Average Error: 0.1 → 0.4
Time: 4.8s
Precision: 64
\[\left(x + \cos y\right) - z \cdot \sin y\]
↓
\[\left(x + \cos y\right) - \left(z \cdot \mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right)\right)\right) \cdot \sqrt[3]{\sin y}\]
\left(x + \cos y\right) - z \cdot \sin y
↓
\left(x + \cos y\right) - \left(z \cdot \mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right)\right)\right) \cdot \sqrt[3]{\sin y}
double f(double x, double y, double z) {
        double r161104 = x;
        double r161105 = y;
        double r161106 = cos(r161105);
        double r161107 = r161104 + r161106;
        double r161108 = z;
        double r161109 = sin(r161105);
        double r161110 = r161108 * r161109;
        double r161111 = r161107 - r161110;
        return r161111;
}
↓
double f(double x, double y, double z) {
        double r161112 = x;
        double r161113 = y;
        double r161114 = cos(r161113);
        double r161115 = r161112 + r161114;
        double r161116 = z;
        double r161117 = sin(r161113);
        double r161118 = cbrt(r161117);
        double r161119 = r161118 * r161118;
        double r161120 = log1p(r161119);
        double r161121 = expm1(r161120);
        double r161122 = r161116 * r161121;
        double r161123 = r161122 * r161118;
        double r161124 = r161115 - r161123;
        return r161124;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

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

  3. Applied add-cube-cbrt0.4

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

  4. Applied associate-*r*0.4

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

  6. Applied expm1-log1p-u0.4

    \[\leadsto \left(x + \cos y\right) - \left(z \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right)\right)}\right) \cdot \sqrt[3]{\sin y}\]

  7. Final simplification0.4

    \[\leadsto \left(x + \cos y\right) - \left(z \cdot \mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right)\right)\right) \cdot \sqrt[3]{\sin y}\]

Reproduce

herbie shell --seed 2020018 +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))))