Average Error: 0.0 → 0.0
Time: 4.9s
Precision: binary64
\[\left(x + y\right) \cdot \left(z + 1\right) \]
↓
\[\mathsf{fma}\left(x + y, z, x + y\right) \]
\left(x + y\right) \cdot \left(z + 1\right)
↓
\mathsf{fma}\left(x + y, z, x + y\right)

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

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 egg-rr0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2022127 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))