Average Error: 1.8 → 0.2
Time: 5.7s
Precision: 64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
↓
\[x - \left(\frac{y}{\left(t - z\right) + 1} - \frac{z}{\left(t - z\right) + 1}\right) \cdot a\]
x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}
↓
x - \left(\frac{y}{\left(t - z\right) + 1} - \frac{z}{\left(t - z\right) + 1}\right) \cdot a
double f(double x, double y, double z, double t, double a) {
        double r489240 = x;
        double r489241 = y;
        double r489242 = z;
        double r489243 = r489241 - r489242;
        double r489244 = t;
        double r489245 = r489244 - r489242;
        double r489246 = 1.0;
        double r489247 = r489245 + r489246;
        double r489248 = a;
        double r489249 = r489247 / r489248;
        double r489250 = r489243 / r489249;
        double r489251 = r489240 - r489250;
        return r489251;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r489252 = x;
        double r489253 = y;
        double r489254 = t;
        double r489255 = z;
        double r489256 = r489254 - r489255;
        double r489257 = 1.0;
        double r489258 = r489256 + r489257;
        double r489259 = r489253 / r489258;
        double r489260 = r489255 / r489258;
        double r489261 = r489259 - r489260;
        double r489262 = a;
        double r489263 = r489261 * r489262;
        double r489264 = r489252 - r489263;
        return r489264;
}

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

Original1.8
Target0.2
Herbie0.2
\[x - \frac{y - z}{\left(t - z\right) + 1} \cdot a\]

Derivation

  1. Initial program 1.8

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

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

Reproduce

herbie shell --seed 2019362 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (- x (* (/ (- y z) (+ (- t z) 1)) a))

  (- x (/ (- y z) (/ (+ (- t z) 1) a))))