Average Error: 2.3 → 0.2
Time: 4.0s
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 r597820 = x;
        double r597821 = y;
        double r597822 = z;
        double r597823 = r597821 - r597822;
        double r597824 = t;
        double r597825 = r597824 - r597822;
        double r597826 = 1.0;
        double r597827 = r597825 + r597826;
        double r597828 = a;
        double r597829 = r597827 / r597828;
        double r597830 = r597823 / r597829;
        double r597831 = r597820 - r597830;
        return r597831;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r597832 = x;
        double r597833 = y;
        double r597834 = z;
        double r597835 = r597833 - r597834;
        double r597836 = t;
        double r597837 = r597836 - r597834;
        double r597838 = 1.0;
        double r597839 = r597837 + r597838;
        double r597840 = r597835 / r597839;
        double r597841 = a;
        double r597842 = r597840 * r597841;
        double r597843 = r597832 - r597842;
        return r597843;
}

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))))