Average Error: 1.4 → 0.5
Time: 21.9s
Precision: 64
\[\frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\]
↓
\[\frac{1}{\sqrt[3]{3} \cdot \sqrt[3]{3}} \cdot \left(\sqrt{\frac{1}{\sqrt[3]{3}}} \cdot \left(\sqrt{\frac{1}{\sqrt[3]{3}}} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\right)\right)\]
\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 \left(\sqrt{\frac{1}{\sqrt[3]{3}}} \cdot \left(\sqrt{\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)\right)
double f(double x, double y, double z, double t) {
        double r596244 = 1.0;
        double r596245 = 3.0;
        double r596246 = r596244 / r596245;
        double r596247 = x;
        double r596248 = y;
        double r596249 = 27.0;
        double r596250 = r596248 * r596249;
        double r596251 = r596247 / r596250;
        double r596252 = r596245 * r596251;
        double r596253 = z;
        double r596254 = 2.0;
        double r596255 = r596253 * r596254;
        double r596256 = r596252 / r596255;
        double r596257 = t;
        double r596258 = sqrt(r596257);
        double r596259 = r596256 * r596258;
        double r596260 = acos(r596259);
        double r596261 = r596246 * r596260;
        return r596261;
}
↓
double f(double x, double y, double z, double t) {
        double r596262 = 1.0;
        double r596263 = 3.0;
        double r596264 = cbrt(r596263);
        double r596265 = r596264 * r596264;
        double r596266 = r596262 / r596265;
        double r596267 = 1.0;
        double r596268 = r596267 / r596264;
        double r596269 = sqrt(r596268);
        double r596270 = x;
        double r596271 = y;
        double r596272 = 27.0;
        double r596273 = r596271 * r596272;
        double r596274 = r596270 / r596273;
        double r596275 = r596263 * r596274;
        double r596276 = z;
        double r596277 = 2.0;
        double r596278 = r596276 * r596277;
        double r596279 = r596275 / r596278;
        double r596280 = t;
        double r596281 = sqrt(r596280);
        double r596282 = r596279 * r596281;
        double r596283 = acos(r596282);
        double r596284 = r596269 * r596283;
        double r596285 = r596269 * r596284;
        double r596286 = r596266 * r596285;
        return r596286;
}

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

Original1.4
Target1.2
Herbie0.5
\[\frac{\cos^{-1} \left(\frac{\frac{x}{27}}{y \cdot z} \cdot \frac{\sqrt{t}}{\frac{2}{3}}\right)}{3}\]

Derivation

  1. Initial program 1.4

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

  3. Applied add-cube-cbrt1.4

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

  4. Applied *-un-lft-identity1.4

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

  5. Applied times-frac0.5

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

  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. Using strategy rm

  8. Applied add-sqr-sqrt1.4

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

  9. Applied associate-*l*0.5

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

  10. Final simplification0.5

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

Reproduce

herbie shell --seed 2019323 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, D"
  :precision binary64

  :herbie-target
  (/ (acos (* (/ (/ x 27) (* y z)) (/ (sqrt t) (/ 2 3)))) 3)

  (* (/ 1 3) (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t)))))