Average Error: 1.9 → 0.3
Time: 15.0s
Precision: 64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
↓
\[x - \frac{1}{\frac{\left(1 + t\right) - z}{y - z}} \cdot a\]
x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}
↓
x - \frac{1}{\frac{\left(1 + t\right) - z}{y - z}} \cdot a
double f(double x, double y, double z, double t, double a) {
        double r442946 = x;
        double r442947 = y;
        double r442948 = z;
        double r442949 = r442947 - r442948;
        double r442950 = t;
        double r442951 = r442950 - r442948;
        double r442952 = 1.0;
        double r442953 = r442951 + r442952;
        double r442954 = a;
        double r442955 = r442953 / r442954;
        double r442956 = r442949 / r442955;
        double r442957 = r442946 - r442956;
        return r442957;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r442958 = x;
        double r442959 = 1.0;
        double r442960 = 1.0;
        double r442961 = t;
        double r442962 = r442960 + r442961;
        double r442963 = z;
        double r442964 = r442962 - r442963;
        double r442965 = y;
        double r442966 = r442965 - r442963;
        double r442967 = r442964 / r442966;
        double r442968 = r442959 / r442967;
        double r442969 = a;
        double r442970 = r442968 * r442969;
        double r442971 = r442958 - r442970;
        return r442971;
}

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

Original1.9
Target0.2
Herbie0.3
\[x - \frac{y - z}{\left(t - z\right) + 1} \cdot a\]

Derivation

  1. Initial program 1.9

    \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
  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. Simplified0.2

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

  6. Applied clear-num0.3

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2019212 
(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))))