Average Error: 10.8 → 0.5
Time: 21.1s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[\frac{\frac{y}{\frac{\sqrt[3]{a - t}}{\sqrt[3]{z - t}} \cdot \frac{\sqrt[3]{a - t}}{\sqrt[3]{z - t}}}}{\frac{\sqrt[3]{a - t}}{\sqrt[3]{z - t}}} + x\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
\frac{\frac{y}{\frac{\sqrt[3]{a - t}}{\sqrt[3]{z - t}} \cdot \frac{\sqrt[3]{a - t}}{\sqrt[3]{z - t}}}}{\frac{\sqrt[3]{a - t}}{\sqrt[3]{z - t}}} + x
double f(double x, double y, double z, double t, double a) {
        double r23911166 = x;
        double r23911167 = y;
        double r23911168 = z;
        double r23911169 = t;
        double r23911170 = r23911168 - r23911169;
        double r23911171 = r23911167 * r23911170;
        double r23911172 = a;
        double r23911173 = r23911172 - r23911169;
        double r23911174 = r23911171 / r23911173;
        double r23911175 = r23911166 + r23911174;
        return r23911175;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r23911176 = y;
        double r23911177 = a;
        double r23911178 = t;
        double r23911179 = r23911177 - r23911178;
        double r23911180 = cbrt(r23911179);
        double r23911181 = z;
        double r23911182 = r23911181 - r23911178;
        double r23911183 = cbrt(r23911182);
        double r23911184 = r23911180 / r23911183;
        double r23911185 = r23911184 * r23911184;
        double r23911186 = r23911176 / r23911185;
        double r23911187 = r23911186 / r23911184;
        double r23911188 = x;
        double r23911189 = r23911187 + r23911188;
        return r23911189;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

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Results

Enter valid numbers for all inputs

Target

Original10.8
Target1.2
Herbie0.5
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Initial program 10.8

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

  3. Applied associate-/l*1.2

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

  5. Applied add-cube-cbrt1.7

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

  6. Applied add-cube-cbrt1.6

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

  7. Applied times-frac1.6

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

  8. Applied associate-/r*0.5

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

  9. Simplified0.5

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

  10. Final simplification0.5

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

Reproduce

herbie shell --seed 2019169 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"

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

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