Average Error: 1.2 → 0.3
Time: 8.8s
Precision: 64
\[\frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\]
↓
\[\frac{1}{\sqrt[3]{3} \cdot \sqrt[3]{3}} \cdot \left(\frac{1}{\sqrt[3]{3}} \cdot \cos^{-1} \left(\frac{3 \cdot x}{\left(z \cdot 2\right) \cdot \left(y \cdot 27\right)} \cdot \sqrt{t}\right)\right)\]
\frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)
↓
\frac{1}{\sqrt[3]{3} \cdot \sqrt[3]{3}} \cdot \left(\frac{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 r738570 = 1.0;
        double r738571 = 3.0;
        double r738572 = r738570 / r738571;
        double r738573 = x;
        double r738574 = y;
        double r738575 = 27.0;
        double r738576 = r738574 * r738575;
        double r738577 = r738573 / r738576;
        double r738578 = r738571 * r738577;
        double r738579 = z;
        double r738580 = 2.0;
        double r738581 = r738579 * r738580;
        double r738582 = r738578 / r738581;
        double r738583 = t;
        double r738584 = sqrt(r738583);
        double r738585 = r738582 * r738584;
        double r738586 = acos(r738585);
        double r738587 = r738572 * r738586;
        return r738587;
}
↓
double f(double x, double y, double z, double t) {
        double r738588 = 1.0;
        double r738589 = 3.0;
        double r738590 = cbrt(r738589);
        double r738591 = r738590 * r738590;
        double r738592 = r738588 / r738591;
        double r738593 = 1.0;
        double r738594 = r738593 / r738590;
        double r738595 = x;
        double r738596 = r738589 * r738595;
        double r738597 = z;
        double r738598 = 2.0;
        double r738599 = r738597 * r738598;
        double r738600 = y;
        double r738601 = 27.0;
        double r738602 = r738600 * r738601;
        double r738603 = r738599 * r738602;
        double r738604 = r738596 / r738603;
        double r738605 = t;
        double r738606 = sqrt(r738605);
        double r738607 = r738604 * r738606;
        double r738608 = acos(r738607);
        double r738609 = r738594 * r738608;
        double r738610 = r738592 * r738609;
        return r738610;
}

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

Original1.2
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 1.2

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

  3. Applied add-cube-cbrt1.2

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

  4. Applied *-un-lft-identity1.2

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

  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. Using strategy rm

  8. Applied associate-*r/0.3

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

  9. Applied associate-/l/0.3

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

  10. Final simplification0.3

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

Reproduce

herbie shell --seed 2019322 
(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)))))