Average Error: 2.0 → 0.2
Time: 5.0s
Precision: 64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
↓
\[x - \frac{y - z}{\left(t - z\right) + 1} \cdot a\]
x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}
↓
x - \frac{y - z}{\left(t - z\right) + 1} \cdot a
double f(double x, double y, double z, double t, double a) {
        double r363896 = x;
        double r363897 = y;
        double r363898 = z;
        double r363899 = r363897 - r363898;
        double r363900 = t;
        double r363901 = r363900 - r363898;
        double r363902 = 1.0;
        double r363903 = r363901 + r363902;
        double r363904 = a;
        double r363905 = r363903 / r363904;
        double r363906 = r363899 / r363905;
        double r363907 = r363896 - r363906;
        return r363907;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r363908 = x;
        double r363909 = y;
        double r363910 = z;
        double r363911 = r363909 - r363910;
        double r363912 = t;
        double r363913 = r363912 - r363910;
        double r363914 = 1.0;
        double r363915 = r363913 + r363914;
        double r363916 = r363911 / r363915;
        double r363917 = a;
        double r363918 = r363916 * r363917;
        double r363919 = r363908 - r363918;
        return r363919;
}

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. Final simplification0.2

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

Reproduce

herbie shell --seed 2020034 +o rules:numerics
(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))))