Average Error: 0.1 → 0.2
Time: 19.3s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[\sqrt[3]{\cos y} \cdot \left({\left(\cos y \cdot \cos y\right)}^{\frac{1}{3}} \cdot x\right) + z \cdot \sin y\]
x \cdot \cos y + z \cdot \sin y
↓
\sqrt[3]{\cos y} \cdot \left({\left(\cos y \cdot \cos y\right)}^{\frac{1}{3}} \cdot x\right) + z \cdot \sin y
double f(double x, double y, double z) {
        double r7026902 = x;
        double r7026903 = y;
        double r7026904 = cos(r7026903);
        double r7026905 = r7026902 * r7026904;
        double r7026906 = z;
        double r7026907 = sin(r7026903);
        double r7026908 = r7026906 * r7026907;
        double r7026909 = r7026905 + r7026908;
        return r7026909;
}
↓
double f(double x, double y, double z) {
        double r7026910 = y;
        double r7026911 = cos(r7026910);
        double r7026912 = cbrt(r7026911);
        double r7026913 = r7026911 * r7026911;
        double r7026914 = 0.3333333333333333;
        double r7026915 = pow(r7026913, r7026914);
        double r7026916 = x;
        double r7026917 = r7026915 * r7026916;
        double r7026918 = r7026912 * r7026917;
        double r7026919 = z;
        double r7026920 = sin(r7026910);
        double r7026921 = r7026919 * r7026920;
        double r7026922 = r7026918 + r7026921;
        return r7026922;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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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. Final simplification0.2

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

Reproduce

herbie shell --seed 2019172 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  (+ (* x (cos y)) (* z (sin y))))