Average Error: 1.3 → 0.4
Time: 15.7s
Precision: 64
\[\frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\]
↓
\[\frac{{\left(\sqrt[3]{1}\right)}^{3} \cdot \frac{\cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)}{\sqrt[3]{3}}}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\]
\frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)
↓
\frac{{\left(\sqrt[3]{1}\right)}^{3} \cdot \frac{\cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)}{\sqrt[3]{3}}}{\sqrt[3]{3} \cdot \sqrt[3]{3}}
double f(double x, double y, double z, double t) {
        double r537991 = 1.0;
        double r537992 = 3.0;
        double r537993 = r537991 / r537992;
        double r537994 = x;
        double r537995 = y;
        double r537996 = 27.0;
        double r537997 = r537995 * r537996;
        double r537998 = r537994 / r537997;
        double r537999 = r537992 * r537998;
        double r538000 = z;
        double r538001 = 2.0;
        double r538002 = r538000 * r538001;
        double r538003 = r537999 / r538002;
        double r538004 = t;
        double r538005 = sqrt(r538004);
        double r538006 = r538003 * r538005;
        double r538007 = acos(r538006);
        double r538008 = r537993 * r538007;
        return r538008;
}
↓
double f(double x, double y, double z, double t) {
        double r538009 = 1.0;
        double r538010 = cbrt(r538009);
        double r538011 = 3.0;
        double r538012 = pow(r538010, r538011);
        double r538013 = 3.0;
        double r538014 = x;
        double r538015 = y;
        double r538016 = 27.0;
        double r538017 = r538015 * r538016;
        double r538018 = r538014 / r538017;
        double r538019 = r538013 * r538018;
        double r538020 = z;
        double r538021 = 2.0;
        double r538022 = r538020 * r538021;
        double r538023 = r538019 / r538022;
        double r538024 = t;
        double r538025 = sqrt(r538024);
        double r538026 = r538023 * r538025;
        double r538027 = acos(r538026);
        double r538028 = cbrt(r538013);
        double r538029 = r538027 / r538028;
        double r538030 = r538012 * r538029;
        double r538031 = r538028 * r538028;
        double r538032 = r538030 / r538031;
        return r538032;
}

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
Target1.1
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 add-cube-cbrt1.3

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

  5. Applied times-frac0.4

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

  6. Applied associate-*l*0.4

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

  7. Final simplification0.4

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

Reproduce

herbie shell --seed 2019294 
(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)))))