Average Error: 10.4 → 1.3
Time: 5.3s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[x + \frac{1}{\frac{\frac{z - a}{z - t}}{y}}\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
x + \frac{1}{\frac{\frac{z - a}{z - t}}{y}}
double f(double x, double y, double z, double t, double a) {
        double r763489 = x;
        double r763490 = y;
        double r763491 = z;
        double r763492 = t;
        double r763493 = r763491 - r763492;
        double r763494 = r763490 * r763493;
        double r763495 = a;
        double r763496 = r763491 - r763495;
        double r763497 = r763494 / r763496;
        double r763498 = r763489 + r763497;
        return r763498;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r763499 = x;
        double r763500 = 1.0;
        double r763501 = z;
        double r763502 = a;
        double r763503 = r763501 - r763502;
        double r763504 = t;
        double r763505 = r763501 - r763504;
        double r763506 = r763503 / r763505;
        double r763507 = y;
        double r763508 = r763506 / r763507;
        double r763509 = r763500 / r763508;
        double r763510 = r763499 + r763509;
        return r763510;
}

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

Original10.4
Target1.2
Herbie1.3
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 10.4

    \[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
  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 clear-num1.3

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

  6. Final simplification1.3

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

Reproduce

herbie shell --seed 2019362 
(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))))