Average Error: 0.1 → 0.4
Time: 4.7s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[x \cdot \sin y + \left(z \cdot \left(\sqrt[3]{\cos y} \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\sqrt[3]{\cos y}\right)\right)\right)\right) \cdot \sqrt[3]{\cos y}\]
x \cdot \sin y + z \cdot \cos y
↓
x \cdot \sin y + \left(z \cdot \left(\sqrt[3]{\cos y} \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\sqrt[3]{\cos y}\right)\right)\right)\right) \cdot \sqrt[3]{\cos y}
double f(double x, double y, double z) {
        double r184182 = x;
        double r184183 = y;
        double r184184 = sin(r184183);
        double r184185 = r184182 * r184184;
        double r184186 = z;
        double r184187 = cos(r184183);
        double r184188 = r184186 * r184187;
        double r184189 = r184185 + r184188;
        return r184189;
}
↓
double f(double x, double y, double z) {
        double r184190 = x;
        double r184191 = y;
        double r184192 = sin(r184191);
        double r184193 = r184190 * r184192;
        double r184194 = z;
        double r184195 = cos(r184191);
        double r184196 = cbrt(r184195);
        double r184197 = expm1(r184196);
        double r184198 = log1p(r184197);
        double r184199 = r184196 * r184198;
        double r184200 = r184194 * r184199;
        double r184201 = r184200 * r184196;
        double r184202 = r184193 + r184201;
        return r184202;
}

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

    \[x \cdot \sin y + z \cdot \cos y\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.4

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

  4. Applied associate-*r*0.4

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

  6. Applied log1p-expm1-u0.4

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

  7. Final simplification0.4

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

Reproduce

herbie shell --seed 2020065 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ (* x (sin y)) (* z (cos y))))