Average Error: 1.2 → 0.3
Time: 8.2s
Precision: 64
\[\frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\]
↓
\[\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{3} \cdot \sqrt[3]{3}} \cdot \left(\frac{\sqrt[3]{1}}{\sqrt[3]{3}} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\right)\]
\frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)
↓
\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{3} \cdot \sqrt[3]{3}} \cdot \left(\frac{\sqrt[3]{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 r692777 = 1.0;
        double r692778 = 3.0;
        double r692779 = r692777 / r692778;
        double r692780 = x;
        double r692781 = y;
        double r692782 = 27.0;
        double r692783 = r692781 * r692782;
        double r692784 = r692780 / r692783;
        double r692785 = r692778 * r692784;
        double r692786 = z;
        double r692787 = 2.0;
        double r692788 = r692786 * r692787;
        double r692789 = r692785 / r692788;
        double r692790 = t;
        double r692791 = sqrt(r692790);
        double r692792 = r692789 * r692791;
        double r692793 = acos(r692792);
        double r692794 = r692779 * r692793;
        return r692794;
}
↓
double f(double x, double y, double z, double t) {
        double r692795 = 1.0;
        double r692796 = cbrt(r692795);
        double r692797 = r692796 * r692796;
        double r692798 = 3.0;
        double r692799 = cbrt(r692798);
        double r692800 = r692799 * r692799;
        double r692801 = r692797 / r692800;
        double r692802 = r692796 / r692799;
        double r692803 = x;
        double r692804 = y;
        double r692805 = 27.0;
        double r692806 = r692804 * r692805;
        double r692807 = r692803 / r692806;
        double r692808 = r692798 * r692807;
        double r692809 = z;
        double r692810 = 2.0;
        double r692811 = r692809 * r692810;
        double r692812 = r692808 / r692811;
        double r692813 = t;
        double r692814 = sqrt(r692813);
        double r692815 = r692812 * r692814;
        double r692816 = acos(r692815);
        double r692817 = r692802 * r692816;
        double r692818 = r692801 * r692817;
        return r692818;
}

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

Original1.2
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 1.2

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

  3. Applied add-cube-cbrt1.2

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

  4. Applied add-cube-cbrt1.2

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

  5. Applied times-frac0.3

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

  6. Applied associate-*l*0.3

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2020045 
(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)))))