Average Error: 2.0 → 0.2
Time: 4.1s
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 r593978 = x;
        double r593979 = y;
        double r593980 = z;
        double r593981 = r593979 - r593980;
        double r593982 = t;
        double r593983 = r593982 - r593980;
        double r593984 = 1.0;
        double r593985 = r593983 + r593984;
        double r593986 = a;
        double r593987 = r593985 / r593986;
        double r593988 = r593981 / r593987;
        double r593989 = r593978 - r593988;
        return r593989;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r593990 = x;
        double r593991 = y;
        double r593992 = z;
        double r593993 = r593991 - r593992;
        double r593994 = t;
        double r593995 = r593994 - r593992;
        double r593996 = 1.0;
        double r593997 = r593995 + r593996;
        double r593998 = r593993 / r593997;
        double r593999 = a;
        double r594000 = r593998 * r593999;
        double r594001 = r593990 - r594000;
        return r594001;
}

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

Derivation

  1. Initial program 2.0

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

  3. Applied 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 2020033 +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))))