Average Error: 1.8 → 0.2
Time: 3.4s
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 r590678 = x;
        double r590679 = y;
        double r590680 = z;
        double r590681 = r590679 - r590680;
        double r590682 = t;
        double r590683 = r590682 - r590680;
        double r590684 = 1.0;
        double r590685 = r590683 + r590684;
        double r590686 = a;
        double r590687 = r590685 / r590686;
        double r590688 = r590681 / r590687;
        double r590689 = r590678 - r590688;
        return r590689;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r590690 = x;
        double r590691 = y;
        double r590692 = z;
        double r590693 = r590691 - r590692;
        double r590694 = t;
        double r590695 = r590694 - r590692;
        double r590696 = 1.0;
        double r590697 = r590695 + r590696;
        double r590698 = r590693 / r590697;
        double r590699 = a;
        double r590700 = r590698 * r590699;
        double r590701 = r590690 - r590700;
        return r590701;
}

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

Original1.8
Target0.2
Herbie0.2
\[x - \frac{y - z}{\left(t - z\right) + 1} \cdot a\]

Derivation

  1. Initial program 1.8

    \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
  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 2020064 +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))))