Average Error: 1.3 → 0.4
Time: 24.7s
Precision: 64
\[\frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\]
↓
\[\left(\frac{1}{\sqrt[3]{3}} \cdot \cos^{-1} \left(\frac{\frac{x}{27 \cdot y} \cdot 3}{2 \cdot z} \cdot \sqrt{t}\right)\right) \cdot \frac{1}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\]
\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 r35730376 = 1.0;
        double r35730377 = 3.0;
        double r35730378 = r35730376 / r35730377;
        double r35730379 = x;
        double r35730380 = y;
        double r35730381 = 27.0;
        double r35730382 = r35730380 * r35730381;
        double r35730383 = r35730379 / r35730382;
        double r35730384 = r35730377 * r35730383;
        double r35730385 = z;
        double r35730386 = 2.0;
        double r35730387 = r35730385 * r35730386;
        double r35730388 = r35730384 / r35730387;
        double r35730389 = t;
        double r35730390 = sqrt(r35730389);
        double r35730391 = r35730388 * r35730390;
        double r35730392 = acos(r35730391);
        double r35730393 = r35730378 * r35730392;
        return r35730393;
}
↓
double f(double x, double y, double z, double t) {
        double r35730394 = 1.0;
        double r35730395 = 3.0;
        double r35730396 = cbrt(r35730395);
        double r35730397 = r35730394 / r35730396;
        double r35730398 = x;
        double r35730399 = 27.0;
        double r35730400 = y;
        double r35730401 = r35730399 * r35730400;
        double r35730402 = r35730398 / r35730401;
        double r35730403 = r35730402 * r35730395;
        double r35730404 = 2.0;
        double r35730405 = z;
        double r35730406 = r35730404 * r35730405;
        double r35730407 = r35730403 / r35730406;
        double r35730408 = t;
        double r35730409 = sqrt(r35730408);
        double r35730410 = r35730407 * r35730409;
        double r35730411 = acos(r35730410);
        double r35730412 = r35730397 * r35730411;
        double r35730413 = 1.0;
        double r35730414 = r35730396 * r35730396;
        double r35730415 = r35730413 / r35730414;
        double r35730416 = r35730412 * r35730415;
        return r35730416;
}

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

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 2019170 
(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)))))