Average Error: 2.0 → 0.2
Time: 18.5s
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 r29874631 = x;
        double r29874632 = y;
        double r29874633 = z;
        double r29874634 = r29874632 - r29874633;
        double r29874635 = t;
        double r29874636 = r29874635 - r29874633;
        double r29874637 = 1.0;
        double r29874638 = r29874636 + r29874637;
        double r29874639 = a;
        double r29874640 = r29874638 / r29874639;
        double r29874641 = r29874634 / r29874640;
        double r29874642 = r29874631 - r29874641;
        return r29874642;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r29874643 = x;
        double r29874644 = a;
        double r29874645 = y;
        double r29874646 = z;
        double r29874647 = r29874645 - r29874646;
        double r29874648 = t;
        double r29874649 = r29874648 - r29874646;
        double r29874650 = 1.0;
        double r29874651 = r29874649 + r29874650;
        double r29874652 = r29874647 / r29874651;
        double r29874653 = r29874644 * r29874652;
        double r29874654 = r29874643 - r29874653;
        return r29874654;
}

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))))