Average Error: 0.1 → 0.2
Time: 18.9s
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 r8070197 = x;
        double r8070198 = y;
        double r8070199 = cos(r8070198);
        double r8070200 = r8070197 * r8070199;
        double r8070201 = z;
        double r8070202 = sin(r8070198);
        double r8070203 = r8070201 * r8070202;
        double r8070204 = r8070200 - r8070203;
        return r8070204;
}
↓
double f(double x, double y, double z) {
        double r8070205 = y;
        double r8070206 = cos(r8070205);
        double r8070207 = cbrt(r8070206);
        double r8070208 = r8070206 * r8070206;
        double r8070209 = log(r8070208);
        double r8070210 = exp(r8070209);
        double r8070211 = 0.3333333333333333;
        double r8070212 = pow(r8070210, r8070211);
        double r8070213 = x;
        double r8070214 = r8070212 * r8070213;
        double r8070215 = r8070207 * r8070214;
        double r8070216 = z;
        double r8070217 = sin(r8070205);
        double r8070218 = r8070216 * r8070217;
        double r8070219 = r8070215 - r8070218;
        return r8070219;
}

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 pow1/316.4

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

  7. Applied pow1/316.3

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

  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))))