Average Error: 2.0 → 0.3
Time: 10.9s
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 r695963 = x;
        double r695964 = y;
        double r695965 = z;
        double r695966 = r695964 - r695965;
        double r695967 = t;
        double r695968 = r695967 - r695965;
        double r695969 = 1.0;
        double r695970 = r695968 + r695969;
        double r695971 = a;
        double r695972 = r695970 / r695971;
        double r695973 = r695966 / r695972;
        double r695974 = r695963 - r695973;
        return r695974;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r695975 = x;
        double r695976 = y;
        double r695977 = z;
        double r695978 = r695976 - r695977;
        double r695979 = t;
        double r695980 = r695979 - r695977;
        double r695981 = 1.0;
        double r695982 = r695980 + r695981;
        double r695983 = r695978 / r695982;
        double r695984 = 1.0;
        double r695985 = a;
        double r695986 = r695984 / r695985;
        double r695987 = r695983 / r695986;
        double r695988 = r695975 - r695987;
        return r695988;
}

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
Target0.3
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-inv2.1

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

  4. Applied associate-/r*0.3

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

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 2020065 
(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))))