Average Error: 10.9 → 0.6
Time: 14.6s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[\frac{\frac{y}{\frac{\frac{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}{\sqrt[3]{z - t}}}{\sqrt[3]{z - t}}}}{\frac{\sqrt[3]{a - t}}{\sqrt[3]{z - t}}} + x\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
\frac{\frac{y}{\frac{\frac{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}{\sqrt[3]{z - 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 r463974 = x;
        double r463975 = y;
        double r463976 = z;
        double r463977 = t;
        double r463978 = r463976 - r463977;
        double r463979 = r463975 * r463978;
        double r463980 = a;
        double r463981 = r463980 - r463977;
        double r463982 = r463979 / r463981;
        double r463983 = r463974 + r463982;
        return r463983;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r463984 = y;
        double r463985 = a;
        double r463986 = t;
        double r463987 = r463985 - r463986;
        double r463988 = cbrt(r463987);
        double r463989 = r463988 * r463988;
        double r463990 = z;
        double r463991 = r463990 - r463986;
        double r463992 = cbrt(r463991);
        double r463993 = r463989 / r463992;
        double r463994 = r463993 / r463992;
        double r463995 = r463984 / r463994;
        double r463996 = r463988 / r463992;
        double r463997 = r463995 / r463996;
        double r463998 = x;
        double r463999 = r463997 + r463998;
        return r463999;
}

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
Herbie0.6
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Initial program 10.9

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

  2. Simplified10.9

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

  4. Applied associate-/l*1.4

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

  6. Applied add-cube-cbrt1.9

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

  7. Applied add-cube-cbrt1.7

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

  8. Applied times-frac1.7

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

  9. Applied associate-/r*0.6

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

  10. Simplified0.6

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

  11. Final simplification0.6

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

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, B"

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

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