Average Error: 0.1 → 0.1
Time: 25.1s
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 r8714146 = x;
        double r8714147 = y;
        double r8714148 = sin(r8714147);
        double r8714149 = r8714146 * r8714148;
        double r8714150 = z;
        double r8714151 = cos(r8714147);
        double r8714152 = r8714150 * r8714151;
        double r8714153 = r8714149 + r8714152;
        return r8714153;
}
↓
double f(double x, double y, double z) {
        double r8714154 = y;
        double r8714155 = cos(r8714154);
        double r8714156 = z;
        double r8714157 = x;
        double r8714158 = sin(r8714154);
        double r8714159 = r8714157 * r8714158;
        double r8714160 = fma(r8714155, r8714156, r8714159);
        return r8714160;
}

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 2019163 +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))))