Average Error: 0.0 → 0.0
Time: 3.1s
Precision: binary64
\[\left(x + y\right) \cdot \left(1 - z\right) \]
↓
\[y + \mathsf{fma}\left(-z, y + x, x\right) \]
\left(x + y\right) \cdot \left(1 - z\right)
↓
y + \mathsf{fma}\left(-z, y + x, x\right)

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

Error

Bits error versus x

Bits error versus y

Bits error versus z

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 associate-+l+_binary640.0

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

  7. Simplified0.0

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

  8. Final simplification0.0

    \[\leadsto y + \mathsf{fma}\left(-z, y + x, x\right) \]

Reproduce

herbie shell --seed 2022077 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, H"
  :precision binary64
  (* (+ x y) (- 1.0 z)))