Average Error: 1.3 → 0.3
Time: 44.7s
Precision: 64
\[\frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\]
↓
\[\frac{1}{\sqrt[3]{3} \cdot \sqrt[3]{3}} \cdot \sqrt[3]{\frac{1 \cdot \left(1 \cdot 1\right)}{3} \cdot \left(\left(\cos^{-1} \left(\sqrt{t} \cdot \frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2}\right) \cdot \cos^{-1} \left(\sqrt{t} \cdot \frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2}\right)\right) \cdot \cos^{-1} \left(\sqrt{t} \cdot \frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2}\right)\right)}\]
\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 \sqrt[3]{\frac{1 \cdot \left(1 \cdot 1\right)}{3} \cdot \left(\left(\cos^{-1} \left(\sqrt{t} \cdot \frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2}\right) \cdot \cos^{-1} \left(\sqrt{t} \cdot \frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2}\right)\right) \cdot \cos^{-1} \left(\sqrt{t} \cdot \frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2}\right)\right)}
double f(double x, double y, double z, double t) {
        double r39166476 = 1.0;
        double r39166477 = 3.0;
        double r39166478 = r39166476 / r39166477;
        double r39166479 = x;
        double r39166480 = y;
        double r39166481 = 27.0;
        double r39166482 = r39166480 * r39166481;
        double r39166483 = r39166479 / r39166482;
        double r39166484 = r39166477 * r39166483;
        double r39166485 = z;
        double r39166486 = 2.0;
        double r39166487 = r39166485 * r39166486;
        double r39166488 = r39166484 / r39166487;
        double r39166489 = t;
        double r39166490 = sqrt(r39166489);
        double r39166491 = r39166488 * r39166490;
        double r39166492 = acos(r39166491);
        double r39166493 = r39166478 * r39166492;
        return r39166493;
}
↓
double f(double x, double y, double z, double t) {
        double r39166494 = 1.0;
        double r39166495 = 3.0;
        double r39166496 = cbrt(r39166495);
        double r39166497 = r39166496 * r39166496;
        double r39166498 = r39166494 / r39166497;
        double r39166499 = 1.0;
        double r39166500 = r39166499 * r39166499;
        double r39166501 = r39166499 * r39166500;
        double r39166502 = r39166501 / r39166495;
        double r39166503 = t;
        double r39166504 = sqrt(r39166503);
        double r39166505 = x;
        double r39166506 = y;
        double r39166507 = 27.0;
        double r39166508 = r39166506 * r39166507;
        double r39166509 = r39166505 / r39166508;
        double r39166510 = r39166495 * r39166509;
        double r39166511 = z;
        double r39166512 = 2.0;
        double r39166513 = r39166511 * r39166512;
        double r39166514 = r39166510 / r39166513;
        double r39166515 = r39166504 * r39166514;
        double r39166516 = acos(r39166515);
        double r39166517 = r39166516 * r39166516;
        double r39166518 = r39166517 * r39166516;
        double r39166519 = r39166502 * r39166518;
        double r39166520 = cbrt(r39166519);
        double r39166521 = r39166498 * r39166520;
        return r39166521;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original1.3
Target1.3
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 *-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-frac0.3

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

  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 add-cbrt-cube1.3

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

  9. Applied add-cbrt-cube1.3

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

  10. Applied cbrt-undiv0.3

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

  11. Applied cbrt-unprod0.3

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

  12. Final simplification0.3

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

Reproduce

herbie shell --seed 2019168 
(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)))))