Average Error: 10.7 → 1.2
Time: 10.1s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[x + \frac{y}{\frac{z - a}{z - t}}\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
x + \frac{y}{\frac{z - a}{z - t}}
double f(double x, double y, double z, double t, double a) {
        double r600445 = x;
        double r600446 = y;
        double r600447 = z;
        double r600448 = t;
        double r600449 = r600447 - r600448;
        double r600450 = r600446 * r600449;
        double r600451 = a;
        double r600452 = r600447 - r600451;
        double r600453 = r600450 / r600452;
        double r600454 = r600445 + r600453;
        return r600454;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r600455 = x;
        double r600456 = y;
        double r600457 = z;
        double r600458 = a;
        double r600459 = r600457 - r600458;
        double r600460 = t;
        double r600461 = r600457 - r600460;
        double r600462 = r600459 / r600461;
        double r600463 = r600456 / r600462;
        double r600464 = r600455 + r600463;
        return r600464;
}

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

Original10.7
Target1.2
Herbie1.2
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 10.7

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

  3. Applied associate-/l*1.2

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

  4. Final simplification1.2

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

Reproduce

herbie shell --seed 2019350 
(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))))