Average Error: 0.0 → 0.0
Time: 14.0s
Precision: 64
\[\left(x + \cos y\right) - z \cdot \sin y\]
↓
\[\left(\left(-z\right) + z\right) \cdot \sin y + \mathsf{fma}\left(\sin y, -z, x + \cos y\right)\]
\left(x + \cos y\right) - z \cdot \sin y
↓
\left(\left(-z\right) + z\right) \cdot \sin y + \mathsf{fma}\left(\sin y, -z, x + \cos y\right)
double f(double x, double y, double z) {
        double r197281 = x;
        double r197282 = y;
        double r197283 = cos(r197282);
        double r197284 = r197281 + r197283;
        double r197285 = z;
        double r197286 = sin(r197282);
        double r197287 = r197285 * r197286;
        double r197288 = r197284 - r197287;
        return r197288;
}
↓
double f(double x, double y, double z) {
        double r197289 = z;
        double r197290 = -r197289;
        double r197291 = r197290 + r197289;
        double r197292 = y;
        double r197293 = sin(r197292);
        double r197294 = r197291 * r197293;
        double r197295 = x;
        double r197296 = cos(r197292);
        double r197297 = r197295 + r197296;
        double r197298 = fma(r197293, r197290, r197297);
        double r197299 = r197294 + r197298;
        return r197299;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

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

  3. Applied add-sqr-sqrt23.9

    \[\leadsto \color{blue}{\sqrt{x + \cos y} \cdot \sqrt{x + \cos y}} - z \cdot \sin y\]

  4. Applied prod-diff23.9

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

  5. Simplified0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, B"
  (- (+ x (cos y)) (* z (sin y))))