Average Error: 1.3 → 0.4
Time: 24.0s
Precision: 64
\[\frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\]
↓
\[\left(\frac{1}{\sqrt[3]{3}} \cdot \cos^{-1} \left(\frac{\frac{x}{27 \cdot y} \cdot 3}{2 \cdot z} \cdot \sqrt{t}\right)\right) \cdot \frac{1}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\]
\frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)
↓
\left(\frac{1}{\sqrt[3]{3}} \cdot \cos^{-1} \left(\frac{\frac{x}{27 \cdot y} \cdot 3}{2 \cdot z} \cdot \sqrt{t}\right)\right) \cdot \frac{1}{\sqrt[3]{3} \cdot \sqrt[3]{3}}
double f(double x, double y, double z, double t) {
        double r37924773 = 1.0;
        double r37924774 = 3.0;
        double r37924775 = r37924773 / r37924774;
        double r37924776 = x;
        double r37924777 = y;
        double r37924778 = 27.0;
        double r37924779 = r37924777 * r37924778;
        double r37924780 = r37924776 / r37924779;
        double r37924781 = r37924774 * r37924780;
        double r37924782 = z;
        double r37924783 = 2.0;
        double r37924784 = r37924782 * r37924783;
        double r37924785 = r37924781 / r37924784;
        double r37924786 = t;
        double r37924787 = sqrt(r37924786);
        double r37924788 = r37924785 * r37924787;
        double r37924789 = acos(r37924788);
        double r37924790 = r37924775 * r37924789;
        return r37924790;
}
↓
double f(double x, double y, double z, double t) {
        double r37924791 = 1.0;
        double r37924792 = 3.0;
        double r37924793 = cbrt(r37924792);
        double r37924794 = r37924791 / r37924793;
        double r37924795 = x;
        double r37924796 = 27.0;
        double r37924797 = y;
        double r37924798 = r37924796 * r37924797;
        double r37924799 = r37924795 / r37924798;
        double r37924800 = r37924799 * r37924792;
        double r37924801 = 2.0;
        double r37924802 = z;
        double r37924803 = r37924801 * r37924802;
        double r37924804 = r37924800 / r37924803;
        double r37924805 = t;
        double r37924806 = sqrt(r37924805);
        double r37924807 = r37924804 * r37924806;
        double r37924808 = acos(r37924807);
        double r37924809 = r37924794 * r37924808;
        double r37924810 = 1.0;
        double r37924811 = r37924793 * r37924793;
        double r37924812 = r37924810 / r37924811;
        double r37924813 = r37924809 * r37924812;
        return r37924813;
}

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 *-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-frac0.4

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

  6. Applied associate-*l*0.4

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

  7. Final simplification0.4

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

Reproduce

herbie shell --seed 2019179 
(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)))))