Average Error: 0.1 → 0.0
Time: 4.3s
Precision: 64
\[\left(x + \cos y\right) - z \cdot \sin y\]
↓
\[\mathsf{fma}\left(-\sin y, z, x + \cos y\right) + \sin y \cdot \left(\left(-z\right) + z\right)\]
\left(x + \cos y\right) - z \cdot \sin y
↓
\mathsf{fma}\left(-\sin y, z, x + \cos y\right) + \sin y \cdot \left(\left(-z\right) + z\right)
double f(double x, double y, double z) {
        double r156390 = x;
        double r156391 = y;
        double r156392 = cos(r156391);
        double r156393 = r156390 + r156392;
        double r156394 = z;
        double r156395 = sin(r156391);
        double r156396 = r156394 * r156395;
        double r156397 = r156393 - r156396;
        return r156397;
}
↓
double f(double x, double y, double z) {
        double r156398 = y;
        double r156399 = sin(r156398);
        double r156400 = -r156399;
        double r156401 = z;
        double r156402 = x;
        double r156403 = cos(r156398);
        double r156404 = r156402 + r156403;
        double r156405 = fma(r156400, r156401, r156404);
        double r156406 = -r156401;
        double r156407 = r156406 + r156401;
        double r156408 = r156399 * r156407;
        double r156409 = r156405 + r156408;
        return r156409;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.1

    \[\left(x + \cos y\right) - z \cdot \sin y\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.8

    \[\leadsto \color{blue}{\left(\sqrt[3]{x + \cos y} \cdot \sqrt[3]{x + \cos y}\right) \cdot \sqrt[3]{x + \cos y}} - z \cdot \sin y\]

  4. Applied prod-diff0.8

    \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt[3]{x + \cos y} \cdot \sqrt[3]{x + \cos y}, \sqrt[3]{x + \cos y}, -\sin y \cdot z\right) + \mathsf{fma}\left(-\sin y, z, \sin y \cdot z\right)}\]

  5. Simplified0.8

    \[\leadsto \color{blue}{\mathsf{fma}\left(-\sin y, z, {\left(\sqrt[3]{x + \cos y}\right)}^{3}\right)} + \mathsf{fma}\left(-\sin y, z, \sin y \cdot z\right)\]

  6. Simplified0.8

    \[\leadsto \mathsf{fma}\left(-\sin y, z, {\left(\sqrt[3]{x + \cos y}\right)}^{3}\right) + \color{blue}{\sin y \cdot \left(\left(-z\right) + z\right)}\]
  7. Using strategy rm

  8. Applied rem-cube-cbrt0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2020035 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, B"
  :precision binary64
  (- (+ x (cos y)) (* z (sin y))))