Average Error: 1.8 → 0.2
Time: 4.6s
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 r610882 = x;
        double r610883 = y;
        double r610884 = z;
        double r610885 = r610883 - r610884;
        double r610886 = t;
        double r610887 = r610886 - r610884;
        double r610888 = 1.0;
        double r610889 = r610887 + r610888;
        double r610890 = a;
        double r610891 = r610889 / r610890;
        double r610892 = r610885 / r610891;
        double r610893 = r610882 - r610892;
        return r610893;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r610894 = x;
        double r610895 = y;
        double r610896 = z;
        double r610897 = r610895 - r610896;
        double r610898 = t;
        double r610899 = r610898 - r610896;
        double r610900 = 1.0;
        double r610901 = r610899 + r610900;
        double r610902 = r610897 / r610901;
        double r610903 = a;
        double r610904 = r610902 * r610903;
        double r610905 = r610894 - r610904;
        return r610905;
}

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

Original1.8
Target0.2
Herbie0.2
\[x - \frac{y - z}{\left(t - z\right) + 1} \cdot a\]

Derivation

  1. Initial program 1.8

    \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
  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 2020047 +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))))