Average Error: 0.1 → 0.6
Time: 15.6s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[x \cdot \cos y - \left(\left(\sqrt[3]{z} \cdot \sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right) \cdot \sqrt[3]{\sqrt[3]{z}}\right) \cdot \left(\sqrt[3]{z} \cdot \sin y\right)\]
x \cdot \cos y - z \cdot \sin y
↓
x \cdot \cos y - \left(\left(\sqrt[3]{z} \cdot \sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right) \cdot \sqrt[3]{\sqrt[3]{z}}\right) \cdot \left(\sqrt[3]{z} \cdot \sin y\right)
double f(double x, double y, double z) {
        double r140018 = x;
        double r140019 = y;
        double r140020 = cos(r140019);
        double r140021 = r140018 * r140020;
        double r140022 = z;
        double r140023 = sin(r140019);
        double r140024 = r140022 * r140023;
        double r140025 = r140021 - r140024;
        return r140025;
}
↓
double f(double x, double y, double z) {
        double r140026 = x;
        double r140027 = y;
        double r140028 = cos(r140027);
        double r140029 = r140026 * r140028;
        double r140030 = z;
        double r140031 = cbrt(r140030);
        double r140032 = r140031 * r140031;
        double r140033 = cbrt(r140032);
        double r140034 = r140031 * r140033;
        double r140035 = cbrt(r140031);
        double r140036 = r140034 * r140035;
        double r140037 = sin(r140027);
        double r140038 = r140031 * r140037;
        double r140039 = r140036 * r140038;
        double r140040 = r140029 - r140039;
        return r140040;
}

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-cbrt0.6

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

  4. Applied associate-*l*0.6

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

  6. Applied add-cube-cbrt0.6

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

  7. Applied cbrt-prod0.6

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

  8. Applied associate-*r*0.6

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

  9. Final simplification0.6

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

Reproduce

herbie shell --seed 2019291 
(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))))