Average Error: 2.1 → 0.3
Time: 4.3s
Precision: 64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
↓
\[x - \left(\left(y - z\right) \cdot \frac{1}{\left(t - z\right) + 1}\right) \cdot a\]
x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}
↓
x - \left(\left(y - z\right) \cdot \frac{1}{\left(t - z\right) + 1}\right) \cdot a
double f(double x, double y, double z, double t, double a) {
        double r714267 = x;
        double r714268 = y;
        double r714269 = z;
        double r714270 = r714268 - r714269;
        double r714271 = t;
        double r714272 = r714271 - r714269;
        double r714273 = 1.0;
        double r714274 = r714272 + r714273;
        double r714275 = a;
        double r714276 = r714274 / r714275;
        double r714277 = r714270 / r714276;
        double r714278 = r714267 - r714277;
        return r714278;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r714279 = x;
        double r714280 = y;
        double r714281 = z;
        double r714282 = r714280 - r714281;
        double r714283 = 1.0;
        double r714284 = t;
        double r714285 = r714284 - r714281;
        double r714286 = 1.0;
        double r714287 = r714285 + r714286;
        double r714288 = r714283 / r714287;
        double r714289 = r714282 * r714288;
        double r714290 = a;
        double r714291 = r714289 * r714290;
        double r714292 = r714279 - r714291;
        return r714292;
}

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

Original2.1
Target0.3
Herbie0.3
\[x - \frac{y - z}{\left(t - z\right) + 1} \cdot a\]

Derivation

  1. Initial program 2.1

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

  3. Applied associate-/r/0.3

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

  5. Applied div-inv0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2019353 
(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))))