Average Error: 2.0 → 0.2
Time: 3.7s
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 r512978 = x;
        double r512979 = y;
        double r512980 = z;
        double r512981 = r512979 - r512980;
        double r512982 = t;
        double r512983 = r512982 - r512980;
        double r512984 = 1.0;
        double r512985 = r512983 + r512984;
        double r512986 = a;
        double r512987 = r512985 / r512986;
        double r512988 = r512981 / r512987;
        double r512989 = r512978 - r512988;
        return r512989;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r512990 = x;
        double r512991 = y;
        double r512992 = z;
        double r512993 = r512991 - r512992;
        double r512994 = t;
        double r512995 = r512994 - r512992;
        double r512996 = 1.0;
        double r512997 = r512995 + r512996;
        double r512998 = r512993 / r512997;
        double r512999 = a;
        double r513000 = r512998 * r512999;
        double r513001 = r512990 - r513000;
        return r513001;
}

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 2020039 +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))))