Average Error: 0.1 → 0.3
Time: 17.3s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[\left(x \cdot \left({\left({\left(\cos y\right)}^{4}\right)}^{\frac{1}{9}} \cdot \sqrt[3]{\sqrt[3]{{\left(\cos y\right)}^{2}}}\right)\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]
x \cdot \cos y - z \cdot \sin y
↓
\left(x \cdot \left({\left({\left(\cos y\right)}^{4}\right)}^{\frac{1}{9}} \cdot \sqrt[3]{\sqrt[3]{{\left(\cos y\right)}^{2}}}\right)\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y
double f(double x, double y, double z) {
        double r233945 = x;
        double r233946 = y;
        double r233947 = cos(r233946);
        double r233948 = r233945 * r233947;
        double r233949 = z;
        double r233950 = sin(r233946);
        double r233951 = r233949 * r233950;
        double r233952 = r233948 - r233951;
        return r233952;
}
↓
double f(double x, double y, double z) {
        double r233953 = x;
        double r233954 = y;
        double r233955 = cos(r233954);
        double r233956 = 4.0;
        double r233957 = pow(r233955, r233956);
        double r233958 = 0.1111111111111111;
        double r233959 = pow(r233957, r233958);
        double r233960 = 2.0;
        double r233961 = pow(r233955, r233960);
        double r233962 = cbrt(r233961);
        double r233963 = cbrt(r233962);
        double r233964 = r233959 * r233963;
        double r233965 = r233953 * r233964;
        double r233966 = cbrt(r233955);
        double r233967 = r233965 * r233966;
        double r233968 = z;
        double r233969 = sin(r233954);
        double r233970 = r233968 * r233969;
        double r233971 = r233967 - r233970;
        return r233971;
}

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 cbrt-unprod0.3

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

  7. Simplified0.3

    \[\leadsto \left(x \cdot \sqrt[3]{\color{blue}{{\left(\cos y\right)}^{2}}}\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]
  8. Using strategy rm

  9. Applied add-cube-cbrt0.3

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

  10. Applied cbrt-prod0.4

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

  11. Simplified0.3

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

  12. Taylor expanded around inf 0.3

    \[\leadsto \left(x \cdot \left(\color{blue}{{\left({\left(\cos y\right)}^{4}\right)}^{\frac{1}{9}}} \cdot \sqrt[3]{\sqrt[3]{{\left(\cos y\right)}^{2}}}\right)\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]

  13. Final simplification0.3

    \[\leadsto \left(x \cdot \left({\left({\left(\cos y\right)}^{4}\right)}^{\frac{1}{9}} \cdot \sqrt[3]{\sqrt[3]{{\left(\cos y\right)}^{2}}}\right)\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]

Reproduce

herbie shell --seed 2020043 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  :precision binary64
  (- (* x (cos y)) (* z (sin y))))