Average Error: 2.0 → 0.2
Time: 4.1s
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 r715244 = x;
        double r715245 = y;
        double r715246 = z;
        double r715247 = r715245 - r715246;
        double r715248 = t;
        double r715249 = r715248 - r715246;
        double r715250 = 1.0;
        double r715251 = r715249 + r715250;
        double r715252 = a;
        double r715253 = r715251 / r715252;
        double r715254 = r715247 / r715253;
        double r715255 = r715244 - r715254;
        return r715255;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r715256 = x;
        double r715257 = y;
        double r715258 = z;
        double r715259 = r715257 - r715258;
        double r715260 = 1.0;
        double r715261 = t;
        double r715262 = r715261 - r715258;
        double r715263 = 1.0;
        double r715264 = r715262 + r715263;
        double r715265 = r715260 / r715264;
        double r715266 = r715259 * r715265;
        double r715267 = a;
        double r715268 = r715266 * r715267;
        double r715269 = r715256 - r715268;
        return r715269;
}

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-inv0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2020034 
(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))))