Average Error: 1.2 → 1.2
Time: 11.6s
Precision: 64
\[\frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\]
↓
\[\cos^{-1} \left(\log \left(e^{\frac{2001599834386887}{36028797018963968} \cdot \left(\sqrt{t} \cdot \frac{x}{z \cdot y}\right)}\right)\right) \cdot \frac{1}{3}\]
\frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)
↓
\cos^{-1} \left(\log \left(e^{\frac{2001599834386887}{36028797018963968} \cdot \left(\sqrt{t} \cdot \frac{x}{z \cdot y}\right)}\right)\right) \cdot \frac{1}{3}
double f(double x, double y, double z, double t) {
        double r436140 = 1.0;
        double r436141 = 3.0;
        double r436142 = r436140 / r436141;
        double r436143 = x;
        double r436144 = y;
        double r436145 = 27.0;
        double r436146 = r436144 * r436145;
        double r436147 = r436143 / r436146;
        double r436148 = r436141 * r436147;
        double r436149 = z;
        double r436150 = 2.0;
        double r436151 = r436149 * r436150;
        double r436152 = r436148 / r436151;
        double r436153 = t;
        double r436154 = sqrt(r436153);
        double r436155 = r436152 * r436154;
        double r436156 = acos(r436155);
        double r436157 = r436142 * r436156;
        return r436157;
}
↓
double f(double x, double y, double z, double t) {
        double r436158 = 2001599834386887.0;
        double r436159 = 3.602879701896397e+16;
        double r436160 = r436158 / r436159;
        double r436161 = t;
        double r436162 = sqrt(r436161);
        double r436163 = x;
        double r436164 = z;
        double r436165 = y;
        double r436166 = r436164 * r436165;
        double r436167 = r436163 / r436166;
        double r436168 = r436162 * r436167;
        double r436169 = r436160 * r436168;
        double r436170 = exp(r436169);
        double r436171 = log(r436170);
        double r436172 = acos(r436171);
        double r436173 = 1.0;
        double r436174 = 3.0;
        double r436175 = r436173 / r436174;
        double r436176 = r436172 * r436175;
        return r436176;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original1.2
Target1.2
Herbie1.2
\[\frac{\cos^{-1} \left(\frac{\frac{x}{27}}{y \cdot z} \cdot \frac{\sqrt{t}}{\frac{2}{3}}\right)}{3}\]

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-sqr-sqrt1.2

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

  5. Applied times-frac0.3

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

  6. Applied associate-*l*0.3

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

  7. Taylor expanded around 0 0.2

    \[\leadsto \frac{\sqrt{1}}{\sqrt[3]{3} \cdot \sqrt[3]{3}} \cdot \color{blue}{\frac{\cos^{-1} \left(0.05555555555555555247160270937456516548991 \cdot \left(\sqrt{t} \cdot \frac{x}{z \cdot y}\right)\right) \cdot \sqrt{1}}{\sqrt[3]{3}}}\]

  8. Simplified0.2

    \[\leadsto \frac{\sqrt{1}}{\sqrt[3]{3} \cdot \sqrt[3]{3}} \cdot \color{blue}{\frac{\cos^{-1} \left(\frac{2001599834386887}{36028797018963968} \cdot \left(\sqrt{t} \cdot \frac{x}{z \cdot y}\right)\right) \cdot \sqrt{1}}{\sqrt[3]{3}}}\]
  9. Using strategy rm

  10. Applied add-log-exp0.2

    \[\leadsto \frac{\sqrt{1}}{\sqrt[3]{3} \cdot \sqrt[3]{3}} \cdot \frac{\cos^{-1} \color{blue}{\left(\log \left(e^{\frac{2001599834386887}{36028797018963968} \cdot \left(\sqrt{t} \cdot \frac{x}{z \cdot y}\right)}\right)\right)} \cdot \sqrt{1}}{\sqrt[3]{3}}\]

  11. Final simplification1.2

    \[\leadsto \cos^{-1} \left(\log \left(e^{\frac{2001599834386887}{36028797018963968} \cdot \left(\sqrt{t} \cdot \frac{x}{z \cdot y}\right)}\right)\right) \cdot \frac{1}{3}\]

Reproduce

herbie shell --seed 2019304 
(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)))))