Average Error: 0.0 → 0.0
Time: 2.3s
Precision: binary64
\[\left(x + y\right) \cdot \left(z + 1\right) \]
↓
\[\mathsf{fma}\left(z, y + x, y + x\right) \]
\left(x + y\right) \cdot \left(z + 1\right)
↓
\mathsf{fma}\left(z, y + x, y + x\right)

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

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

    \[\left(x + y\right) \cdot \left(z + 1\right) \]

  2. Applied distribute-rgt-in_binary640.0

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

  3. Simplified0.0

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

  4. Simplified0.0

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

  5. Applied fma-def_binary640.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2022068 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))