Average Error: 10.6 → 1.2
Time: 4.7s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[x + \frac{y}{\frac{z}{z - t} - \frac{a}{z - t}}\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
x + \frac{y}{\frac{z}{z - t} - \frac{a}{z - t}}
double f(double x, double y, double z, double t, double a) {
        double r584956 = x;
        double r584957 = y;
        double r584958 = z;
        double r584959 = t;
        double r584960 = r584958 - r584959;
        double r584961 = r584957 * r584960;
        double r584962 = a;
        double r584963 = r584958 - r584962;
        double r584964 = r584961 / r584963;
        double r584965 = r584956 + r584964;
        return r584965;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r584966 = x;
        double r584967 = y;
        double r584968 = z;
        double r584969 = t;
        double r584970 = r584968 - r584969;
        double r584971 = r584968 / r584970;
        double r584972 = a;
        double r584973 = r584972 / r584970;
        double r584974 = r584971 - r584973;
        double r584975 = r584967 / r584974;
        double r584976 = r584966 + r584975;
        return r584976;
}

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

Original10.6
Target1.2
Herbie1.2
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 10.6

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

  3. Applied associate-/l*1.2

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

  5. Applied div-sub1.2

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

  6. Final simplification1.2

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

Reproduce

herbie shell --seed 2020018 
(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))))