Average Error: 1.3 → 0.5
Time: 5.5s
Precision: 64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[x + \frac{y}{\frac{\sqrt[3]{z - a} \cdot \sqrt[3]{z - a}}{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}} \cdot \frac{\sqrt[3]{1}}{\frac{\sqrt[3]{z - a}}{\sqrt[3]{z - t}}}\]
x + y \cdot \frac{z - t}{z - a}
↓
x + \frac{y}{\frac{\sqrt[3]{z - a} \cdot \sqrt[3]{z - a}}{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}} \cdot \frac{\sqrt[3]{1}}{\frac{\sqrt[3]{z - a}}{\sqrt[3]{z - t}}}
double f(double x, double y, double z, double t, double a) {
        double r655248 = x;
        double r655249 = y;
        double r655250 = z;
        double r655251 = t;
        double r655252 = r655250 - r655251;
        double r655253 = a;
        double r655254 = r655250 - r655253;
        double r655255 = r655252 / r655254;
        double r655256 = r655249 * r655255;
        double r655257 = r655248 + r655256;
        return r655257;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r655258 = x;
        double r655259 = y;
        double r655260 = z;
        double r655261 = a;
        double r655262 = r655260 - r655261;
        double r655263 = cbrt(r655262);
        double r655264 = r655263 * r655263;
        double r655265 = t;
        double r655266 = r655260 - r655265;
        double r655267 = cbrt(r655266);
        double r655268 = r655267 * r655267;
        double r655269 = r655264 / r655268;
        double r655270 = r655259 / r655269;
        double r655271 = 1.0;
        double r655272 = cbrt(r655271);
        double r655273 = r655263 / r655267;
        double r655274 = r655272 / r655273;
        double r655275 = r655270 * r655274;
        double r655276 = r655258 + r655275;
        return r655276;
}

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

Original1.3
Target1.2
Herbie0.5
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 1.3

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

  3. Applied clear-num1.4

    \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{z - a}{z - t}}}\]
  4. Using strategy rm

  5. Applied add-cube-cbrt1.9

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

  6. Applied add-cube-cbrt1.7

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

  7. Applied times-frac1.7

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

  8. Applied add-cube-cbrt1.7

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

  9. Applied times-frac1.7

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

  10. Applied associate-*r*0.5

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

  11. Simplified0.5

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

  12. Final simplification0.5

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

Reproduce

herbie shell --seed 2019354 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

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

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