Average Error: 2.1 → 0.2
Time: 3.8s
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 r610948 = x;
        double r610949 = y;
        double r610950 = z;
        double r610951 = r610949 - r610950;
        double r610952 = t;
        double r610953 = r610952 - r610950;
        double r610954 = 1.0;
        double r610955 = r610953 + r610954;
        double r610956 = a;
        double r610957 = r610955 / r610956;
        double r610958 = r610951 / r610957;
        double r610959 = r610948 - r610958;
        return r610959;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r610960 = x;
        double r610961 = y;
        double r610962 = z;
        double r610963 = r610961 - r610962;
        double r610964 = t;
        double r610965 = r610964 - r610962;
        double r610966 = 1.0;
        double r610967 = r610965 + r610966;
        double r610968 = r610963 / r610967;
        double r610969 = a;
        double r610970 = r610968 * r610969;
        double r610971 = r610960 - r610970;
        return r610971;
}

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. Final simplification0.2

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

Reproduce

herbie shell --seed 2020081 +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))))