Average Error: 1.3 → 0.4
Time: 23.0s
Precision: 64
\[\frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\]
↓
\[\frac{1}{\sqrt[3]{3} \cdot \sqrt[3]{3}} \cdot \left(\frac{1}{\sqrt[3]{3}} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\right)\]
\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 r131564700 = 1.0;
        double r131564701 = 3.0;
        double r131564702 = r131564700 / r131564701;
        double r131564703 = x;
        double r131564704 = y;
        double r131564705 = 27.0;
        double r131564706 = r131564704 * r131564705;
        double r131564707 = r131564703 / r131564706;
        double r131564708 = r131564701 * r131564707;
        double r131564709 = z;
        double r131564710 = 2.0;
        double r131564711 = r131564709 * r131564710;
        double r131564712 = r131564708 / r131564711;
        double r131564713 = t;
        double r131564714 = sqrt(r131564713);
        double r131564715 = r131564712 * r131564714;
        double r131564716 = acos(r131564715);
        double r131564717 = r131564702 * r131564716;
        return r131564717;
}
↓
double f(double x, double y, double z, double t) {
        double r131564718 = 1.0;
        double r131564719 = 3.0;
        double r131564720 = cbrt(r131564719);
        double r131564721 = r131564720 * r131564720;
        double r131564722 = r131564718 / r131564721;
        double r131564723 = 1.0;
        double r131564724 = r131564723 / r131564720;
        double r131564725 = x;
        double r131564726 = y;
        double r131564727 = 27.0;
        double r131564728 = r131564726 * r131564727;
        double r131564729 = r131564725 / r131564728;
        double r131564730 = r131564719 * r131564729;
        double r131564731 = z;
        double r131564732 = 2.0;
        double r131564733 = r131564731 * r131564732;
        double r131564734 = r131564730 / r131564733;
        double r131564735 = t;
        double r131564736 = sqrt(r131564735);
        double r131564737 = r131564734 * r131564736;
        double r131564738 = acos(r131564737);
        double r131564739 = r131564724 * r131564738;
        double r131564740 = r131564722 * r131564739;
        return r131564740;
}

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
Target1.3
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

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

Reproduce

herbie shell --seed 2019173 
(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)))))