Average Error: 2.3 → 0.2
Time: 4.8s
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 r566857 = x;
        double r566858 = y;
        double r566859 = z;
        double r566860 = r566858 - r566859;
        double r566861 = t;
        double r566862 = r566861 - r566859;
        double r566863 = 1.0;
        double r566864 = r566862 + r566863;
        double r566865 = a;
        double r566866 = r566864 / r566865;
        double r566867 = r566860 / r566866;
        double r566868 = r566857 - r566867;
        return r566868;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r566869 = x;
        double r566870 = y;
        double r566871 = z;
        double r566872 = r566870 - r566871;
        double r566873 = t;
        double r566874 = r566873 - r566871;
        double r566875 = 1.0;
        double r566876 = r566874 + r566875;
        double r566877 = r566872 / r566876;
        double r566878 = a;
        double r566879 = r566877 * r566878;
        double r566880 = r566869 - r566879;
        return r566880;
}

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

Original2.3
Target0.2
Herbie0.2
\[x - \frac{y - z}{\left(t - z\right) + 1} \cdot a\]

Derivation

  1. Initial program 2.3

    \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
  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. Final simplification0.2

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

Reproduce

herbie shell --seed 2020036 +o rules:numerics
(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))))