Average Error: 1.3 → 1.6
Time: 10.1s
Precision: 64
\[x + y \cdot \frac{z - t}{a - t}\]
↓
\[x + y \cdot \left(\frac{z}{a - t} - \frac{\frac{t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}}{\sqrt[3]{a - t}}\right)\]
x + y \cdot \frac{z - t}{a - t}
↓
x + y \cdot \left(\frac{z}{a - t} - \frac{\frac{t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}}{\sqrt[3]{a - t}}\right)
double f(double x, double y, double z, double t, double a) {
        double r270255 = x;
        double r270256 = y;
        double r270257 = z;
        double r270258 = t;
        double r270259 = r270257 - r270258;
        double r270260 = a;
        double r270261 = r270260 - r270258;
        double r270262 = r270259 / r270261;
        double r270263 = r270256 * r270262;
        double r270264 = r270255 + r270263;
        return r270264;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r270265 = x;
        double r270266 = y;
        double r270267 = z;
        double r270268 = a;
        double r270269 = t;
        double r270270 = r270268 - r270269;
        double r270271 = r270267 / r270270;
        double r270272 = cbrt(r270270);
        double r270273 = r270272 * r270272;
        double r270274 = r270269 / r270273;
        double r270275 = r270274 / r270272;
        double r270276 = r270271 - r270275;
        double r270277 = r270266 * r270276;
        double r270278 = r270265 + r270277;
        return r270278;
}

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

Original1.3
Target0.4
Herbie1.6
\[\begin{array}{l} \mathbf{if}\;y \lt -8.50808486055124107 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Initial program 1.3

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

  3. Applied div-sub1.3

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

  5. Applied add-cube-cbrt1.6

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

  6. Applied associate-/r*1.6

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

  7. Final simplification1.6

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

Reproduce

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

  :herbie-target
  (if (< y -8.508084860551241e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.894426862792089e-49) (+ x (* (* y (- z t)) (/ 1 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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