Average Error: 1.6 → 2.2
Time: 14.8s
Precision: 64
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\left|\frac{4 + x}{y} - \left(\frac{x}{\sqrt[3]{y}} \cdot z\right) \cdot \frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right|\]
\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|
↓
\left|\frac{4 + x}{y} - \left(\frac{x}{\sqrt[3]{y}} \cdot z\right) \cdot \frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right|
double f(double x, double y, double z) {
        double r1721508 = x;
        double r1721509 = 4.0;
        double r1721510 = r1721508 + r1721509;
        double r1721511 = y;
        double r1721512 = r1721510 / r1721511;
        double r1721513 = r1721508 / r1721511;
        double r1721514 = z;
        double r1721515 = r1721513 * r1721514;
        double r1721516 = r1721512 - r1721515;
        double r1721517 = fabs(r1721516);
        return r1721517;
}
↓
double f(double x, double y, double z) {
        double r1721518 = 4.0;
        double r1721519 = x;
        double r1721520 = r1721518 + r1721519;
        double r1721521 = y;
        double r1721522 = r1721520 / r1721521;
        double r1721523 = cbrt(r1721521);
        double r1721524 = r1721519 / r1721523;
        double r1721525 = z;
        double r1721526 = r1721524 * r1721525;
        double r1721527 = 1.0;
        double r1721528 = r1721523 * r1721523;
        double r1721529 = r1721527 / r1721528;
        double r1721530 = r1721526 * r1721529;
        double r1721531 = r1721522 - r1721530;
        double r1721532 = fabs(r1721531);
        return r1721532;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 1.6

    \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
  2. Using strategy rm

  3. Applied add-cube-cbrt1.9

    \[\leadsto \left|\frac{x + 4}{y} - \frac{x}{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}} \cdot z\right|\]

  4. Applied *-un-lft-identity1.9

    \[\leadsto \left|\frac{x + 4}{y} - \frac{\color{blue}{1 \cdot x}}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}} \cdot z\right|\]

  5. Applied times-frac1.9

    \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\left(\frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{x}{\sqrt[3]{y}}\right)} \cdot z\right|\]

  6. Applied associate-*l*2.2

    \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \left(\frac{x}{\sqrt[3]{y}} \cdot z\right)}\right|\]

  7. Final simplification2.2

    \[\leadsto \left|\frac{4 + x}{y} - \left(\frac{x}{\sqrt[3]{y}} \cdot z\right) \cdot \frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right|\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y z)
  :name "fabs fraction 1"
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))