Average Error: 1.4 → 0.5
Time: 22.5s
Precision: 64
\[\frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\]
↓
\[\frac{1}{\sqrt[3]{3} \cdot \sqrt[3]{3}} \cdot \left(\sqrt{\frac{1}{\sqrt[3]{3}}} \cdot \left(\sqrt{\frac{1}{\sqrt[3]{3}}} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\right)\right)\]
\frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)
↓
\frac{1}{\sqrt[3]{3} \cdot \sqrt[3]{3}} \cdot \left(\sqrt{\frac{1}{\sqrt[3]{3}}} \cdot \left(\sqrt{\frac{1}{\sqrt[3]{3}}} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\right)\right)
double f(double x, double y, double z, double t) {
        double r465773 = 1.0;
        double r465774 = 3.0;
        double r465775 = r465773 / r465774;
        double r465776 = x;
        double r465777 = y;
        double r465778 = 27.0;
        double r465779 = r465777 * r465778;
        double r465780 = r465776 / r465779;
        double r465781 = r465774 * r465780;
        double r465782 = z;
        double r465783 = 2.0;
        double r465784 = r465782 * r465783;
        double r465785 = r465781 / r465784;
        double r465786 = t;
        double r465787 = sqrt(r465786);
        double r465788 = r465785 * r465787;
        double r465789 = acos(r465788);
        double r465790 = r465775 * r465789;
        return r465790;
}
↓
double f(double x, double y, double z, double t) {
        double r465791 = 1.0;
        double r465792 = 3.0;
        double r465793 = cbrt(r465792);
        double r465794 = r465793 * r465793;
        double r465795 = r465791 / r465794;
        double r465796 = 1.0;
        double r465797 = r465796 / r465793;
        double r465798 = sqrt(r465797);
        double r465799 = x;
        double r465800 = y;
        double r465801 = 27.0;
        double r465802 = r465800 * r465801;
        double r465803 = r465799 / r465802;
        double r465804 = r465792 * r465803;
        double r465805 = z;
        double r465806 = 2.0;
        double r465807 = r465805 * r465806;
        double r465808 = r465804 / r465807;
        double r465809 = t;
        double r465810 = sqrt(r465809);
        double r465811 = r465808 * r465810;
        double r465812 = acos(r465811);
        double r465813 = r465798 * r465812;
        double r465814 = r465798 * r465813;
        double r465815 = r465795 * r465814;
        return r465815;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original1.4
Target1.2
Herbie0.5
\[\frac{\cos^{-1} \left(\frac{\frac{x}{27}}{y \cdot z} \cdot \frac{\sqrt{t}}{\frac{2}{3}}\right)}{3}\]

Derivation

  1. Initial program 1.4

    \[\frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\]
  2. Using strategy rm

  3. Applied add-cube-cbrt1.4

    \[\leadsto \frac{1}{\color{blue}{\left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right) \cdot \sqrt[3]{3}}} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\]

  4. Applied *-un-lft-identity1.4

    \[\leadsto \frac{\color{blue}{1 \cdot 1}}{\left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right) \cdot \sqrt[3]{3}} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\]

  5. Applied times-frac0.5

    \[\leadsto \color{blue}{\left(\frac{1}{\sqrt[3]{3} \cdot \sqrt[3]{3}} \cdot \frac{1}{\sqrt[3]{3}}\right)} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\]

  6. Applied associate-*l*0.4

    \[\leadsto \color{blue}{\frac{1}{\sqrt[3]{3} \cdot \sqrt[3]{3}} \cdot \left(\frac{1}{\sqrt[3]{3}} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\right)}\]
  7. Using strategy rm

  8. Applied add-sqr-sqrt1.4

    \[\leadsto \frac{1}{\sqrt[3]{3} \cdot \sqrt[3]{3}} \cdot \left(\color{blue}{\left(\sqrt{\frac{1}{\sqrt[3]{3}}} \cdot \sqrt{\frac{1}{\sqrt[3]{3}}}\right)} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\right)\]

  9. Applied associate-*l*0.5

    \[\leadsto \frac{1}{\sqrt[3]{3} \cdot \sqrt[3]{3}} \cdot \color{blue}{\left(\sqrt{\frac{1}{\sqrt[3]{3}}} \cdot \left(\sqrt{\frac{1}{\sqrt[3]{3}}} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\right)\right)}\]

  10. Final simplification0.5

    \[\leadsto \frac{1}{\sqrt[3]{3} \cdot \sqrt[3]{3}} \cdot \left(\sqrt{\frac{1}{\sqrt[3]{3}}} \cdot \left(\sqrt{\frac{1}{\sqrt[3]{3}}} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\right)\right)\]

Reproduce

herbie shell --seed 2019323 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, D"
  :precision binary64

  :herbie-target
  (/ (acos (* (/ (/ x 27) (* y z)) (/ (sqrt t) (/ 2 3)))) 3)

  (* (/ 1 3) (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t)))))