Average Error: 0.1 → 0.2
Time: 15.8s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[x \cdot \sin y + \left(z \cdot {\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y}\]
x \cdot \sin y + z \cdot \cos y
↓
x \cdot \sin y + \left(z \cdot {\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y}
double f(double x, double y, double z) {
        double r136963 = x;
        double r136964 = y;
        double r136965 = sin(r136964);
        double r136966 = r136963 * r136965;
        double r136967 = z;
        double r136968 = cos(r136964);
        double r136969 = r136967 * r136968;
        double r136970 = r136966 + r136969;
        return r136970;
}
↓
double f(double x, double y, double z) {
        double r136971 = x;
        double r136972 = y;
        double r136973 = sin(r136972);
        double r136974 = r136971 * r136973;
        double r136975 = z;
        double r136976 = cos(r136972);
        double r136977 = 2.0;
        double r136978 = pow(r136976, r136977);
        double r136979 = 0.3333333333333333;
        double r136980 = pow(r136978, r136979);
        double r136981 = r136975 * r136980;
        double r136982 = cbrt(r136976);
        double r136983 = r136981 * r136982;
        double r136984 = r136974 + r136983;
        return r136984;
}

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

    \[x \cdot \sin y + z \cdot \cos y\]
  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. Simplified0.4

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

  7. Applied pow1/315.9

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

  8. Applied pow1/315.8

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

  9. Applied pow-prod-down0.2

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

  10. Simplified0.2

    \[\leadsto x \cdot \sin y + \left({\color{blue}{\left({\left(\cos y\right)}^{2}\right)}}^{\frac{1}{3}} \cdot z\right) \cdot \sqrt[3]{\cos y}\]

  11. Final simplification0.2

    \[\leadsto x \cdot \sin y + \left(z \cdot {\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y}\]

Reproduce

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