Average Error: 0.0 → 0.0
Time: 2.6s
Precision: binary64
\[\left(x + y\right) \cdot \left(1 - z\right) \]
↓
\[\left(x + y\right) - \left(x + y\right) \cdot z \]
\left(x + y\right) \cdot \left(1 - z\right)
↓
\left(x + y\right) - \left(x + y\right) \cdot z

(FPCore (x y z) :precision binary64 (* (+ x y) (- 1.0 z)))
↓
(FPCore (x y z) :precision binary64 (- (+ x y) (* (+ x y) z)))
double code(double x, double y, double z) {
	return (x + y) * (1.0 - z);
}
↓
double code(double x, double y, double z) {
	return (x + y) - ((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

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

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

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

  4. Applied cancel-sign-sub-inv_binary640.0

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

  5. Applied distribute-lft-in_binary640.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2021207 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, H"
  :precision binary64
  (* (+ x y) (- 1.0 z)))