0

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

  7. Applied associate-+r+_binary640.0

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

  8. Simplified0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2020232 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))