Average Error: 10.9 → 1.2
Time: 18.4s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[x + \frac{y}{\frac{a - t}{z - t}}\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
x + \frac{y}{\frac{a - t}{z - t}}
double f(double x, double y, double z, double t, double a) {
        double r503012 = x;
        double r503013 = y;
        double r503014 = z;
        double r503015 = t;
        double r503016 = r503014 - r503015;
        double r503017 = r503013 * r503016;
        double r503018 = a;
        double r503019 = r503018 - r503015;
        double r503020 = r503017 / r503019;
        double r503021 = r503012 + r503020;
        return r503021;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r503022 = x;
        double r503023 = y;
        double r503024 = a;
        double r503025 = t;
        double r503026 = r503024 - r503025;
        double r503027 = z;
        double r503028 = r503027 - r503025;
        double r503029 = r503026 / r503028;
        double r503030 = r503023 / r503029;
        double r503031 = r503022 + r503030;
        return r503031;
}

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

Original10.9
Target1.2
Herbie1.2
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Initial program 10.9

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

  3. Applied associate-/l*1.2

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

  4. Final simplification1.2

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

Reproduce

herbie shell --seed 2019303 
(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))))