Average Error: 1.3 → 0.3
Time: 23.3s
Precision: 64
\[\frac{1.0}{3.0} \cdot \cos^{-1} \left(\frac{3.0 \cdot \frac{x}{y \cdot 27.0}}{z \cdot 2.0} \cdot \sqrt{t}\right)\]
↓
\[\frac{1}{\sqrt[3]{3.0} \cdot \sqrt[3]{3.0}} \cdot \sqrt[3]{\frac{1.0 \cdot \left(1.0 \cdot 1.0\right)}{3.0} \cdot \left(\left(\cos^{-1} \left(\sqrt{t} \cdot \frac{3.0 \cdot \frac{x}{y \cdot 27.0}}{z \cdot 2.0}\right) \cdot \cos^{-1} \left(\sqrt{t} \cdot \frac{3.0 \cdot \frac{x}{y \cdot 27.0}}{z \cdot 2.0}\right)\right) \cdot \cos^{-1} \left(\sqrt{t} \cdot \frac{3.0 \cdot \frac{x}{y \cdot 27.0}}{z \cdot 2.0}\right)\right)}\]
\frac{1.0}{3.0} \cdot \cos^{-1} \left(\frac{3.0 \cdot \frac{x}{y \cdot 27.0}}{z \cdot 2.0} \cdot \sqrt{t}\right)
↓
\frac{1}{\sqrt[3]{3.0} \cdot \sqrt[3]{3.0}} \cdot \sqrt[3]{\frac{1.0 \cdot \left(1.0 \cdot 1.0\right)}{3.0} \cdot \left(\left(\cos^{-1} \left(\sqrt{t} \cdot \frac{3.0 \cdot \frac{x}{y \cdot 27.0}}{z \cdot 2.0}\right) \cdot \cos^{-1} \left(\sqrt{t} \cdot \frac{3.0 \cdot \frac{x}{y \cdot 27.0}}{z \cdot 2.0}\right)\right) \cdot \cos^{-1} \left(\sqrt{t} \cdot \frac{3.0 \cdot \frac{x}{y \cdot 27.0}}{z \cdot 2.0}\right)\right)}
double f(double x, double y, double z, double t) {
        double r35569786 = 1.0;
        double r35569787 = 3.0;
        double r35569788 = r35569786 / r35569787;
        double r35569789 = x;
        double r35569790 = y;
        double r35569791 = 27.0;
        double r35569792 = r35569790 * r35569791;
        double r35569793 = r35569789 / r35569792;
        double r35569794 = r35569787 * r35569793;
        double r35569795 = z;
        double r35569796 = 2.0;
        double r35569797 = r35569795 * r35569796;
        double r35569798 = r35569794 / r35569797;
        double r35569799 = t;
        double r35569800 = sqrt(r35569799);
        double r35569801 = r35569798 * r35569800;
        double r35569802 = acos(r35569801);
        double r35569803 = r35569788 * r35569802;
        return r35569803;
}
↓
double f(double x, double y, double z, double t) {
        double r35569804 = 1.0;
        double r35569805 = 3.0;
        double r35569806 = cbrt(r35569805);
        double r35569807 = r35569806 * r35569806;
        double r35569808 = r35569804 / r35569807;
        double r35569809 = 1.0;
        double r35569810 = r35569809 * r35569809;
        double r35569811 = r35569809 * r35569810;
        double r35569812 = r35569811 / r35569805;
        double r35569813 = t;
        double r35569814 = sqrt(r35569813);
        double r35569815 = x;
        double r35569816 = y;
        double r35569817 = 27.0;
        double r35569818 = r35569816 * r35569817;
        double r35569819 = r35569815 / r35569818;
        double r35569820 = r35569805 * r35569819;
        double r35569821 = z;
        double r35569822 = 2.0;
        double r35569823 = r35569821 * r35569822;
        double r35569824 = r35569820 / r35569823;
        double r35569825 = r35569814 * r35569824;
        double r35569826 = acos(r35569825);
        double r35569827 = r35569826 * r35569826;
        double r35569828 = r35569827 * r35569826;
        double r35569829 = r35569812 * r35569828;
        double r35569830 = cbrt(r35569829);
        double r35569831 = r35569808 * r35569830;
        return r35569831;
}

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

Original1.3
Target1.3
Herbie0.3
\[\frac{\cos^{-1} \left(\frac{\frac{x}{27.0}}{y \cdot z} \cdot \frac{\sqrt{t}}{\frac{2.0}{3.0}}\right)}{3.0}\]

Derivation

  1. Initial program 1.3

    \[\frac{1.0}{3.0} \cdot \cos^{-1} \left(\frac{3.0 \cdot \frac{x}{y \cdot 27.0}}{z \cdot 2.0} \cdot \sqrt{t}\right)\]
  2. Using strategy rm

  3. Applied add-cube-cbrt1.3

    \[\leadsto \frac{1.0}{\color{blue}{\left(\sqrt[3]{3.0} \cdot \sqrt[3]{3.0}\right) \cdot \sqrt[3]{3.0}}} \cdot \cos^{-1} \left(\frac{3.0 \cdot \frac{x}{y \cdot 27.0}}{z \cdot 2.0} \cdot \sqrt{t}\right)\]

  4. Applied *-un-lft-identity1.3

    \[\leadsto \frac{\color{blue}{1 \cdot 1.0}}{\left(\sqrt[3]{3.0} \cdot \sqrt[3]{3.0}\right) \cdot \sqrt[3]{3.0}} \cdot \cos^{-1} \left(\frac{3.0 \cdot \frac{x}{y \cdot 27.0}}{z \cdot 2.0} \cdot \sqrt{t}\right)\]

