Average Error: 2.0 → 0.2
Time: 17.9s
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 r30663569 = x;
        double r30663570 = y;
        double r30663571 = z;
        double r30663572 = r30663570 - r30663571;
        double r30663573 = t;
        double r30663574 = r30663573 - r30663571;
        double r30663575 = 1.0;
        double r30663576 = r30663574 + r30663575;
        double r30663577 = a;
        double r30663578 = r30663576 / r30663577;
        double r30663579 = r30663572 / r30663578;
        double r30663580 = r30663569 - r30663579;
        return r30663580;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r30663581 = x;
        double r30663582 = a;
        double r30663583 = y;
        double r30663584 = z;
        double r30663585 = r30663583 - r30663584;
        double r30663586 = t;
        double r30663587 = r30663586 - r30663584;
        double r30663588 = 1.0;
        double r30663589 = r30663587 + r30663588;
        double r30663590 = r30663585 / r30663589;
        double r30663591 = r30663582 * r30663590;
        double r30663592 = r30663581 - r30663591;
        return r30663592;
}

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))))