Average Error: 6.6 → 1.7
Time: 22.1s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[x + \left(\left(y \cdot \left(\sqrt[3]{\frac{\sqrt[3]{z - x} \cdot \sqrt[3]{z - x}}{\sqrt[3]{t} \cdot \sqrt[3]{t}}} \cdot \sqrt[3]{\frac{\sqrt[3]{z - x} \cdot \sqrt[3]{z - x}}{\sqrt[3]{t} \cdot \sqrt[3]{t}}}\right)\right) \cdot \sqrt[3]{\frac{\sqrt[3]{z - x} \cdot \sqrt[3]{z - x}}{\sqrt[3]{t} \cdot \sqrt[3]{t}}}\right) \cdot \frac{\sqrt[3]{z - x}}{\sqrt[3]{t}}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
x + \left(\left(y \cdot \left(\sqrt[3]{\frac{\sqrt[3]{z - x} \cdot \sqrt[3]{z - x}}{\sqrt[3]{t} \cdot \sqrt[3]{t}}} \cdot \sqrt[3]{\frac{\sqrt[3]{z - x} \cdot \sqrt[3]{z - x}}{\sqrt[3]{t} \cdot \sqrt[3]{t}}}\right)\right) \cdot \sqrt[3]{\frac{\sqrt[3]{z - x} \cdot \sqrt[3]{z - x}}{\sqrt[3]{t} \cdot \sqrt[3]{t}}}\right) \cdot \frac{\sqrt[3]{z - x}}{\sqrt[3]{t}}
double f(double x, double y, double z, double t) {
        double r170945 = x;
        double r170946 = y;
        double r170947 = z;
        double r170948 = r170947 - r170945;
        double r170949 = r170946 * r170948;
        double r170950 = t;
        double r170951 = r170949 / r170950;
        double r170952 = r170945 + r170951;
        return r170952;
}
↓
double f(double x, double y, double z, double t) {
        double r170953 = x;
        double r170954 = y;
        double r170955 = z;
        double r170956 = r170955 - r170953;
        double r170957 = cbrt(r170956);
        double r170958 = r170957 * r170957;
        double r170959 = t;
        double r170960 = cbrt(r170959);
        double r170961 = r170960 * r170960;
        double r170962 = r170958 / r170961;
        double r170963 = cbrt(r170962);
        double r170964 = r170963 * r170963;
        double r170965 = r170954 * r170964;
        double r170966 = r170965 * r170963;
        double r170967 = r170957 / r170960;
        double r170968 = r170966 * r170967;
        double r170969 = r170953 + r170968;
        return r170969;
}

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

Original6.6
Target2.0
Herbie1.7
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Initial program 6.6

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

  3. Applied *-un-lft-identity6.6

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

  4. Applied times-frac6.9

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

  5. Simplified6.9

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

  7. Applied add-cube-cbrt7.3

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

  8. Applied add-cube-cbrt7.5

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

  9. Applied times-frac7.5

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

  10. Applied associate-*r*1.6

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

  12. Applied add-cube-cbrt1.7

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

  13. Applied associate-*r*1.7

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

  14. Final simplification1.7

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

Reproduce

herbie shell --seed 2019326 
(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)))