Average Error: 0.1 → 0.5
Time: 16.3s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[x \cdot \cos y - \left(\sqrt[3]{z} \cdot \sqrt[3]{\sin y}\right) \cdot \left(\sqrt[3]{z \cdot \sin y} \cdot \sqrt[3]{z \cdot \sin y}\right)\]
x \cdot \cos y - z \cdot \sin y
↓
x \cdot \cos y - \left(\sqrt[3]{z} \cdot \sqrt[3]{\sin y}\right) \cdot \left(\sqrt[3]{z \cdot \sin y} \cdot \sqrt[3]{z \cdot \sin y}\right)
double f(double x, double y, double z) {
        double r163184 = x;
        double r163185 = y;
        double r163186 = cos(r163185);
        double r163187 = r163184 * r163186;
        double r163188 = z;
        double r163189 = sin(r163185);
        double r163190 = r163188 * r163189;
        double r163191 = r163187 - r163190;
        return r163191;
}
↓
double f(double x, double y, double z) {
        double r163192 = x;
        double r163193 = y;
        double r163194 = cos(r163193);
        double r163195 = r163192 * r163194;
        double r163196 = z;
        double r163197 = cbrt(r163196);
        double r163198 = sin(r163193);
        double r163199 = cbrt(r163198);
        double r163200 = r163197 * r163199;
        double r163201 = r163196 * r163198;
        double r163202 = cbrt(r163201);
        double r163203 = r163202 * r163202;
        double r163204 = r163200 * r163203;
        double r163205 = r163195 - r163204;
        return r163205;
}

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

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

  3. Applied add-cube-cbrt0.6

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

  5. Applied cbrt-prod0.5

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

  6. Final simplification0.5

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

Reproduce

herbie shell --seed 2019196 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  (- (* x (cos y)) (* z (sin y))))