Average Error: 0.0 → 0.0
Time: 3.0s
Precision: binary64
\[\left(x + y\right) \cdot \left(1 - z\right)\]
↓
\[y + \left(x - \left(y + x\right) \cdot z\right)\]
\left(x + y\right) \cdot \left(1 - z\right)
↓
y + \left(x - \left(y + x\right) \cdot z\right)
(FPCore (x y z) :precision binary64 (* (+ x y) (- 1.0 z)))
↓
(FPCore (x y z) :precision binary64 (+ y (- x (* (+ y x) z))))
double code(double x, double y, double z) {
	return (x + y) * (1.0 - z);
}
↓
double code(double x, double y, double z) {
	return y + (x - ((y + x) * 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 sub-neg_binary640.0

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

  4. Applied distribute-rgt-in_binary640.0

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

  5. Simplified0.0

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

  6. Simplified0.0

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

  8. Applied associate-+l+_binary640.0

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

  9. Simplified0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2021174 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, H"
  :precision binary64
  (* (+ x y) (- 1.0 z)))