Average Error: 1.3 → 0.3
Time: 23.9s
Precision: 64
\[\frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\]
↓
\[\frac{\sqrt{1}}{\sqrt[3]{3} \cdot \sqrt[3]{3}} \cdot \left(\frac{\sqrt{1}}{\sqrt[3]{3}} \cdot \cos^{-1} \left(\frac{3 \cdot x}{\left(z \cdot 2\right) \cdot \left(y \cdot 27\right)} \cdot \sqrt{t}\right)\right)\]
\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 x}{\left(z \cdot 2\right) \cdot \left(y \cdot 27\right)} \cdot \sqrt{t}\right)\right)
double f(double x, double y, double z, double t) {
        double r440851 = 1.0;
        double r440852 = 3.0;
        double r440853 = r440851 / r440852;
        double r440854 = x;
        double r440855 = y;
        double r440856 = 27.0;
        double r440857 = r440855 * r440856;
        double r440858 = r440854 / r440857;
        double r440859 = r440852 * r440858;
        double r440860 = z;
        double r440861 = 2.0;
        double r440862 = r440860 * r440861;
        double r440863 = r440859 / r440862;
        double r440864 = t;
        double r440865 = sqrt(r440864);
        double r440866 = r440863 * r440865;
        double r440867 = acos(r440866);
        double r440868 = r440853 * r440867;
        return r440868;
}
↓
double f(double x, double y, double z, double t) {
        double r440869 = 1.0;
        double r440870 = sqrt(r440869);
        double r440871 = 3.0;
        double r440872 = cbrt(r440871);
        double r440873 = r440872 * r440872;
        double r440874 = r440870 / r440873;
        double r440875 = r440870 / r440872;
        double r440876 = x;
        double r440877 = r440871 * r440876;
        double r440878 = z;
        double r440879 = 2.0;
        double r440880 = r440878 * r440879;
        double r440881 = y;
        double r440882 = 27.0;
        double r440883 = r440881 * r440882;
        double r440884 = r440880 * r440883;
        double r440885 = r440877 / r440884;
        double r440886 = t;
        double r440887 = sqrt(r440886);
        double r440888 = r440885 * r440887;
        double r440889 = acos(r440888);
        double r440890 = r440875 * r440889;
        double r440891 = r440874 * r440890;
        return r440891;
}

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 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-frac0.3

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

  6. Applied associate-*l*0.3

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

  8. Applied associate-*r/0.3

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

  9. Applied associate-/l/0.3

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

  10. Final simplification0.3

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

Reproduce

herbie shell --seed 2019347 +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)))))