Average Error: 1.3 → 0.3
Time: 43.0s
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 r34531259 = 1.0;
        double r34531260 = 3.0;
        double r34531261 = r34531259 / r34531260;
        double r34531262 = x;
        double r34531263 = y;
        double r34531264 = 27.0;
        double r34531265 = r34531263 * r34531264;
        double r34531266 = r34531262 / r34531265;
        double r34531267 = r34531260 * r34531266;
        double r34531268 = z;
        double r34531269 = 2.0;
        double r34531270 = r34531268 * r34531269;
        double r34531271 = r34531267 / r34531270;
        double r34531272 = t;
        double r34531273 = sqrt(r34531272);
        double r34531274 = r34531271 * r34531273;
        double r34531275 = acos(r34531274);
        double r34531276 = r34531261 * r34531275;
        return r34531276;
}
↓
double f(double x, double y, double z, double t) {
        double r34531277 = 1.0;
        double r34531278 = 3.0;
        double r34531279 = cbrt(r34531278);
        double r34531280 = r34531277 / r34531279;
        double r34531281 = x;
        double r34531282 = 27.0;
        double r34531283 = y;
        double r34531284 = r34531282 * r34531283;
        double r34531285 = r34531281 / r34531284;
        double r34531286 = r34531285 * r34531278;
        double r34531287 = 2.0;
        double r34531288 = z;
        double r34531289 = r34531287 * r34531288;
        double r34531290 = r34531286 / r34531289;
        double r34531291 = t;
        double r34531292 = sqrt(r34531291);
        double r34531293 = r34531290 * r34531292;
        double r34531294 = acos(r34531293);
        double r34531295 = r34531280 * r34531294;
        double r34531296 = 1.0;
        double r34531297 = r34531279 * r34531279;
        double r34531298 = r34531296 / r34531297;
        double r34531299 = r34531295 * r34531298;
        return r34531299;
}

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 2019165 
(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)))))