Average Error: 2.0 → 0.2
Time: 51.5s
Precision: 64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
↓
\[x - \left(\frac{y}{1 + \left(t - z\right)} - \frac{z}{1 + \left(t - z\right)}\right) \cdot a\]
x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}
↓
x - \left(\frac{y}{1 + \left(t - z\right)} - \frac{z}{1 + \left(t - z\right)}\right) \cdot a
double f(double x, double y, double z, double t, double a) {
        double r31390353 = x;
        double r31390354 = y;
        double r31390355 = z;
        double r31390356 = r31390354 - r31390355;
        double r31390357 = t;
        double r31390358 = r31390357 - r31390355;
        double r31390359 = 1.0;
        double r31390360 = r31390358 + r31390359;
        double r31390361 = a;
        double r31390362 = r31390360 / r31390361;
        double r31390363 = r31390356 / r31390362;
        double r31390364 = r31390353 - r31390363;
        return r31390364;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r31390365 = x;
        double r31390366 = y;
        double r31390367 = 1.0;
        double r31390368 = t;
        double r31390369 = z;
        double r31390370 = r31390368 - r31390369;
        double r31390371 = r31390367 + r31390370;
        double r31390372 = r31390366 / r31390371;
        double r31390373 = r31390369 / r31390371;
        double r31390374 = r31390372 - r31390373;
        double r31390375 = a;
        double r31390376 = r31390374 * r31390375;
        double r31390377 = r31390365 - r31390376;
        return r31390377;
}

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

Original2.0
Target0.2
Herbie0.2
\[x - \frac{y - z}{\left(t - z\right) + 1} \cdot a\]

Derivation

  1. Initial program 2.0

    \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
  2. Using strategy rm

  3. Applied associate-/r/0.2

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

  5. Applied div-sub0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019200 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"

  :herbie-target
  (- x (* (/ (- y z) (+ (- t z) 1.0)) a))

  (- x (/ (- y z) (/ (+ (- t z) 1.0) a))))