Average Error: 0.1 → 0.1
Time: 6.4s
Precision: binary64
\[x \cdot \cos y - z \cdot \sin y \]
↓
\[\mathsf{fma}\left(x, \cos y, -z \cdot \sin y\right) \]
x \cdot \cos y - z \cdot \sin y
↓
\mathsf{fma}\left(x, \cos y, -z \cdot \sin y\right)

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

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.1

    \[x \cdot \cos y - z \cdot \sin y \]

  2. Applied fma-neg_binary640.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2022104 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  :precision binary64
  (- (* x (cos y)) (* z (sin y))))