Average Error: 0.0 → 0.0
Time: 2.4s
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. Applied sub-neg_binary640.0

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

  3. Applied distribute-rgt-in_binary640.0

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

  4. Simplified0.0

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

  5. Simplified0.0

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

  6. Applied neg-sub0_binary640.0

    \[\leadsto \left(y + x\right) + \color{blue}{\left(0 - z \cdot \left(y + x\right)\right)} \]

  7. Applied associate-+r-_binary640.0

    \[\leadsto \color{blue}{\left(\left(y + x\right) + 0\right) - z \cdot \left(y + x\right)} \]

  8. Simplified0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2022081 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, H"
  :precision binary64
  (* (+ x y) (- 1.0 z)))