Average Error: 10.6 → 1.6
Time: 15.8s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[x + \left(\frac{\sqrt[3]{y}}{a - t} \cdot \left(z - t\right)\right) \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
x + \left(\frac{\sqrt[3]{y}}{a - t} \cdot \left(z - t\right)\right) \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)
double f(double x, double y, double z, double t, double a) {
        double r550606 = x;
        double r550607 = y;
        double r550608 = z;
        double r550609 = t;
        double r550610 = r550608 - r550609;
        double r550611 = r550607 * r550610;
        double r550612 = a;
        double r550613 = r550612 - r550609;
        double r550614 = r550611 / r550613;
        double r550615 = r550606 + r550614;
        return r550615;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r550616 = x;
        double r550617 = y;
        double r550618 = cbrt(r550617);
        double r550619 = a;
        double r550620 = t;
        double r550621 = r550619 - r550620;
        double r550622 = r550618 / r550621;
        double r550623 = z;
        double r550624 = r550623 - r550620;
        double r550625 = r550622 * r550624;
        double r550626 = r550618 * r550618;
        double r550627 = r550625 * r550626;
        double r550628 = r550616 + r550627;
        return r550628;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original10.6
Target1.2
Herbie1.6
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Initial program 10.6

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

  3. Applied associate-/l*1.2

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

  5. Applied *-un-lft-identity1.2

    \[\leadsto x + \frac{y}{\frac{a - t}{\color{blue}{1 \cdot \left(z - t\right)}}}\]

  6. Applied *-un-lft-identity1.2

    \[\leadsto x + \frac{y}{\frac{\color{blue}{1 \cdot \left(a - t\right)}}{1 \cdot \left(z - t\right)}}\]

  7. Applied times-frac1.2

    \[\leadsto x + \frac{y}{\color{blue}{\frac{1}{1} \cdot \frac{a - t}{z - t}}}\]

  8. Applied add-cube-cbrt1.7

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

  9. Applied times-frac1.7

    \[\leadsto x + \color{blue}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\frac{1}{1}} \cdot \frac{\sqrt[3]{y}}{\frac{a - t}{z - t}}}\]

  10. Simplified1.7

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

  11. Simplified1.6

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

  12. Final simplification1.6

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

Reproduce

herbie shell --seed 2019194 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"

  :herbie-target
  (+ x (/ y (/ (- a t) (- z t))))

  (+ x (/ (* y (- z t)) (- a t))))