Average Error: 0.1 → 0.1
Time: 23.9s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[\mathsf{fma}\left(\cos y, z, x \cdot \sin y\right)\]
x \cdot \sin y + z \cdot \cos y
↓
\mathsf{fma}\left(\cos y, z, x \cdot \sin y\right)
double f(double x, double y, double z) {
        double r9418081 = x;
        double r9418082 = y;
        double r9418083 = sin(r9418082);
        double r9418084 = r9418081 * r9418083;
        double r9418085 = z;
        double r9418086 = cos(r9418082);
        double r9418087 = r9418085 * r9418086;
        double r9418088 = r9418084 + r9418087;
        return r9418088;
}
↓
double f(double x, double y, double z) {
        double r9418089 = y;
        double r9418090 = cos(r9418089);
        double r9418091 = z;
        double r9418092 = x;
        double r9418093 = sin(r9418089);
        double r9418094 = r9418092 * r9418093;
        double r9418095 = fma(r9418090, r9418091, r9418094);
        return r9418095;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.1

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

  2. Simplified0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019162 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  (+ (* x (sin y)) (* z (cos y))))