Average Error: 0.1 → 0.1
Time: 22.4s
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 r7579012 = x;
        double r7579013 = y;
        double r7579014 = sin(r7579013);
        double r7579015 = r7579012 * r7579014;
        double r7579016 = z;
        double r7579017 = cos(r7579013);
        double r7579018 = r7579016 * r7579017;
        double r7579019 = r7579015 + r7579018;
        return r7579019;
}
↓
double f(double x, double y, double z) {
        double r7579020 = y;
        double r7579021 = cos(r7579020);
        double r7579022 = z;
        double r7579023 = x;
        double r7579024 = sin(r7579020);
        double r7579025 = r7579023 * r7579024;
        double r7579026 = fma(r7579021, r7579022, r7579025);
        return r7579026;
}

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 2019172 +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))))