Average Error: 1.3 → 0.4
Time: 9.8s
Precision: 64
\[\frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\]
↓
\[\frac{\sqrt{1}}{\sqrt[3]{3} \cdot \sqrt[3]{3}} \cdot \left(\frac{\sqrt{1}}{\sqrt[3]{3}} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\right)\]
\frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)
↓
\frac{\sqrt{1}}{\sqrt[3]{3} \cdot \sqrt[3]{3}} \cdot \left(\frac{\sqrt{1}}{\sqrt[3]{3}} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\right)
double f(double x, double y, double z, double t) {
        double r670848 = 1.0;
        double r670849 = 3.0;
        double r670850 = r670848 / r670849;
        double r670851 = x;
        double r670852 = y;
        double r670853 = 27.0;
        double r670854 = r670852 * r670853;
        double r670855 = r670851 / r670854;
        double r670856 = r670849 * r670855;
        double r670857 = z;
        double r670858 = 2.0;
        double r670859 = r670857 * r670858;
        double r670860 = r670856 / r670859;
        double r670861 = t;
        double r670862 = sqrt(r670861);
        double r670863 = r670860 * r670862;
        double r670864 = acos(r670863);
        double r670865 = r670850 * r670864;
        return r670865;
}
↓
double f(double x, double y, double z, double t) {
        double r670866 = 1.0;
        double r670867 = sqrt(r670866);
        double r670868 = 3.0;
        double r670869 = cbrt(r670868);
        double r670870 = r670869 * r670869;
        double r670871 = r670867 / r670870;
        double r670872 = r670867 / r670869;
        double r670873 = x;
        double r670874 = y;
        double r670875 = 27.0;
        double r670876 = r670874 * r670875;
        double r670877 = r670873 / r670876;
        double r670878 = r670868 * r670877;
        double r670879 = z;
        double r670880 = 2.0;
        double r670881 = r670879 * r670880;
        double r670882 = r670878 / r670881;
        double r670883 = t;
        double r670884 = sqrt(r670883);
        double r670885 = r670882 * r670884;
        double r670886 = acos(r670885);
        double r670887 = r670872 * r670886;
        double r670888 = r670871 * r670887;
        return r670888;
}

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

Derivation

  1. Initial program 1.3

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

  3. Applied add-cube-cbrt1.3

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

  4. Applied add-sqr-sqrt1.3

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

  5. Applied times-frac0.4

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

  6. Applied associate-*l*0.4

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

  7. Final simplification0.4

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

Reproduce

herbie shell --seed 2020035 +o rules:numerics
(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)))))