Average Error: 2.0 → 0.2
Time: 15.5s
Precision: 64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
↓
\[x - \left(\frac{y}{\left(t - z\right) + 1} - \frac{z}{\left(t - z\right) + 1}\right) \cdot a\]
x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}
↓
x - \left(\frac{y}{\left(t - z\right) + 1} - \frac{z}{\left(t - z\right) + 1}\right) \cdot a
double f(double x, double y, double z, double t, double a) {
        double r510618 = x;
        double r510619 = y;
        double r510620 = z;
        double r510621 = r510619 - r510620;
        double r510622 = t;
        double r510623 = r510622 - r510620;
        double r510624 = 1.0;
        double r510625 = r510623 + r510624;
        double r510626 = a;
        double r510627 = r510625 / r510626;
        double r510628 = r510621 / r510627;
        double r510629 = r510618 - r510628;
        return r510629;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r510630 = x;
        double r510631 = y;
        double r510632 = t;
        double r510633 = z;
        double r510634 = r510632 - r510633;
        double r510635 = 1.0;
        double r510636 = r510634 + r510635;
        double r510637 = r510631 / r510636;
        double r510638 = r510633 / r510636;
        double r510639 = r510637 - r510638;
        double r510640 = a;
        double r510641 = r510639 * r510640;
        double r510642 = r510630 - r510641;
        return r510642;
}

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. Using strategy rm

  5. Applied div-sub0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019306 
(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))))