Average Error: 1.3 → 0.3
Time: 10.7s
Precision: 64
\[\frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\]
↓
\[\frac{1}{\sqrt[3]{3} \cdot \sqrt[3]{3}} \cdot \left(\frac{1}{\sqrt[3]{3}} \cdot \cos^{-1} \left(\frac{3 \cdot x}{\left(z \cdot 2\right) \cdot \left(y \cdot 27\right)} \cdot \sqrt{t}\right)\right)\]
\frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)
↓
\frac{1}{\sqrt[3]{3} \cdot \sqrt[3]{3}} \cdot \left(\frac{1}{\sqrt[3]{3}} \cdot \cos^{-1} \left(\frac{3 \cdot x}{\left(z \cdot 2\right) \cdot \left(y \cdot 27\right)} \cdot \sqrt{t}\right)\right)
double f(double x, double y, double z, double t) {
        double r874044 = 1.0;
        double r874045 = 3.0;
        double r874046 = r874044 / r874045;
        double r874047 = x;
        double r874048 = y;
        double r874049 = 27.0;
        double r874050 = r874048 * r874049;
        double r874051 = r874047 / r874050;
        double r874052 = r874045 * r874051;
        double r874053 = z;
        double r874054 = 2.0;
        double r874055 = r874053 * r874054;
        double r874056 = r874052 / r874055;
        double r874057 = t;
        double r874058 = sqrt(r874057);
        double r874059 = r874056 * r874058;
        double r874060 = acos(r874059);
        double r874061 = r874046 * r874060;
        return r874061;
}
↓
double f(double x, double y, double z, double t) {
        double r874062 = 1.0;
        double r874063 = 3.0;
        double r874064 = cbrt(r874063);
        double r874065 = r874064 * r874064;
        double r874066 = r874062 / r874065;
        double r874067 = 1.0;
        double r874068 = r874067 / r874064;
        double r874069 = x;
        double r874070 = r874063 * r874069;
        double r874071 = z;
        double r874072 = 2.0;
        double r874073 = r874071 * r874072;
        double r874074 = y;
        double r874075 = 27.0;
        double r874076 = r874074 * r874075;
        double r874077 = r874073 * r874076;
        double r874078 = r874070 / r874077;
        double r874079 = t;
        double r874080 = sqrt(r874079);
        double r874081 = r874078 * r874080;
        double r874082 = acos(r874081);
        double r874083 = r874068 * r874082;
        double r874084 = r874066 * r874083;
        return r874084;
}

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

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*0.3

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

  8. Applied associate-*r/0.4

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

  9. Applied associate-/l/0.3

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

  10. Final simplification0.3

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

Reproduce

herbie shell --seed 2020046 
(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)))))