Average Error: 2.1 → 0.2
Time: 17.5s
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 r400197 = x;
        double r400198 = y;
        double r400199 = z;
        double r400200 = r400198 - r400199;
        double r400201 = t;
        double r400202 = r400201 - r400199;
        double r400203 = 1.0;
        double r400204 = r400202 + r400203;
        double r400205 = a;
        double r400206 = r400204 / r400205;
        double r400207 = r400200 / r400206;
        double r400208 = r400197 - r400207;
        return r400208;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r400209 = x;
        double r400210 = y;
        double r400211 = t;
        double r400212 = z;
        double r400213 = r400211 - r400212;
        double r400214 = 1.0;
        double r400215 = r400213 + r400214;
        double r400216 = r400210 / r400215;
        double r400217 = r400212 / r400215;
        double r400218 = r400216 - r400217;
        double r400219 = a;
        double r400220 = r400218 * r400219;
        double r400221 = r400209 - r400220;
        return r400221;
}

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

Original2.1
Target0.2
Herbie0.2
\[x - \frac{y - z}{\left(t - z\right) + 1} \cdot a\]

Derivation

  1. Initial program 2.1

    \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
  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 2019322 
(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))))