Average Error: 11.1 → 0.8
Time: 45.0s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[\frac{\sqrt[3]{y}}{\frac{\sqrt[3]{z - a}}{\sqrt[3]{z - t}}} \cdot \left(\frac{\sqrt[3]{y}}{\frac{\sqrt[3]{z - a}}{\sqrt[3]{z - t}}} \cdot \frac{\sqrt[3]{y}}{\frac{\sqrt[3]{z - a}}{\sqrt[3]{z - t}}}\right) + x\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
\frac{\sqrt[3]{y}}{\frac{\sqrt[3]{z - a}}{\sqrt[3]{z - t}}} \cdot \left(\frac{\sqrt[3]{y}}{\frac{\sqrt[3]{z - a}}{\sqrt[3]{z - t}}} \cdot \frac{\sqrt[3]{y}}{\frac{\sqrt[3]{z - a}}{\sqrt[3]{z - t}}}\right) + x
double f(double x, double y, double z, double t, double a) {
        double r27371518 = x;
        double r27371519 = y;
        double r27371520 = z;
        double r27371521 = t;
        double r27371522 = r27371520 - r27371521;
        double r27371523 = r27371519 * r27371522;
        double r27371524 = a;
        double r27371525 = r27371520 - r27371524;
        double r27371526 = r27371523 / r27371525;
        double r27371527 = r27371518 + r27371526;
        return r27371527;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r27371528 = y;
        double r27371529 = cbrt(r27371528);
        double r27371530 = z;
        double r27371531 = a;
        double r27371532 = r27371530 - r27371531;
        double r27371533 = cbrt(r27371532);
        double r27371534 = t;
        double r27371535 = r27371530 - r27371534;
        double r27371536 = cbrt(r27371535);
        double r27371537 = r27371533 / r27371536;
        double r27371538 = r27371529 / r27371537;
        double r27371539 = r27371538 * r27371538;
        double r27371540 = r27371538 * r27371539;
        double r27371541 = x;
        double r27371542 = r27371540 + r27371541;
        return r27371542;
}

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

Original11.1
Target1.3
Herbie0.8
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 11.1

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

  3. Applied associate-/l*1.3

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

  5. Applied add-cube-cbrt1.8

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

  6. Applied add-cube-cbrt1.7

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

  7. Applied times-frac1.7

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

  8. Applied add-cube-cbrt2.0

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

  9. Applied times-frac0.8

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

  10. Simplified0.8

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

  11. Final simplification0.8

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

Reproduce

herbie shell --seed 2019168 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"

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

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