Average Error: 0.1 → 0.0
Time: 16.0s
Precision: 64
\[\left(x + \cos y\right) - z \cdot \sin y\]
↓
\[\mathsf{fma}\left(\sin y, -z, \cos y + x\right)\]
\left(x + \cos y\right) - z \cdot \sin y
↓
\mathsf{fma}\left(\sin y, -z, \cos y + x\right)
double f(double x, double y, double z) {
        double r171133 = x;
        double r171134 = y;
        double r171135 = cos(r171134);
        double r171136 = r171133 + r171135;
        double r171137 = z;
        double r171138 = sin(r171134);
        double r171139 = r171137 * r171138;
        double r171140 = r171136 - r171139;
        return r171140;
}
↓
double f(double x, double y, double z) {
        double r171141 = y;
        double r171142 = sin(r171141);
        double r171143 = z;
        double r171144 = -r171143;
        double r171145 = cos(r171141);
        double r171146 = x;
        double r171147 = r171145 + r171146;
        double r171148 = fma(r171142, r171144, r171147);
        return r171148;
}

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. Simplified0.0

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

  6. Simplified0.0

    \[\leadsto \mathsf{fma}\left(\sin y, -z, \cos y + x\right) + \color{blue}{0}\]

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019303 +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))))