Average Error: 0.1 → 0.2
Time: 50.9s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[\sqrt[3]{\cos y} \cdot \left({\left(e^{\log \left(\cos y \cdot \cos y\right)}\right)}^{\frac{1}{3}} \cdot x\right) - z \cdot \sin y\]
x \cdot \cos y - z \cdot \sin y
↓
\sqrt[3]{\cos y} \cdot \left({\left(e^{\log \left(\cos y \cdot \cos y\right)}\right)}^{\frac{1}{3}} \cdot x\right) - z \cdot \sin y
double f(double x, double y, double z) {
        double r8510185 = x;
        double r8510186 = y;
        double r8510187 = cos(r8510186);
        double r8510188 = r8510185 * r8510187;
        double r8510189 = z;
        double r8510190 = sin(r8510186);
        double r8510191 = r8510189 * r8510190;
        double r8510192 = r8510188 - r8510191;
        return r8510192;
}
↓
double f(double x, double y, double z) {
        double r8510193 = y;
        double r8510194 = cos(r8510193);
        double r8510195 = cbrt(r8510194);
        double r8510196 = r8510194 * r8510194;
        double r8510197 = log(r8510196);
        double r8510198 = exp(r8510197);
        double r8510199 = 0.3333333333333333;
        double r8510200 = pow(r8510198, r8510199);
        double r8510201 = x;
        double r8510202 = r8510200 * r8510201;
        double r8510203 = r8510195 * r8510202;
        double r8510204 = z;
        double r8510205 = sin(r8510193);
        double r8510206 = r8510204 * r8510205;
        double r8510207 = r8510203 - r8510206;
        return r8510207;
}

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-cbrt0.4

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

  4. Applied associate-*r*0.4

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

  6. Applied pow1/316.8

    \[\leadsto \left(x \cdot \left(\sqrt[3]{\cos y} \cdot \color{blue}{{\left(\cos y\right)}^{\frac{1}{3}}}\right)\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]

  7. Applied pow1/316.8

    \[\leadsto \left(x \cdot \left(\color{blue}{{\left(\cos y\right)}^{\frac{1}{3}}} \cdot {\left(\cos y\right)}^{\frac{1}{3}}\right)\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]

  8. Applied pow-prod-down0.2

    \[\leadsto \left(x \cdot \color{blue}{{\left(\cos y \cdot \cos y\right)}^{\frac{1}{3}}}\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]
  9. Using strategy rm

  10. Applied add-exp-log0.2

    \[\leadsto \left(x \cdot {\color{blue}{\left(e^{\log \left(\cos y \cdot \cos y\right)}\right)}}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]

  11. Final simplification0.2

    \[\leadsto \sqrt[3]{\cos y} \cdot \left({\left(e^{\log \left(\cos y \cdot \cos y\right)}\right)}^{\frac{1}{3}} \cdot x\right) - z \cdot \sin y\]

Reproduce

herbie shell --seed 2019165 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  (- (* x (cos y)) (* z (sin y))))