Average Error: 1.3 → 0.4
Time: 21.4s
Precision: 64
\[\frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\]
↓
\[\left(\frac{1}{\sqrt[3]{3}} \cdot \cos^{-1} \left(\frac{\frac{x}{27 \cdot y} \cdot 3}{2 \cdot z} \cdot \sqrt{t}\right)\right) \cdot \frac{1}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\]
\frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)
↓
\left(\frac{1}{\sqrt[3]{3}} \cdot \cos^{-1} \left(\frac{\frac{x}{27 \cdot y} \cdot 3}{2 \cdot z} \cdot \sqrt{t}\right)\right) \cdot \frac{1}{\sqrt[3]{3} \cdot \sqrt[3]{3}}
double f(double x, double y, double z, double t) {
        double r32694333 = 1.0;
        double r32694334 = 3.0;
        double r32694335 = r32694333 / r32694334;
        double r32694336 = x;
        double r32694337 = y;
        double r32694338 = 27.0;
        double r32694339 = r32694337 * r32694338;
        double r32694340 = r32694336 / r32694339;
        double r32694341 = r32694334 * r32694340;
        double r32694342 = z;
        double r32694343 = 2.0;
        double r32694344 = r32694342 * r32694343;
        double r32694345 = r32694341 / r32694344;
        double r32694346 = t;
        double r32694347 = sqrt(r32694346);
        double r32694348 = r32694345 * r32694347;
        double r32694349 = acos(r32694348);
        double r32694350 = r32694335 * r32694349;
        return r32694350;
}
↓
double f(double x, double y, double z, double t) {
        double r32694351 = 1.0;
        double r32694352 = 3.0;
        double r32694353 = cbrt(r32694352);
        double r32694354 = r32694351 / r32694353;
        double r32694355 = x;
        double r32694356 = 27.0;
        double r32694357 = y;
        double r32694358 = r32694356 * r32694357;
        double r32694359 = r32694355 / r32694358;
        double r32694360 = r32694359 * r32694352;
        double r32694361 = 2.0;
        double r32694362 = z;
        double r32694363 = r32694361 * r32694362;
        double r32694364 = r32694360 / r32694363;
        double r32694365 = t;
        double r32694366 = sqrt(r32694365);
        double r32694367 = r32694364 * r32694366;
        double r32694368 = acos(r32694367);
        double r32694369 = r32694354 * r32694368;
        double r32694370 = 1.0;
        double r32694371 = r32694353 * r32694353;
        double r32694372 = r32694370 / r32694371;
        double r32694373 = r32694369 * r32694372;
        return r32694373;
}

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
Target1.3
Herbie0.4
\[\frac{\cos^{-1} \left(\frac{\frac{x}{27}}{y \cdot z} \cdot \frac{\sqrt{t}}{\frac{2}{3}}\right)}{3}\]

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-frac0.4

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

  6. Applied associate-*l*0.4

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

  7. Final simplification0.4

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

Reproduce

herbie shell --seed 2019169 
(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)))))