Average Error: 2.0 → 0.3
Time: 4.3s
Precision: 64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
↓
\[x - \left(\frac{\frac{y}{\left(t - z\right) + 1}}{\frac{1}{a}} - \frac{\frac{z}{\left(t - z\right) + 1}}{\frac{1}{a}}\right)\]
x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}
↓
x - \left(\frac{\frac{y}{\left(t - z\right) + 1}}{\frac{1}{a}} - \frac{\frac{z}{\left(t - z\right) + 1}}{\frac{1}{a}}\right)
double f(double x, double y, double z, double t, double a) {
        double r587882 = x;
        double r587883 = y;
        double r587884 = z;
        double r587885 = r587883 - r587884;
        double r587886 = t;
        double r587887 = r587886 - r587884;
        double r587888 = 1.0;
        double r587889 = r587887 + r587888;
        double r587890 = a;
        double r587891 = r587889 / r587890;
        double r587892 = r587885 / r587891;
        double r587893 = r587882 - r587892;
        return r587893;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r587894 = x;
        double r587895 = y;
        double r587896 = t;
        double r587897 = z;
        double r587898 = r587896 - r587897;
        double r587899 = 1.0;
        double r587900 = r587898 + r587899;
        double r587901 = r587895 / r587900;
        double r587902 = 1.0;
        double r587903 = a;
        double r587904 = r587902 / r587903;
        double r587905 = r587901 / r587904;
        double r587906 = r587897 / r587900;
        double r587907 = r587906 / r587904;
        double r587908 = r587905 - r587907;
        double r587909 = r587894 - r587908;
        return r587909;
}

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
Herbie0.3
\[x - \frac{y - z}{\left(t - z\right) + 1} \cdot a\]

Derivation

  1. Initial program 2.0

    \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
  2. Using strategy rm

  3. Applied div-inv2.0

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

  4. Applied associate-/r*0.3

    \[\leadsto x - \color{blue}{\frac{\frac{y - z}{\left(t - z\right) + 1}}{\frac{1}{a}}}\]
  5. Using strategy rm

  6. Applied div-sub0.3

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

  7. Applied div-sub0.3

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

  8. Final simplification0.3

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

Reproduce

herbie shell --seed 2020056 +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))))