Average Error: 6.6 → 3.3
Time: 20.8s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[x + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z - x}{\sqrt[3]{t}}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
x + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z - x}{\sqrt[3]{t}}
double f(double x, double y, double z, double t) {
        double r216582 = x;
        double r216583 = y;
        double r216584 = z;
        double r216585 = r216584 - r216582;
        double r216586 = r216583 * r216585;
        double r216587 = t;
        double r216588 = r216586 / r216587;
        double r216589 = r216582 + r216588;
        return r216589;
}
↓
double f(double x, double y, double z, double t) {
        double r216590 = x;
        double r216591 = y;
        double r216592 = t;
        double r216593 = cbrt(r216592);
        double r216594 = r216593 * r216593;
        double r216595 = r216591 / r216594;
        double r216596 = z;
        double r216597 = r216596 - r216590;
        double r216598 = r216597 / r216593;
        double r216599 = r216595 * r216598;
        double r216600 = r216590 + r216599;
        return r216600;
}

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
Target2.1
Herbie3.3
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Initial program 6.6

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

  3. Applied add-cube-cbrt7.0

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

  4. Applied times-frac3.3

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

  5. Final simplification3.3

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

Reproduce

herbie shell --seed 2019325 +o rules:numerics
(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)))