Average Error: 6.8 → 1.8
Time: 13.6s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[x + \left(\frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt[3]{z - x} \cdot \sqrt[3]{z - x}}{\sqrt[3]{1}}\right) \cdot \frac{\sqrt[3]{z - x}}{\sqrt[3]{t}}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
x + \left(\frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt[3]{z - x} \cdot \sqrt[3]{z - x}}{\sqrt[3]{1}}\right) \cdot \frac{\sqrt[3]{z - x}}{\sqrt[3]{t}}
double f(double x, double y, double z, double t) {
        double r277153 = x;
        double r277154 = y;
        double r277155 = z;
        double r277156 = r277155 - r277153;
        double r277157 = r277154 * r277156;
        double r277158 = t;
        double r277159 = r277157 / r277158;
        double r277160 = r277153 + r277159;
        return r277160;
}
↓
double f(double x, double y, double z, double t) {
        double r277161 = x;
        double r277162 = y;
        double r277163 = t;
        double r277164 = cbrt(r277163);
        double r277165 = r277164 * r277164;
        double r277166 = r277162 / r277165;
        double r277167 = z;
        double r277168 = r277167 - r277161;
        double r277169 = cbrt(r277168);
        double r277170 = r277169 * r277169;
        double r277171 = 1.0;
        double r277172 = cbrt(r277171);
        double r277173 = r277170 / r277172;
        double r277174 = r277166 * r277173;
        double r277175 = r277169 / r277164;
        double r277176 = r277174 * r277175;
        double r277177 = r277161 + r277176;
        return r277177;
}

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

Original6.8
Target2.1
Herbie1.8
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Initial program 6.8

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

  3. Applied add-cube-cbrt7.3

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

  4. Applied times-frac3.2

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

  6. Applied *-un-lft-identity3.2

    \[\leadsto x + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z - x}{\sqrt[3]{\color{blue}{1 \cdot t}}}\]

  7. Applied cbrt-prod3.2

    \[\leadsto x + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z - x}{\color{blue}{\sqrt[3]{1} \cdot \sqrt[3]{t}}}\]

  8. Applied add-cube-cbrt3.3

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

  9. Applied times-frac3.3

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

  10. Applied associate-*r*1.8

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

  11. Final simplification1.8

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

Reproduce

herbie shell --seed 2019303 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"
  :precision binary64

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

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