Average Error: 1.6 → 1.8
Time: 23.1s
Precision: 64
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\left|\frac{4 + x}{y} - \left(\sqrt[3]{z} \cdot \left(\frac{\sqrt[3]{z}}{y} \cdot x\right)\right) \cdot \left(\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z}}\right)\right|\]
\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|
↓
\left|\frac{4 + x}{y} - \left(\sqrt[3]{z} \cdot \left(\frac{\sqrt[3]{z}}{y} \cdot x\right)\right) \cdot \left(\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z}}\right)\right|
double f(double x, double y, double z) {
        double r1724548 = x;
        double r1724549 = 4.0;
        double r1724550 = r1724548 + r1724549;
        double r1724551 = y;
        double r1724552 = r1724550 / r1724551;
        double r1724553 = r1724548 / r1724551;
        double r1724554 = z;
        double r1724555 = r1724553 * r1724554;
        double r1724556 = r1724552 - r1724555;
        double r1724557 = fabs(r1724556);
        return r1724557;
}
↓
double f(double x, double y, double z) {
        double r1724558 = 4.0;
        double r1724559 = x;
        double r1724560 = r1724558 + r1724559;
        double r1724561 = y;
        double r1724562 = r1724560 / r1724561;
        double r1724563 = z;
        double r1724564 = cbrt(r1724563);
        double r1724565 = r1724564 / r1724561;
        double r1724566 = r1724565 * r1724559;
        double r1724567 = r1724564 * r1724566;
        double r1724568 = r1724564 * r1724564;
        double r1724569 = cbrt(r1724568);
        double r1724570 = cbrt(r1724564);
        double r1724571 = r1724569 * r1724570;
        double r1724572 = r1724567 * r1724571;
        double r1724573 = r1724562 - r1724572;
        double r1724574 = fabs(r1724573);
        return r1724574;
}

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

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

  4. Applied associate-*r*1.9

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

  6. Applied add-cube-cbrt1.9

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

  7. Applied cbrt-prod1.9

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

  9. Applied associate-*r*1.9

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

  11. Applied div-inv1.9

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

  12. Applied associate-*l*1.8

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

  13. Simplified1.8

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

  14. Final simplification1.8

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

Reproduce

herbie shell --seed 2019141 +o rules:numerics
(FPCore (x y z)
  :name "fabs fraction 1"
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))