Average Error: 2.1 → 0.2
Time: 4.8s
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 r662713 = x;
        double r662714 = y;
        double r662715 = z;
        double r662716 = r662714 - r662715;
        double r662717 = t;
        double r662718 = r662717 - r662715;
        double r662719 = 1.0;
        double r662720 = r662718 + r662719;
        double r662721 = a;
        double r662722 = r662720 / r662721;
        double r662723 = r662716 / r662722;
        double r662724 = r662713 - r662723;
        return r662724;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r662725 = x;
        double r662726 = y;
        double r662727 = z;
        double r662728 = r662726 - r662727;
        double r662729 = t;
        double r662730 = r662729 - r662727;
        double r662731 = 1.0;
        double r662732 = r662730 + r662731;
        double r662733 = r662728 / r662732;
        double r662734 = a;
        double r662735 = r662733 * r662734;
        double r662736 = r662725 - r662735;
        return r662736;
}

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

Original2.1
Target0.2
Herbie0.2
\[x - \frac{y - z}{\left(t - z\right) + 1} \cdot a\]

Derivation

  1. Initial program 2.1

    \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
  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 2020025 +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))))