Average Error: 1.3 → 0.4
Time: 20.6s
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 r37324425 = 1.0;
        double r37324426 = 3.0;
        double r37324427 = r37324425 / r37324426;
        double r37324428 = x;
        double r37324429 = y;
        double r37324430 = 27.0;
        double r37324431 = r37324429 * r37324430;
        double r37324432 = r37324428 / r37324431;
        double r37324433 = r37324426 * r37324432;
        double r37324434 = z;
        double r37324435 = 2.0;
        double r37324436 = r37324434 * r37324435;
        double r37324437 = r37324433 / r37324436;
        double r37324438 = t;
        double r37324439 = sqrt(r37324438);
        double r37324440 = r37324437 * r37324439;
        double r37324441 = acos(r37324440);
        double r37324442 = r37324427 * r37324441;
        return r37324442;
}
↓
double f(double x, double y, double z, double t) {
        double r37324443 = 1.0;
        double r37324444 = 3.0;
        double r37324445 = cbrt(r37324444);
        double r37324446 = r37324443 / r37324445;
        double r37324447 = x;
        double r37324448 = 27.0;
        double r37324449 = y;
        double r37324450 = r37324448 * r37324449;
        double r37324451 = r37324447 / r37324450;
        double r37324452 = r37324451 * r37324444;
        double r37324453 = 2.0;
        double r37324454 = z;
        double r37324455 = r37324453 * r37324454;
        double r37324456 = r37324452 / r37324455;
        double r37324457 = t;
        double r37324458 = sqrt(r37324457);
        double r37324459 = r37324456 * r37324458;
        double r37324460 = acos(r37324459);
        double r37324461 = r37324446 * r37324460;
        double r37324462 = 1.0;
        double r37324463 = r37324445 * r37324445;
        double r37324464 = r37324462 / r37324463;
        double r37324465 = r37324461 * r37324464;
        return r37324465;
}

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

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

Reproduce

herbie shell --seed 2019192 
(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)))))