Average Error: 2.0 → 0.2
Time: 4.6s
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 r614129 = x;
        double r614130 = y;
        double r614131 = z;
        double r614132 = r614130 - r614131;
        double r614133 = t;
        double r614134 = r614133 - r614131;
        double r614135 = 1.0;
        double r614136 = r614134 + r614135;
        double r614137 = a;
        double r614138 = r614136 / r614137;
        double r614139 = r614132 / r614138;
        double r614140 = r614129 - r614139;
        return r614140;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r614141 = x;
        double r614142 = y;
        double r614143 = t;
        double r614144 = z;
        double r614145 = r614143 - r614144;
        double r614146 = 1.0;
        double r614147 = r614145 + r614146;
        double r614148 = r614142 / r614147;
        double r614149 = r614144 / r614147;
        double r614150 = r614148 - r614149;
        double r614151 = a;
        double r614152 = r614150 * r614151;
        double r614153 = r614141 - r614152;
        return r614153;
}

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 2020100 
(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))))