Average Error: 2.1 → 0.4
Time: 4.6s
Precision: 64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
↓
\[x - \frac{\frac{y - z}{\left(t - z\right) + 1}}{\frac{1}{a}}\]
x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}
↓
x - \frac{\frac{y - z}{\left(t - z\right) + 1}}{\frac{1}{a}}
double f(double x, double y, double z, double t, double a) {
        double r623975 = x;
        double r623976 = y;
        double r623977 = z;
        double r623978 = r623976 - r623977;
        double r623979 = t;
        double r623980 = r623979 - r623977;
        double r623981 = 1.0;
        double r623982 = r623980 + r623981;
        double r623983 = a;
        double r623984 = r623982 / r623983;
        double r623985 = r623978 / r623984;
        double r623986 = r623975 - r623985;
        return r623986;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r623987 = x;
        double r623988 = y;
        double r623989 = z;
        double r623990 = r623988 - r623989;
        double r623991 = t;
        double r623992 = r623991 - r623989;
        double r623993 = 1.0;
        double r623994 = r623992 + r623993;
        double r623995 = r623990 / r623994;
        double r623996 = 1.0;
        double r623997 = a;
        double r623998 = r623996 / r623997;
        double r623999 = r623995 / r623998;
        double r624000 = r623987 - r623999;
        return r624000;
}

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
Target0.3
Herbie0.4
\[x - \frac{y - z}{\left(t - z\right) + 1} \cdot a\]

Derivation

  1. Initial program 2.1

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

  3. Applied div-inv2.1

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

  4. Applied associate-/r*0.4

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

  5. Final simplification0.4

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

Reproduce

herbie shell --seed 2020020 +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))))