Average Error: 10.7 → 0.5
Time: 8.9s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[x + \frac{\frac{y}{\frac{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}}}{\frac{\sqrt[3]{a - t}}{\sqrt[3]{z - t}}}\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
x + \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}}}
double f(double x, double y, double z, double t, double a) {
        double r246147 = x;
        double r246148 = y;
        double r246149 = z;
        double r246150 = t;
        double r246151 = r246149 - r246150;
        double r246152 = r246148 * r246151;
        double r246153 = a;
        double r246154 = r246153 - r246150;
        double r246155 = r246152 / r246154;
        double r246156 = r246147 + r246155;
        return r246156;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r246157 = x;
        double r246158 = y;
        double r246159 = a;
        double r246160 = t;
        double r246161 = r246159 - r246160;
        double r246162 = cbrt(r246161);
        double r246163 = r246162 * r246162;
        double r246164 = z;
        double r246165 = r246164 - r246160;
        double r246166 = cbrt(r246165);
        double r246167 = r246166 * r246166;
        double r246168 = r246163 / r246167;
        double r246169 = r246158 / r246168;
        double r246170 = r246162 / r246166;
        double r246171 = r246169 / r246170;
        double r246172 = r246157 + r246171;
        return r246172;
}

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

Original10.7
Target1.3
Herbie0.5
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Initial program 10.7

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

  3. Applied associate-/l*1.3

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

  5. Applied add-cube-cbrt1.8

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

  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. Final simplification0.5

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

Reproduce

herbie shell --seed 2020042 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

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

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