Average Error: 1.4 → 1.4
Time: 5.3s
Precision: 64
\[x + y \cdot \frac{z - t}{a - t}\]
↓
\[x + y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)\]
x + y \cdot \frac{z - t}{a - t}
↓
x + y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)
double f(double x, double y, double z, double t, double a) {
        double r603970 = x;
        double r603971 = y;
        double r603972 = z;
        double r603973 = t;
        double r603974 = r603972 - r603973;
        double r603975 = a;
        double r603976 = r603975 - r603973;
        double r603977 = r603974 / r603976;
        double r603978 = r603971 * r603977;
        double r603979 = r603970 + r603978;
        return r603979;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r603980 = x;
        double r603981 = y;
        double r603982 = z;
        double r603983 = a;
        double r603984 = t;
        double r603985 = r603983 - r603984;
        double r603986 = r603982 / r603985;
        double r603987 = r603984 / r603985;
        double r603988 = r603986 - r603987;
        double r603989 = r603981 * r603988;
        double r603990 = r603980 + r603989;
        return r603990;
}

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

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

Derivation

  1. Initial program 1.4

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

  3. Applied div-sub1.4

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

  4. Final simplification1.4

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

Reproduce

herbie shell --seed 2020039 
(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)))))