  5. Applied times-frac0.3

    \[\leadsto \color{blue}{\left(\frac{1}{\sqrt[3]{3.0} \cdot \sqrt[3]{3.0}} \cdot \frac{1.0}{\sqrt[3]{3.0}}\right)} \cdot \cos^{-1} \left(\frac{3.0 \cdot \frac{x}{y \cdot 27.0}}{z \cdot 2.0} \cdot \sqrt{t}\right)\]

  6. Applied associate-*l*0.3

    \[\leadsto \color{blue}{\frac{1}{\sqrt[3]{3.0} \cdot \sqrt[3]{3.0}} \cdot \left(\frac{1.0}{\sqrt[3]{3.0}} \cdot \cos^{-1} \left(\frac{3.0 \cdot \frac{x}{y \cdot 27.0}}{z \cdot 2.0} \cdot \sqrt{t}\right)\right)}\]
  7. Using strategy rm

  8. Applied add-cbrt-cube1.3

    \[\leadsto \frac{1}{\sqrt[3]{3.0} \cdot \sqrt[3]{3.0}} \cdot \left(\frac{1.0}{\sqrt[3]{3.0}} \cdot \color{blue}{\sqrt[3]{\left(\cos^{-1} \left(\frac{3.0 \cdot \frac{x}{y \cdot 27.0}}{z \cdot 2.0} \cdot \sqrt{t}\right) \cdot \cos^{-1} \left(\frac{3.0 \cdot \frac{x}{y \cdot 27.0}}{z \cdot 2.0} \cdot \sqrt{t}\right)\right) \cdot \cos^{-1} \left(\frac{3.0 \cdot \frac{x}{y \cdot 27.0}}{z \cdot 2.0} \cdot \sqrt{t}\right)}}\right)\]

  9. Applied add-cbrt-cube1.3

    \[\leadsto \frac{1}{\sqrt[3]{3.0} \cdot \sqrt[3]{3.0}} \cdot \left(\frac{\color{blue}{\sqrt[3]{\left(1.0 \cdot 1.0\right) \cdot 1.0}}}{\sqrt[3]{3.0}} \cdot \sqrt[3]{\left(\cos^{-1} \left(\frac{3.0 \cdot \frac{x}{y \cdot 27.0}}{z \cdot 2.0} \cdot \sqrt{t}\right) \cdot \cos^{-1} \left(\frac{3.0 \cdot \frac{x}{y \cdot 27.0}}{z \cdot 2.0} \cdot \sqrt{t}\right)\right) \cdot \cos^{-1} \left(\frac{3.0 \cdot \frac{x}{y \cdot 27.0}}{z \cdot 2.0} \cdot \sqrt{t}\right)}\right)\]

  10. Applied cbrt-undiv0.3

    \[\leadsto \frac{1}{\sqrt[3]{3.0} \cdot \sqrt[3]{3.0}} \cdot \left(\color{blue}{\sqrt[3]{\frac{\left(1.0 \cdot 1.0\right) \cdot 1.0}{3.0}}} \cdot \sqrt[3]{\left(\cos^{-1} \left(\frac{3.0 \cdot \frac{x}{y \cdot 27.0}}{z \cdot 2.0} \cdot \sqrt{t}\right) \cdot \cos^{-1} \left(\frac{3.0 \cdot \frac{x}{y \cdot 27.0}}{z \cdot 2.0} \cdot \sqrt{t}\right)\right) \cdot \cos^{-1} \left(\frac{3.0 \cdot \frac{x}{y \cdot 27.0}}{z \cdot 2.0} \cdot \sqrt{t}\right)}\right)\]

  11. Applied cbrt-unprod0.3

    \[\leadsto \frac{1}{\sqrt[3]{3.0} \cdot \sqrt[3]{3.0}} \cdot \color{blue}{\sqrt[3]{\frac{\left(1.0 \cdot 1.0\right) \cdot 1.0}{3.0} \cdot \left(\left(\cos^{-1} \left(\frac{3.0 \cdot \frac{x}{y \cdot 27.0}}{z \cdot 2.0} \cdot \sqrt{t}\right) \cdot \cos^{-1} \left(\frac{3.0 \cdot \frac{x}{y \cdot 27.0}}{z \cdot 2.0} \cdot \sqrt{t}\right)\right) \cdot \cos^{-1} \left(\frac{3.0 \cdot \frac{x}{y \cdot 27.0}}{z \cdot 2.0} \cdot \sqrt{t}\right)\right)}}\]

  12. Final simplification0.3

    \[\leadsto \frac{1}{\sqrt[3]{3.0} \cdot \sqrt[3]{3.0}} \cdot \sqrt[3]{\frac{1.0 \cdot \left(1.0 \cdot 1.0\right)}{3.0} \cdot \left(\left(\cos^{-1} \left(\sqrt{t} \cdot \frac{3.0 \cdot \frac{x}{y \cdot 27.0}}{z \cdot 2.0}\right) \cdot \cos^{-1} \left(\sqrt{t} \cdot \frac{3.0 \cdot \frac{x}{y \cdot 27.0}}{z \cdot 2.0}\right)\right) \cdot \cos^{-1} \left(\sqrt{t} \cdot \frac{3.0 \cdot \frac{x}{y \cdot 27.0}}{z \cdot 2.0}\right)\right)}\]

Reproduce

herbie shell --seed 2019168 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, D"

  :herbie-target
  (/ (acos (* (/ (/ x 27.0) (* y z)) (/ (sqrt t) (/ 2.0 3.0)))) 3.0)

  (* (/ 1.0 3.0) (acos (* (/ (* 3.0 (/ x (* y 27.0))) (* z 2.0)) (sqrt t)))))