Average Error: 1.8 → 0.2
Time: 10.0s
Precision: 64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
↓
\[x - \frac{y - z}{\left(t - z\right) + 1} \cdot a\]
x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}
↓
x - \frac{y - z}{\left(t - z\right) + 1} \cdot a
double f(double x, double y, double z, double t, double a) {
        double r705865 = x;
        double r705866 = y;
        double r705867 = z;
        double r705868 = r705866 - r705867;
        double r705869 = t;
        double r705870 = r705869 - r705867;
        double r705871 = 1.0;
        double r705872 = r705870 + r705871;
        double r705873 = a;
        double r705874 = r705872 / r705873;
        double r705875 = r705868 / r705874;
        double r705876 = r705865 - r705875;
        return r705876;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r705877 = x;
        double r705878 = y;
        double r705879 = z;
        double r705880 = r705878 - r705879;
        double r705881 = t;
        double r705882 = r705881 - r705879;
        double r705883 = 1.0;
        double r705884 = r705882 + r705883;
        double r705885 = r705880 / r705884;
        double r705886 = a;
        double r705887 = r705885 * r705886;
        double r705888 = r705877 - r705887;
        return r705888;
}

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

Original1.8
Target0.2
Herbie0.2
\[x - \frac{y - z}{\left(t - z\right) + 1} \cdot a\]

Derivation

  1. Initial program 1.8

    \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity1.8

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

  4. Applied *-un-lft-identity1.8

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

  5. Applied times-frac1.8

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

  6. Applied *-un-lft-identity1.8

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

  7. Applied times-frac1.8

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

  8. Simplified1.8

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

  9. Simplified0.2

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

  10. Final simplification0.2

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

Reproduce

herbie shell --seed 2020047 
(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))))