Average Error: 2.0 → 0.3
Time: 22.5s
Precision: 64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1.0}{a}}\]
↓
\[x - \left(\left(y - z\right) \cdot \frac{1}{1.0 + \left(t - z\right)}\right) \cdot a\]
x - \frac{y - z}{\frac{\left(t - z\right) + 1.0}{a}}
↓
x - \left(\left(y - z\right) \cdot \frac{1}{1.0 + \left(t - z\right)}\right) \cdot a
double f(double x, double y, double z, double t, double a) {
        double r41118744 = x;
        double r41118745 = y;
        double r41118746 = z;
        double r41118747 = r41118745 - r41118746;
        double r41118748 = t;
        double r41118749 = r41118748 - r41118746;
        double r41118750 = 1.0;
        double r41118751 = r41118749 + r41118750;
        double r41118752 = a;
        double r41118753 = r41118751 / r41118752;
        double r41118754 = r41118747 / r41118753;
        double r41118755 = r41118744 - r41118754;
        return r41118755;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r41118756 = x;
        double r41118757 = y;
        double r41118758 = z;
        double r41118759 = r41118757 - r41118758;
        double r41118760 = 1.0;
        double r41118761 = 1.0;
        double r41118762 = t;
        double r41118763 = r41118762 - r41118758;
        double r41118764 = r41118761 + r41118763;
        double r41118765 = r41118760 / r41118764;
        double r41118766 = r41118759 * r41118765;
        double r41118767 = a;
        double r41118768 = r41118766 * r41118767;
        double r41118769 = r41118756 - r41118768;
        return r41118769;
}

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
Herbie0.3
\[x - \frac{y - z}{\left(t - z\right) + 1.0} \cdot a\]

Derivation

  1. Initial program 2.0

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

  3. Applied *-un-lft-identity2.0

    \[\leadsto x - \frac{y - z}{\frac{\left(t - z\right) + 1.0}{\color{blue}{1 \cdot a}}}\]

  4. Applied associate-/r*2.0

    \[\leadsto x - \frac{y - z}{\color{blue}{\frac{\frac{\left(t - z\right) + 1.0}{1}}{a}}}\]

  5. Applied associate-/r/0.2

    \[\leadsto x - \color{blue}{\frac{y - z}{\frac{\left(t - z\right) + 1.0}{1}} \cdot a}\]

  6. Simplified0.2

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

  8. Applied div-inv0.3

    \[\leadsto x - \color{blue}{\left(\left(y - z\right) \cdot \frac{1}{1.0 + \left(t - z\right)}\right)} \cdot a\]

  9. Final simplification0.3

    \[\leadsto x - \left(\left(y - z\right) \cdot \frac{1}{1.0 + \left(t - z\right)}\right) \cdot a\]

Reproduce

herbie shell --seed 2019158 
(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))))