Average Error: 10.9 → 1.2
Time: 4.4s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[x + \frac{1}{\frac{\frac{a - t}{z - t}}{y}}\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
x + \frac{1}{\frac{\frac{a - t}{z - t}}{y}}
double f(double x, double y, double z, double t, double a) {
        double r615297 = x;
        double r615298 = y;
        double r615299 = z;
        double r615300 = t;
        double r615301 = r615299 - r615300;
        double r615302 = r615298 * r615301;
        double r615303 = a;
        double r615304 = r615303 - r615300;
        double r615305 = r615302 / r615304;
        double r615306 = r615297 + r615305;
        return r615306;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r615307 = x;
        double r615308 = 1.0;
        double r615309 = a;
        double r615310 = t;
        double r615311 = r615309 - r615310;
        double r615312 = z;
        double r615313 = r615312 - r615310;
        double r615314 = r615311 / r615313;
        double r615315 = y;
        double r615316 = r615314 / r615315;
        double r615317 = r615308 / r615316;
        double r615318 = r615307 + r615317;
        return r615318;
}

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
Target1.1
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*1.1

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

  5. Applied clear-num1.2

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

  6. Final simplification1.2

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

Reproduce

herbie shell --seed 2020001 
(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))))