Average Error: 10.9 → 0.5
Time: 16.0s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[x + \frac{\frac{\frac{y}{\frac{\sqrt[3]{z - a}}{\sqrt[3]{z - t}}}}{\frac{\sqrt[3]{z - a}}{\sqrt[3]{z - t}}}}{\frac{\sqrt[3]{z - a}}{\sqrt[3]{z - t}}}\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
x + \frac{\frac{\frac{y}{\frac{\sqrt[3]{z - a}}{\sqrt[3]{z - t}}}}{\frac{\sqrt[3]{z - a}}{\sqrt[3]{z - t}}}}{\frac{\sqrt[3]{z - a}}{\sqrt[3]{z - t}}}
double f(double x, double y, double z, double t, double a) {
        double r26113446 = x;
        double r26113447 = y;
        double r26113448 = z;
        double r26113449 = t;
        double r26113450 = r26113448 - r26113449;
        double r26113451 = r26113447 * r26113450;
        double r26113452 = a;
        double r26113453 = r26113448 - r26113452;
        double r26113454 = r26113451 / r26113453;
        double r26113455 = r26113446 + r26113454;
        return r26113455;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r26113456 = x;
        double r26113457 = y;
        double r26113458 = z;
        double r26113459 = a;
        double r26113460 = r26113458 - r26113459;
        double r26113461 = cbrt(r26113460);
        double r26113462 = t;
        double r26113463 = r26113458 - r26113462;
        double r26113464 = cbrt(r26113463);
        double r26113465 = r26113461 / r26113464;
        double r26113466 = r26113457 / r26113465;
        double r26113467 = r26113466 / r26113465;
        double r26113468 = r26113467 / r26113465;
        double r26113469 = r26113456 + r26113468;
        return r26113469;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

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Results

Enter valid numbers for all inputs

Target

Original10.9
Target1.1
Herbie0.5
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 10.9

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

  3. Applied associate-/l*1.1

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

  5. Applied +-commutative1.1

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

  7. Applied add-cube-cbrt1.6

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

  8. Applied add-cube-cbrt1.5

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

  9. Applied times-frac1.5

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

  10. Applied associate-/r*0.5

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

  11. Simplified0.5

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

  12. Final simplification0.5

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

Reproduce

herbie shell --seed 2019192 
(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))))