Average Error: 6.6 → 3.3
Time: 20.5s
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 r206501 = x;
        double r206502 = y;
        double r206503 = z;
        double r206504 = r206503 - r206501;
        double r206505 = r206502 * r206504;
        double r206506 = t;
        double r206507 = r206505 / r206506;
        double r206508 = r206501 + r206507;
        return r206508;
}
↓
double f(double x, double y, double z, double t) {
        double r206509 = x;
        double r206510 = y;
        double r206511 = t;
        double r206512 = cbrt(r206511);
        double r206513 = r206512 * r206512;
        double r206514 = r206510 / r206513;
        double r206515 = z;
        double r206516 = r206515 - r206509;
        double r206517 = r206516 / r206512;
        double r206518 = r206514 * r206517;
        double r206519 = r206509 + r206518;
        return r206519;
}

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)))