Average Error: 10.7 → 0.6
Time: 4.1s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[x + \frac{\frac{y}{\frac{\sqrt[3]{z - a} \cdot \sqrt[3]{z - a}}{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}}}{\frac{\sqrt[3]{z - a}}{\sqrt[3]{z - t}}}\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
x + \frac{\frac{y}{\frac{\sqrt[3]{z - a} \cdot \sqrt[3]{z - a}}{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}}}{\frac{\sqrt[3]{z - a}}{\sqrt[3]{z - t}}}
double f(double x, double y, double z, double t, double a) {
        double r552210 = x;
        double r552211 = y;
        double r552212 = z;
        double r552213 = t;
        double r552214 = r552212 - r552213;
        double r552215 = r552211 * r552214;
        double r552216 = a;
        double r552217 = r552212 - r552216;
        double r552218 = r552215 / r552217;
        double r552219 = r552210 + r552218;
        return r552219;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r552220 = x;
        double r552221 = y;
        double r552222 = z;
        double r552223 = a;
        double r552224 = r552222 - r552223;
        double r552225 = cbrt(r552224);
        double r552226 = r552225 * r552225;
        double r552227 = t;
        double r552228 = r552222 - r552227;
        double r552229 = cbrt(r552228);
        double r552230 = r552229 * r552229;
        double r552231 = r552226 / r552230;
        double r552232 = r552221 / r552231;
        double r552233 = r552225 / r552229;
        double r552234 = r552232 / r552233;
        double r552235 = r552220 + r552234;
        return r552235;
}

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
Target1.4
Herbie0.6
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 10.7

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

  3. Applied associate-/l*1.4

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

  5. Applied add-cube-cbrt1.9

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

  6. Applied add-cube-cbrt1.8

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

  7. Applied times-frac1.8

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

  8. Applied associate-/r*0.6

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

  9. Final simplification0.6

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

Reproduce

herbie shell --seed 2020083 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

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

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