Average Error: 1.3 → 0.3
Time: 25.8s
Precision: 64
\[\frac{1.0}{3.0} \cdot \cos^{-1} \left(\frac{3.0 \cdot \frac{x}{y \cdot 27.0}}{z \cdot 2.0} \cdot \sqrt{t}\right)\]
↓
\[\left(\frac{1.0}{\sqrt[3]{3.0}} \cdot \cos^{-1} \left(\frac{\frac{x}{27.0 \cdot y} \cdot 3.0}{2.0 \cdot z} \cdot \sqrt{t}\right)\right) \cdot \frac{1}{\sqrt[3]{3.0} \cdot \sqrt[3]{3.0}}\]
\frac{1.0}{3.0} \cdot \cos^{-1} \left(\frac{3.0 \cdot \frac{x}{y \cdot 27.0}}{z \cdot 2.0} \cdot \sqrt{t}\right)
↓
\left(\frac{1.0}{\sqrt[3]{3.0}} \cdot \cos^{-1} \left(\frac{\frac{x}{27.0 \cdot y} \cdot 3.0}{2.0 \cdot z} \cdot \sqrt{t}\right)\right) \cdot \frac{1}{\sqrt[3]{3.0} \cdot \sqrt[3]{3.0}}
double f(double x, double y, double z, double t) {
        double r33595746 = 1.0;
        double r33595747 = 3.0;
        double r33595748 = r33595746 / r33595747;
        double r33595749 = x;
        double r33595750 = y;
        double r33595751 = 27.0;
        double r33595752 = r33595750 * r33595751;
        double r33595753 = r33595749 / r33595752;
        double r33595754 = r33595747 * r33595753;
        double r33595755 = z;
        double r33595756 = 2.0;
        double r33595757 = r33595755 * r33595756;
        double r33595758 = r33595754 / r33595757;
        double r33595759 = t;
        double r33595760 = sqrt(r33595759);
        double r33595761 = r33595758 * r33595760;
        double r33595762 = acos(r33595761);
        double r33595763 = r33595748 * r33595762;
        return r33595763;
}
↓
double f(double x, double y, double z, double t) {
        double r33595764 = 1.0;
        double r33595765 = 3.0;
        double r33595766 = cbrt(r33595765);
        double r33595767 = r33595764 / r33595766;
        double r33595768 = x;
        double r33595769 = 27.0;
        double r33595770 = y;
        double r33595771 = r33595769 * r33595770;
        double r33595772 = r33595768 / r33595771;
        double r33595773 = r33595772 * r33595765;
        double r33595774 = 2.0;
        double r33595775 = z;
        double r33595776 = r33595774 * r33595775;
        double r33595777 = r33595773 / r33595776;
        double r33595778 = t;
        double r33595779 = sqrt(r33595778);
        double r33595780 = r33595777 * r33595779;
        double r33595781 = acos(r33595780);
        double r33595782 = r33595767 * r33595781;
        double r33595783 = 1.0;
        double r33595784 = r33595766 * r33595766;
        double r33595785 = r33595783 / r33595784;
        double r33595786 = r33595782 * r33595785;
        return r33595786;
}

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
\[\frac{\cos^{-1} \left(\frac{\frac{x}{27.0}}{y \cdot z} \cdot \frac{\sqrt{t}}{\frac{2.0}{3.0}}\right)}{3.0}\]

Derivation

  1. Initial program 1.3

    \[\frac{1.0}{3.0} \cdot \cos^{-1} \left(\frac{3.0 \cdot \frac{x}{y \cdot 27.0}}{z \cdot 2.0} \cdot \sqrt{t}\right)\]
  2. Using strategy rm

  3. Applied add-cube-cbrt1.3

    \[\leadsto \frac{1.0}{\color{blue}{\left(\sqrt[3]{3.0} \cdot \sqrt[3]{3.0}\right) \cdot \sqrt[3]{3.0}}} \cdot \cos^{-1} \left(\frac{3.0 \cdot \frac{x}{y \cdot 27.0}}{z \cdot 2.0} \cdot \sqrt{t}\right)\]

  4. Applied *-un-lft-identity1.3

    \[\leadsto \frac{\color{blue}{1 \cdot 1.0}}{\left(\sqrt[3]{3.0} \cdot \sqrt[3]{3.0}\right) \cdot \sqrt[3]{3.0}} \cdot \cos^{-1} \left(\frac{3.0 \cdot \frac{x}{y \cdot 27.0}}{z \cdot 2.0} \cdot \sqrt{t}\right)\]

  5. Applied times-frac0.3

    \[\leadsto \color{blue}{\left(\frac{1}{\sqrt[3]{3.0} \cdot \sqrt[3]{3.0}} \cdot \frac{1.0}{\sqrt[3]{3.0}}\right)} \cdot \cos^{-1} \left(\frac{3.0 \cdot \frac{x}{y \cdot 27.0}}{z \cdot 2.0} \cdot \sqrt{t}\right)\]

  6. Applied associate-*l*0.3

    \[\leadsto \color{blue}{\frac{1}{\sqrt[3]{3.0} \cdot \sqrt[3]{3.0}} \cdot \left(\frac{1.0}{\sqrt[3]{3.0}} \cdot \cos^{-1} \left(\frac{3.0 \cdot \frac{x}{y \cdot 27.0}}{z \cdot 2.0} \cdot \sqrt{t}\right)\right)}\]

  7. Final simplification0.3

    \[\leadsto \left(\frac{1.0}{\sqrt[3]{3.0}} \cdot \cos^{-1} \left(\frac{\frac{x}{27.0 \cdot y} \cdot 3.0}{2.0 \cdot z} \cdot \sqrt{t}\right)\right) \cdot \frac{1}{\sqrt[3]{3.0} \cdot \sqrt[3]{3.0}}\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(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)))))