Average Error: 2.0 → 1.8
Time: 19.4s
Precision: 64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1.0}{a}}\]
↓
\[x - \left(y - z\right) \cdot \frac{a}{1.0 + \left(t - z\right)}\]
x - \frac{y - z}{\frac{\left(t - z\right) + 1.0}{a}}
↓
x - \left(y - z\right) \cdot \frac{a}{1.0 + \left(t - z\right)}
double f(double x, double y, double z, double t, double a) {
        double r27084505 = x;
        double r27084506 = y;
        double r27084507 = z;
        double r27084508 = r27084506 - r27084507;
        double r27084509 = t;
        double r27084510 = r27084509 - r27084507;
        double r27084511 = 1.0;
        double r27084512 = r27084510 + r27084511;
        double r27084513 = a;
        double r27084514 = r27084512 / r27084513;
        double r27084515 = r27084508 / r27084514;
        double r27084516 = r27084505 - r27084515;
        return r27084516;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r27084517 = x;
        double r27084518 = y;
        double r27084519 = z;
        double r27084520 = r27084518 - r27084519;
        double r27084521 = a;
        double r27084522 = 1.0;
        double r27084523 = t;
        double r27084524 = r27084523 - r27084519;
        double r27084525 = r27084522 + r27084524;
        double r27084526 = r27084521 / r27084525;
        double r27084527 = r27084520 * r27084526;
        double r27084528 = r27084517 - r27084527;
        return r27084528;
}

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
Herbie1.8
\[x - \frac{y - z}{\left(t - z\right) + 1.0} \cdot a\]

Derivation

  1. Initial program 2.0

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

  3. Applied div-inv2.0

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

  4. Simplified1.8

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

  5. Final simplification1.8

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

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(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))))