Average Error: 1.3 → 0.3
Time: 22.5s
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 r30893457 = 1.0;
        double r30893458 = 3.0;
        double r30893459 = r30893457 / r30893458;
        double r30893460 = x;
        double r30893461 = y;
        double r30893462 = 27.0;
        double r30893463 = r30893461 * r30893462;
        double r30893464 = r30893460 / r30893463;
        double r30893465 = r30893458 * r30893464;
        double r30893466 = z;
        double r30893467 = 2.0;
        double r30893468 = r30893466 * r30893467;
        double r30893469 = r30893465 / r30893468;
        double r30893470 = t;
        double r30893471 = sqrt(r30893470);
        double r30893472 = r30893469 * r30893471;
        double r30893473 = acos(r30893472);
        double r30893474 = r30893459 * r30893473;
        return r30893474;
}
↓
double f(double x, double y, double z, double t) {
        double r30893475 = 1.0;
        double r30893476 = 3.0;
        double r30893477 = cbrt(r30893476);
        double r30893478 = r30893475 / r30893477;
        double r30893479 = x;
        double r30893480 = 27.0;
        double r30893481 = y;
        double r30893482 = r30893480 * r30893481;
        double r30893483 = r30893479 / r30893482;
        double r30893484 = r30893483 * r30893476;
        double r30893485 = 2.0;
        double r30893486 = z;
        double r30893487 = r30893485 * r30893486;
        double r30893488 = r30893484 / r30893487;
        double r30893489 = t;
        double r30893490 = sqrt(r30893489);
        double r30893491 = r30893488 * r30893490;
        double r30893492 = acos(r30893491);
        double r30893493 = r30893478 * r30893492;
        double r30893494 = 1.0;
        double r30893495 = r30893477 * r30893477;
        double r30893496 = r30893494 / r30893495;
        double r30893497 = r30893493 * r30893496;
        return r30893497;
}

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)))))