Average Error: 1.4 → 0.7
Time: 20.9s
Precision: 64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[\frac{y}{\frac{\sqrt[3]{z - a}}{\sqrt[3]{z - t}} \cdot \frac{\sqrt[3]{z - a}}{\sqrt[3]{z - t}}} \cdot \frac{\sqrt[3]{\sqrt[3]{z - t}} \cdot \sqrt[3]{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}}{\sqrt[3]{z - a}} + x\]
x + y \cdot \frac{z - t}{z - a}
↓
\frac{y}{\frac{\sqrt[3]{z - a}}{\sqrt[3]{z - t}} \cdot \frac{\sqrt[3]{z - a}}{\sqrt[3]{z - t}}} \cdot \frac{\sqrt[3]{\sqrt[3]{z - t}} \cdot \sqrt[3]{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}}{\sqrt[3]{z - a}} + x
double f(double x, double y, double z, double t, double a) {
        double r30768254 = x;
        double r30768255 = y;
        double r30768256 = z;
        double r30768257 = t;
        double r30768258 = r30768256 - r30768257;
        double r30768259 = a;
        double r30768260 = r30768256 - r30768259;
        double r30768261 = r30768258 / r30768260;
        double r30768262 = r30768255 * r30768261;
        double r30768263 = r30768254 + r30768262;
        return r30768263;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r30768264 = y;
        double r30768265 = z;
        double r30768266 = a;
        double r30768267 = r30768265 - r30768266;
        double r30768268 = cbrt(r30768267);
        double r30768269 = t;
        double r30768270 = r30768265 - r30768269;
        double r30768271 = cbrt(r30768270);
        double r30768272 = r30768268 / r30768271;
        double r30768273 = r30768272 * r30768272;
        double r30768274 = r30768264 / r30768273;
        double r30768275 = cbrt(r30768271);
        double r30768276 = r30768271 * r30768271;
        double r30768277 = cbrt(r30768276);
        double r30768278 = r30768275 * r30768277;
        double r30768279 = r30768278 / r30768268;
        double r30768280 = r30768274 * r30768279;
        double r30768281 = x;
        double r30768282 = r30768280 + r30768281;
        return r30768282;
}

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

Original1.4
Target1.3
Herbie0.7
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 1.4

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

  3. Applied add-cube-cbrt1.9

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

  4. Applied add-cube-cbrt1.8

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

  5. Applied times-frac1.8

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

  6. Applied associate-*r*0.6

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

  7. Simplified0.5

    \[\leadsto x + \color{blue}{\frac{y}{\frac{\sqrt[3]{z - a}}{\sqrt[3]{z - t}} \cdot \frac{\sqrt[3]{z - a}}{\sqrt[3]{z - t}}}} \cdot \frac{\sqrt[3]{z - t}}{\sqrt[3]{z - a}}\]
  8. Using strategy rm

  9. Applied add-cube-cbrt0.6

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

  10. Applied cbrt-prod0.7

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

  11. Final simplification0.7

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

Reproduce

herbie shell --seed 2019171 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"

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

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