Average Error: 1.3 → 0.3
Time: 23.0s
Precision: 64
\[\frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\]
↓
\[\frac{1 \cdot \cos^{-1} \left(\log \left(e^{\frac{\frac{x}{y \cdot 27} \cdot 3}{2 \cdot z} \cdot \sqrt{t}}\right)\right)}{\sqrt[3]{3}} \cdot \frac{1}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\]
\frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)
↓
\frac{1 \cdot \cos^{-1} \left(\log \left(e^{\frac{\frac{x}{y \cdot 27} \cdot 3}{2 \cdot z} \cdot \sqrt{t}}\right)\right)}{\sqrt[3]{3}} \cdot \frac{1}{\sqrt[3]{3} \cdot \sqrt[3]{3}}
double f(double x, double y, double z, double t) {
        double r35138874 = 1.0;
        double r35138875 = 3.0;
        double r35138876 = r35138874 / r35138875;
        double r35138877 = x;
        double r35138878 = y;
        double r35138879 = 27.0;
        double r35138880 = r35138878 * r35138879;
        double r35138881 = r35138877 / r35138880;
        double r35138882 = r35138875 * r35138881;
        double r35138883 = z;
        double r35138884 = 2.0;
        double r35138885 = r35138883 * r35138884;
        double r35138886 = r35138882 / r35138885;
        double r35138887 = t;
        double r35138888 = sqrt(r35138887);
        double r35138889 = r35138886 * r35138888;
        double r35138890 = acos(r35138889);
        double r35138891 = r35138876 * r35138890;
        return r35138891;
}
↓
double f(double x, double y, double z, double t) {
        double r35138892 = 1.0;
        double r35138893 = x;
        double r35138894 = y;
        double r35138895 = 27.0;
        double r35138896 = r35138894 * r35138895;
        double r35138897 = r35138893 / r35138896;
        double r35138898 = 3.0;
        double r35138899 = r35138897 * r35138898;
        double r35138900 = 2.0;
        double r35138901 = z;
        double r35138902 = r35138900 * r35138901;
        double r35138903 = r35138899 / r35138902;
        double r35138904 = t;
        double r35138905 = sqrt(r35138904);
        double r35138906 = r35138903 * r35138905;
        double r35138907 = exp(r35138906);
        double r35138908 = log(r35138907);
        double r35138909 = acos(r35138908);
        double r35138910 = r35138892 * r35138909;
        double r35138911 = cbrt(r35138898);
        double r35138912 = r35138910 / r35138911;
        double r35138913 = 1.0;
        double r35138914 = r35138911 * r35138911;
        double r35138915 = r35138913 / r35138914;
        double r35138916 = r35138912 * r35138915;
        return r35138916;
}

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

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 *-un-lft-identity1.3

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

  5. Applied times-frac0.3

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

  6. Applied associate-*l*0.3

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

  8. Applied associate-*l/0.3

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

  10. Applied add-log-exp0.3

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

  11. Final simplification0.3

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

Reproduce

herbie shell --seed 2019172 
(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)))))