Average Error: 1.3 → 0.3
Time: 7.7s
Precision: 64
\[\frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\]
↓
\[\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{3} \cdot \sqrt[3]{3}} \cdot \left(\frac{\sqrt[3]{1}}{\sqrt[3]{3}} \cdot \cos^{-1} \left(\frac{3 \cdot x}{\left(z \cdot 2\right) \cdot \left(y \cdot 27\right)} \cdot \sqrt{t}\right)\right)\]
\frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)
↓
\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{3} \cdot \sqrt[3]{3}} \cdot \left(\frac{\sqrt[3]{1}}{\sqrt[3]{3}} \cdot \cos^{-1} \left(\frac{3 \cdot x}{\left(z \cdot 2\right) \cdot \left(y \cdot 27\right)} \cdot \sqrt{t}\right)\right)
double f(double x, double y, double z, double t) {
        double r750598 = 1.0;
        double r750599 = 3.0;
        double r750600 = r750598 / r750599;
        double r750601 = x;
        double r750602 = y;
        double r750603 = 27.0;
        double r750604 = r750602 * r750603;
        double r750605 = r750601 / r750604;
        double r750606 = r750599 * r750605;
        double r750607 = z;
        double r750608 = 2.0;
        double r750609 = r750607 * r750608;
        double r750610 = r750606 / r750609;
        double r750611 = t;
        double r750612 = sqrt(r750611);
        double r750613 = r750610 * r750612;
        double r750614 = acos(r750613);
        double r750615 = r750600 * r750614;
        return r750615;
}
↓
double f(double x, double y, double z, double t) {
        double r750616 = 1.0;
        double r750617 = cbrt(r750616);
        double r750618 = r750617 * r750617;
        double r750619 = 3.0;
        double r750620 = cbrt(r750619);
        double r750621 = r750620 * r750620;
        double r750622 = r750618 / r750621;
        double r750623 = r750617 / r750620;
        double r750624 = x;
        double r750625 = r750619 * r750624;
        double r750626 = z;
        double r750627 = 2.0;
        double r750628 = r750626 * r750627;
        double r750629 = y;
        double r750630 = 27.0;
        double r750631 = r750629 * r750630;
        double r750632 = r750628 * r750631;
        double r750633 = r750625 / r750632;
        double r750634 = t;
        double r750635 = sqrt(r750634);
        double r750636 = r750633 * r750635;
        double r750637 = acos(r750636);
        double r750638 = r750623 * r750637;
        double r750639 = r750622 * r750638;
        return r750639;
}

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 add-cube-cbrt1.3

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

  5. Applied times-frac0.4

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

  6. Applied associate-*l*0.4

    \[\leadsto \color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{3} \cdot \sqrt[3]{3}} \cdot \left(\frac{\sqrt[3]{1}}{\sqrt[3]{3}} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\right)}\]
  7. Using strategy rm

  8. Applied associate-*r/0.4

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

  9. Applied associate-/l/0.3

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

  10. Final simplification0.3

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

Reproduce

herbie shell --seed 2020024 +o rules:numerics
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, D"
  :precision binary64

  :herbie-target
  (/ (acos (* (/ (/ x 27) (* y z)) (/ (sqrt t) (/ 2 3)))) 3)

  (* (/ 1 3) (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t)))))