Average Error: 6.4 → 1.3
Time: 3.6s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[x + \frac{\frac{y}{\frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{\sqrt[3]{z - x} \cdot \sqrt[3]{z - x}}}}{\frac{\sqrt[3]{t}}{\sqrt[3]{z - x}}}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
x + \frac{\frac{y}{\frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{\sqrt[3]{z - x} \cdot \sqrt[3]{z - x}}}}{\frac{\sqrt[3]{t}}{\sqrt[3]{z - x}}}
double f(double x, double y, double z, double t) {
        double r353163 = x;
        double r353164 = y;
        double r353165 = z;
        double r353166 = r353165 - r353163;
        double r353167 = r353164 * r353166;
        double r353168 = t;
        double r353169 = r353167 / r353168;
        double r353170 = r353163 + r353169;
        return r353170;
}
↓
double f(double x, double y, double z, double t) {
        double r353171 = x;
        double r353172 = y;
        double r353173 = t;
        double r353174 = cbrt(r353173);
        double r353175 = r353174 * r353174;
        double r353176 = z;
        double r353177 = r353176 - r353171;
        double r353178 = cbrt(r353177);
        double r353179 = r353178 * r353178;
        double r353180 = r353175 / r353179;
        double r353181 = r353172 / r353180;
        double r353182 = r353174 / r353178;
        double r353183 = r353181 / r353182;
        double r353184 = r353171 + r353183;
        return r353184;
}

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

Original6.4
Target2.2
Herbie1.3
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Initial program 6.4

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

  3. Applied associate-/l*5.6

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

  5. Applied add-cube-cbrt6.1

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

  6. Applied add-cube-cbrt6.2

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

  7. Applied times-frac6.2

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

  8. Applied associate-/r*1.3

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

  9. Final simplification1.3

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

Reproduce

herbie shell --seed 2020020 
(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)))