Average Error: 1.3 → 0.3
Time: 20.2s
Precision: 64
\[\frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\]
↓
\[\frac{1}{\sqrt[3]{3} \cdot \sqrt[3]{3}} \cdot \left(\frac{1}{\sqrt[3]{3}} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\right)\]
\frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)
↓
\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)
double f(double x, double y, double z, double t) {
        double r53747725 = 1.0;
        double r53747726 = 3.0;
        double r53747727 = r53747725 / r53747726;
        double r53747728 = x;
        double r53747729 = y;
        double r53747730 = 27.0;
        double r53747731 = r53747729 * r53747730;
        double r53747732 = r53747728 / r53747731;
        double r53747733 = r53747726 * r53747732;
        double r53747734 = z;
        double r53747735 = 2.0;
        double r53747736 = r53747734 * r53747735;
        double r53747737 = r53747733 / r53747736;
        double r53747738 = t;
        double r53747739 = sqrt(r53747738);
        double r53747740 = r53747737 * r53747739;
        double r53747741 = acos(r53747740);
        double r53747742 = r53747727 * r53747741;
        return r53747742;
}
↓
double f(double x, double y, double z, double t) {
        double r53747743 = 1.0;
        double r53747744 = 3.0;
        double r53747745 = cbrt(r53747744);
        double r53747746 = r53747745 * r53747745;
        double r53747747 = r53747743 / r53747746;
        double r53747748 = 1.0;
        double r53747749 = r53747748 / r53747745;
        double r53747750 = x;
        double r53747751 = y;
        double r53747752 = 27.0;
        double r53747753 = r53747751 * r53747752;
        double r53747754 = r53747750 / r53747753;
        double r53747755 = r53747744 * r53747754;
        double r53747756 = z;
        double r53747757 = 2.0;
        double r53747758 = r53747756 * r53747757;
        double r53747759 = r53747755 / r53747758;
        double r53747760 = t;
        double r53747761 = sqrt(r53747760);
        double r53747762 = r53747759 * r53747761;
        double r53747763 = acos(r53747762);
        double r53747764 = r53747749 * r53747763;
        double r53747765 = r53747747 * r53747764;
        return r53747765;
}

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. Final simplification0.3

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

Reproduce

herbie shell --seed 2019174 
(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)))))