Average Error: 3.7 → 1.6
Time: 1.5m
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[x - \left(\frac{\frac{1}{\sqrt[3]{3} \cdot \sqrt[3]{3}}}{\frac{z}{\frac{y}{\sqrt[3]{3}}}} - \frac{\frac{\frac{t}{3}}{z}}{y}\right)\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
x - \left(\frac{\frac{1}{\sqrt[3]{3} \cdot \sqrt[3]{3}}}{\frac{z}{\frac{y}{\sqrt[3]{3}}}} - \frac{\frac{\frac{t}{3}}{z}}{y}\right)
double f(double x, double y, double z, double t) {
        double r1158154 = x;
        double r1158155 = y;
        double r1158156 = z;
        double r1158157 = 3.0;
        double r1158158 = r1158156 * r1158157;
        double r1158159 = r1158155 / r1158158;
        double r1158160 = r1158154 - r1158159;
        double r1158161 = t;
        double r1158162 = r1158158 * r1158155;
        double r1158163 = r1158161 / r1158162;
        double r1158164 = r1158160 + r1158163;
        return r1158164;
}
↓
double f(double x, double y, double z, double t) {
        double r1158165 = x;
        double r1158166 = 1.0;
        double r1158167 = 3.0;
        double r1158168 = cbrt(r1158167);
        double r1158169 = r1158168 * r1158168;
        double r1158170 = r1158166 / r1158169;
        double r1158171 = z;
        double r1158172 = y;
        double r1158173 = r1158172 / r1158168;
        double r1158174 = r1158171 / r1158173;
        double r1158175 = r1158170 / r1158174;
        double r1158176 = t;
        double r1158177 = r1158176 / r1158167;
        double r1158178 = r1158177 / r1158171;
        double r1158179 = r1158178 / r1158172;
        double r1158180 = r1158175 - r1158179;
        double r1158181 = r1158165 - r1158180;
        return r1158181;
}

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

Original3.7
Target1.6
Herbie1.6
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Initial program 3.7

    \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
  2. Using strategy rm

  3. Applied associate-/r*1.6

    \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\frac{t}{z \cdot 3}}{y}}\]

  4. Simplified1.5

    \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{\color{blue}{\frac{\frac{t}{3}}{z}}}{y}\]
  5. Using strategy rm

  6. Applied associate-+l-1.5

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

  7. Simplified1.5

    \[\leadsto x - \color{blue}{\left(\frac{\frac{y}{3}}{z} - \frac{\frac{\frac{t}{3}}{z}}{y}\right)}\]
  8. Using strategy rm

  9. Applied add-cube-cbrt1.5

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

  10. Applied *-un-lft-identity1.5

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

  11. Applied times-frac1.6

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

  12. Applied associate-/l*1.6

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

  13. Final simplification1.6

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

Reproduce

herbie shell --seed 2019196 +o rules:numerics
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, H"

  :herbie-target
  (+ (- x (/ y (* z 3.0))) (/ (/ t (* z 3.0)) y))

  (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))