Average Error: 10.9 → 1.0
Time: 17.0s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[\left(\frac{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{z - a}}}{\sqrt[3]{z - a}} \cdot \left(\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}\right)\right) \cdot \frac{\sqrt[3]{y}}{\frac{\sqrt[3]{z - a}}{\sqrt[3]{z - t}}} + x\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
\left(\frac{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{z - a}}}{\sqrt[3]{z - a}} \cdot \left(\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}\right)\right) \cdot \frac{\sqrt[3]{y}}{\frac{\sqrt[3]{z - a}}{\sqrt[3]{z - t}}} + x
double f(double x, double y, double z, double t, double a) {
        double r362412 = x;
        double r362413 = y;
        double r362414 = z;
        double r362415 = t;
        double r362416 = r362414 - r362415;
        double r362417 = r362413 * r362416;
        double r362418 = a;
        double r362419 = r362414 - r362418;
        double r362420 = r362417 / r362419;
        double r362421 = r362412 + r362420;
        return r362421;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r362422 = y;
        double r362423 = cbrt(r362422);
        double r362424 = r362423 * r362423;
        double r362425 = z;
        double r362426 = a;
        double r362427 = r362425 - r362426;
        double r362428 = cbrt(r362427);
        double r362429 = r362424 / r362428;
        double r362430 = r362429 / r362428;
        double r362431 = t;
        double r362432 = r362425 - r362431;
        double r362433 = cbrt(r362432);
        double r362434 = r362433 * r362433;
        double r362435 = r362430 * r362434;
        double r362436 = r362428 / r362433;
        double r362437 = r362423 / r362436;
        double r362438 = r362435 * r362437;
        double r362439 = x;
        double r362440 = r362438 + r362439;
        return r362440;
}

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

Original10.9
Target1.4
Herbie1.0
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 10.9

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

  3. Applied *-un-lft-identity10.9

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

  4. Applied *-un-lft-identity10.9

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

  5. Applied distribute-lft-out10.9

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

  6. Simplified1.4

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

  8. Applied add-cube-cbrt1.9

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

  9. Applied add-cube-cbrt1.8

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

  10. Applied times-frac1.8

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

  11. Applied add-cube-cbrt2.1

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

  12. Applied times-frac0.8

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

  13. Simplified1.0

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

  14. Final simplification1.0

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

Reproduce

herbie shell --seed 2019195 
(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))))