Average Error: 0.0 → 0.0
Time: 1.8s
Precision: binary64
\[\left(x + y\right) \cdot \left(z + 1\right) \]
↓
\[y + \left(x + z \cdot \left(y + x\right)\right) \]
\left(x + y\right) \cdot \left(z + 1\right)
↓
y + \left(x + z \cdot \left(y + x\right)\right)

(FPCore (x y z) :precision binary64 (* (+ x y) (+ z 1.0)))
↓
(FPCore (x y z) :precision binary64 (+ y (+ x (* z (+ y x)))))
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 + (z * (y + x)));
}

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. Taylor expanded in x around 0 1.3

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

  3. Applied associate-+r+_binary641.3

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2022088 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))