Average Error: 0.1 → 0.5
Time: 4.7s
Precision: 64
\[\left(x + \cos y\right) - z \cdot \sin y\]
↓
\[\left(x + \cos y\right) - \left(z \cdot \left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right)\right) \cdot \mathsf{expm1}\left(\mathsf{log1p}\left(\left(\sqrt[3]{\sqrt[3]{\sin y}} \cdot \sqrt[3]{\sqrt[3]{\sin y}}\right) \cdot \left(\sqrt[3]{\sqrt[3]{\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{\sin y}}}\right)\right)\right)\]
\left(x + \cos y\right) - z \cdot \sin y
↓
\left(x + \cos y\right) - \left(z \cdot \left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right)\right) \cdot \mathsf{expm1}\left(\mathsf{log1p}\left(\left(\sqrt[3]{\sqrt[3]{\sin y}} \cdot \sqrt[3]{\sqrt[3]{\sin y}}\right) \cdot \left(\sqrt[3]{\sqrt[3]{\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{\sin y}}}\right)\right)\right)
double f(double x, double y, double z) {
        double r149161 = x;
        double r149162 = y;
        double r149163 = cos(r149162);
        double r149164 = r149161 + r149163;
        double r149165 = z;
        double r149166 = sin(r149162);
        double r149167 = r149165 * r149166;
        double r149168 = r149164 - r149167;
        return r149168;
}
↓
double f(double x, double y, double z) {
        double r149169 = x;
        double r149170 = y;
        double r149171 = cos(r149170);
        double r149172 = r149169 + r149171;
        double r149173 = z;
        double r149174 = sin(r149170);
        double r149175 = cbrt(r149174);
        double r149176 = r149175 * r149175;
        double r149177 = r149173 * r149176;
        double r149178 = cbrt(r149175);
        double r149179 = r149178 * r149178;
        double r149180 = cbrt(r149176);
        double r149181 = cbrt(r149180);
        double r149182 = cbrt(r149178);
        double r149183 = r149181 * r149182;
        double r149184 = r149179 * r149183;
        double r149185 = log1p(r149184);
        double r149186 = expm1(r149185);
        double r149187 = r149177 * r149186;
        double r149188 = r149172 - r149187;
        return r149188;
}

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

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

  8. Applied add-cube-cbrt0.5

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

  10. Applied add-cube-cbrt0.5

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

  11. Applied cbrt-prod0.5

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

  12. Applied cbrt-prod0.5

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

  13. Final simplification0.5

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

Reproduce

herbie shell --seed 2019352 +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))))