Average Error: 10.8 → 1.6
Time: 9.7s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[x + y \cdot \frac{z - t}{a - t}\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
x + y \cdot \frac{z - t}{a - t}
double f(double x, double y, double z, double t, double a) {
        double r563971 = x;
        double r563972 = y;
        double r563973 = z;
        double r563974 = t;
        double r563975 = r563973 - r563974;
        double r563976 = r563972 * r563975;
        double r563977 = a;
        double r563978 = r563977 - r563974;
        double r563979 = r563976 / r563978;
        double r563980 = r563971 + r563979;
        return r563980;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r563981 = x;
        double r563982 = y;
        double r563983 = z;
        double r563984 = t;
        double r563985 = r563983 - r563984;
        double r563986 = a;
        double r563987 = r563986 - r563984;
        double r563988 = r563985 / r563987;
        double r563989 = r563982 * r563988;
        double r563990 = r563981 + r563989;
        return r563990;
}

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

Original10.8
Target1.4
Herbie1.6
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Initial program 10.8

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

  3. Applied *-un-lft-identity10.8

    \[\leadsto x + \frac{y \cdot \left(z - t\right)}{\color{blue}{1 \cdot \left(a - t\right)}}\]

  4. Applied times-frac1.6

    \[\leadsto x + \color{blue}{\frac{y}{1} \cdot \frac{z - t}{a - t}}\]

  5. Simplified1.6

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

  6. Final simplification1.6

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

Reproduce

herbie shell --seed 2020045 +o rules:numerics
(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))))