Average Error: 0.1 → 0.3
Time: 5.5s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[\left(x \cdot {\left(\log \left(e^{{\left(\cos y\right)}^{2}}\right)\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]
x \cdot \cos y - z \cdot \sin y
↓
\left(x \cdot {\left(\log \left(e^{{\left(\cos y\right)}^{2}}\right)\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y
double f(double x, double y, double z) {
        double r240550 = x;
        double r240551 = y;
        double r240552 = cos(r240551);
        double r240553 = r240550 * r240552;
        double r240554 = z;
        double r240555 = sin(r240551);
        double r240556 = r240554 * r240555;
        double r240557 = r240553 - r240556;
        return r240557;
}
↓
double f(double x, double y, double z) {
        double r240558 = x;
        double r240559 = y;
        double r240560 = cos(r240559);
        double r240561 = 2.0;
        double r240562 = pow(r240560, r240561);
        double r240563 = exp(r240562);
        double r240564 = log(r240563);
        double r240565 = 0.3333333333333333;
        double r240566 = pow(r240564, r240565);
        double r240567 = r240558 * r240566;
        double r240568 = cbrt(r240560);
        double r240569 = r240567 * r240568;
        double r240570 = z;
        double r240571 = sin(r240559);
        double r240572 = r240570 * r240571;
        double r240573 = r240569 - r240572;
        return r240573;
}

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 pow1/316.2

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

  7. Applied pow1/316.2

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

  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. Simplified0.2

    \[\leadsto \left(x \cdot {\color{blue}{\left({\left(\cos y\right)}^{2}\right)}}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]
  10. Using strategy rm

  11. Applied add-log-exp0.3

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

  12. Final simplification0.3

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

Reproduce

herbie shell --seed 2020035 
(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))))