Average Error: 2.1 → 0.2
Time: 6.8s
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 r551788 = x;
        double r551789 = y;
        double r551790 = z;
        double r551791 = r551789 - r551790;
        double r551792 = t;
        double r551793 = r551792 - r551790;
        double r551794 = 1.0;
        double r551795 = r551793 + r551794;
        double r551796 = a;
        double r551797 = r551795 / r551796;
        double r551798 = r551791 / r551797;
        double r551799 = r551788 - r551798;
        return r551799;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r551800 = x;
        double r551801 = y;
        double r551802 = t;
        double r551803 = z;
        double r551804 = r551802 - r551803;
        double r551805 = 1.0;
        double r551806 = r551804 + r551805;
        double r551807 = r551801 / r551806;
        double r551808 = r551803 / r551806;
        double r551809 = r551807 - r551808;
        double r551810 = a;
        double r551811 = r551809 * r551810;
        double r551812 = r551800 - r551811;
        return r551812;
}

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

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/0.2

    \[\leadsto x - \color{blue}{\frac{y - z}{\left(t - z\right) + 1} \cdot a}\]
  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 2019322 
(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))))