Average Error: 2.0 → 0.2
Time: 19.2s
Precision: 64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1.0}{a}}\]
↓
\[x - a \cdot \frac{y - z}{\left(t - z\right) + 1.0}\]
x - \frac{y - z}{\frac{\left(t - z\right) + 1.0}{a}}
↓
x - a \cdot \frac{y - z}{\left(t - z\right) + 1.0}
double f(double x, double y, double z, double t, double a) {
        double r30252763 = x;
        double r30252764 = y;
        double r30252765 = z;
        double r30252766 = r30252764 - r30252765;
        double r30252767 = t;
        double r30252768 = r30252767 - r30252765;
        double r30252769 = 1.0;
        double r30252770 = r30252768 + r30252769;
        double r30252771 = a;
        double r30252772 = r30252770 / r30252771;
        double r30252773 = r30252766 / r30252772;
        double r30252774 = r30252763 - r30252773;
        return r30252774;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r30252775 = x;
        double r30252776 = a;
        double r30252777 = y;
        double r30252778 = z;
        double r30252779 = r30252777 - r30252778;
        double r30252780 = t;
        double r30252781 = r30252780 - r30252778;
        double r30252782 = 1.0;
        double r30252783 = r30252781 + r30252782;
        double r30252784 = r30252779 / r30252783;
        double r30252785 = r30252776 * r30252784;
        double r30252786 = r30252775 - r30252785;
        return r30252786;
}

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
\[x - \frac{y - z}{\left(t - z\right) + 1.0} \cdot a\]

Derivation

  1. Initial program 2.0

    \[x - \frac{y - z}{\frac{\left(t - z\right) + 1.0}{a}}\]
  2. Using strategy rm

  3. Applied associate-/r/0.2

    \[\leadsto x - \color{blue}{\frac{y - z}{\left(t - z\right) + 1.0} \cdot a}\]

  4. Final simplification0.2

    \[\leadsto x - a \cdot \frac{y - z}{\left(t - z\right) + 1.0}\]

Reproduce

herbie shell --seed 2019163 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"

  :herbie-target
  (- x (* (/ (- y z) (+ (- t z) 1.0)) a))

  (- x (/ (- y z) (/ (+ (- t z) 1.0) a))))