Average Error: 2.0 → 1.8
Time: 18.5s
Precision: 64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1.0}{a}}\]
↓
\[x - \left(y - z\right) \cdot \frac{a}{t - \left(z - 1.0\right)}\]
x - \frac{y - z}{\frac{\left(t - z\right) + 1.0}{a}}
↓
x - \left(y - z\right) \cdot \frac{a}{t - \left(z - 1.0\right)}
double f(double x, double y, double z, double t, double a) {
        double r27360863 = x;
        double r27360864 = y;
        double r27360865 = z;
        double r27360866 = r27360864 - r27360865;
        double r27360867 = t;
        double r27360868 = r27360867 - r27360865;
        double r27360869 = 1.0;
        double r27360870 = r27360868 + r27360869;
        double r27360871 = a;
        double r27360872 = r27360870 / r27360871;
        double r27360873 = r27360866 / r27360872;
        double r27360874 = r27360863 - r27360873;
        return r27360874;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r27360875 = x;
        double r27360876 = y;
        double r27360877 = z;
        double r27360878 = r27360876 - r27360877;
        double r27360879 = a;
        double r27360880 = t;
        double r27360881 = 1.0;
        double r27360882 = r27360877 - r27360881;
        double r27360883 = r27360880 - r27360882;
        double r27360884 = r27360879 / r27360883;
        double r27360885 = r27360878 * r27360884;
        double r27360886 = r27360875 - r27360885;
        return r27360886;
}

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
Herbie1.8
\[x - \frac{y - z}{\left(t - z\right) + 1.0} \cdot a\]

Derivation

  1. Initial program 2.0

    \[x - \frac{y - z}{\frac{\left(t - z\right) + 1.0}{a}}\]
  2. Using strategy rm

  3. Applied associate-/r/0.2

    \[\leadsto x - \color{blue}{\frac{y - z}{\left(t - z\right) + 1.0} \cdot a}\]
  4. Using strategy rm

  5. Applied div-inv0.3

    \[\leadsto x - \color{blue}{\left(\left(y - z\right) \cdot \frac{1}{\left(t - z\right) + 1.0}\right)} \cdot a\]

  6. Applied associate-*l*1.8

    \[\leadsto x - \color{blue}{\left(y - z\right) \cdot \left(\frac{1}{\left(t - z\right) + 1.0} \cdot a\right)}\]

  7. Simplified1.8

    \[\leadsto x - \left(y - z\right) \cdot \color{blue}{\frac{a}{t - \left(z - 1.0\right)}}\]

  8. Final simplification1.8

    \[\leadsto x - \left(y - z\right) \cdot \frac{a}{t - \left(z - 1.0\right)}\]

Reproduce

herbie shell --seed 2019168 
(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))))