Average Error: 1.2 → 0.2
Time: 5.7s
Precision: 64
\[\frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\]
↓
\[\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{3} \cdot \sqrt[3]{3}} \cdot \left(\frac{\sqrt[3]{1}}{\sqrt[3]{3}} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\right)\]
\frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)
↓
\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{3} \cdot \sqrt[3]{3}} \cdot \left(\frac{\sqrt[3]{1}}{\sqrt[3]{3}} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\right)
double f(double x, double y, double z, double t) {
        double r989244 = 1.0;
        double r989245 = 3.0;
        double r989246 = r989244 / r989245;
        double r989247 = x;
        double r989248 = y;
        double r989249 = 27.0;
        double r989250 = r989248 * r989249;
        double r989251 = r989247 / r989250;
        double r989252 = r989245 * r989251;
        double r989253 = z;
        double r989254 = 2.0;
        double r989255 = r989253 * r989254;
        double r989256 = r989252 / r989255;
        double r989257 = t;
        double r989258 = sqrt(r989257);
        double r989259 = r989256 * r989258;
        double r989260 = acos(r989259);
        double r989261 = r989246 * r989260;
        return r989261;
}
↓
double f(double x, double y, double z, double t) {
        double r989262 = 1.0;
        double r989263 = cbrt(r989262);
        double r989264 = r989263 * r989263;
        double r989265 = 3.0;
        double r989266 = cbrt(r989265);
        double r989267 = r989266 * r989266;
        double r989268 = r989264 / r989267;
        double r989269 = r989263 / r989266;
        double r989270 = x;
        double r989271 = y;
        double r989272 = 27.0;
        double r989273 = r989271 * r989272;
        double r989274 = r989270 / r989273;
        double r989275 = r989265 * r989274;
        double r989276 = z;
        double r989277 = 2.0;
        double r989278 = r989276 * r989277;
        double r989279 = r989275 / r989278;
        double r989280 = t;
        double r989281 = sqrt(r989280);
        double r989282 = r989279 * r989281;
        double r989283 = acos(r989282);
        double r989284 = r989269 * r989283;
        double r989285 = r989268 * r989284;
        return r989285;
}

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

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

Derivation

  1. Initial program 1.2

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

  3. Applied add-cube-cbrt1.2

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

  4. Applied add-cube-cbrt1.2

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

  5. Applied times-frac0.2

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

  6. Applied associate-*l*0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2020060 +o rules:numerics
(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)))))