Average Error: 1.3 → 0.3
Time: 25.6s
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 r28657635 = 1.0;
        double r28657636 = 3.0;
        double r28657637 = r28657635 / r28657636;
        double r28657638 = x;
        double r28657639 = y;
        double r28657640 = 27.0;
        double r28657641 = r28657639 * r28657640;
        double r28657642 = r28657638 / r28657641;
        double r28657643 = r28657636 * r28657642;
        double r28657644 = z;
        double r28657645 = 2.0;
        double r28657646 = r28657644 * r28657645;
        double r28657647 = r28657643 / r28657646;
        double r28657648 = t;
        double r28657649 = sqrt(r28657648);
        double r28657650 = r28657647 * r28657649;
        double r28657651 = acos(r28657650);
        double r28657652 = r28657637 * r28657651;
        return r28657652;
}
↓
double f(double x, double y, double z, double t) {
        double r28657653 = 1.0;
        double r28657654 = 3.0;
        double r28657655 = cbrt(r28657654);
        double r28657656 = r28657653 / r28657655;
        double r28657657 = x;
        double r28657658 = 27.0;
        double r28657659 = y;
        double r28657660 = r28657658 * r28657659;
        double r28657661 = r28657657 / r28657660;
        double r28657662 = r28657661 * r28657654;
        double r28657663 = 2.0;
        double r28657664 = z;
        double r28657665 = r28657663 * r28657664;
        double r28657666 = r28657662 / r28657665;
        double r28657667 = t;
        double r28657668 = sqrt(r28657667);
        double r28657669 = r28657666 * r28657668;
        double r28657670 = acos(r28657669);
        double r28657671 = r28657656 * r28657670;
        double r28657672 = 1.0;
        double r28657673 = r28657655 * r28657655;
        double r28657674 = r28657672 / r28657673;
        double r28657675 = r28657671 * r28657674;
        return r28657675;
}

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)))))