Average Error: 2.0 → 0.2
Time: 35.8s
Precision: 64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1.0}{a}}\]
↓
\[x - a \cdot \frac{y - z}{\left(t - z\right) + 1.0}\]
x - \frac{y - z}{\frac{\left(t - z\right) + 1.0}{a}}
↓
x - a \cdot \frac{y - z}{\left(t - z\right) + 1.0}
double f(double x, double y, double z, double t, double a) {
        double r24612821 = x;
        double r24612822 = y;
        double r24612823 = z;
        double r24612824 = r24612822 - r24612823;
        double r24612825 = t;
        double r24612826 = r24612825 - r24612823;
        double r24612827 = 1.0;
        double r24612828 = r24612826 + r24612827;
        double r24612829 = a;
        double r24612830 = r24612828 / r24612829;
        double r24612831 = r24612824 / r24612830;
        double r24612832 = r24612821 - r24612831;
        return r24612832;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r24612833 = x;
        double r24612834 = a;
        double r24612835 = y;
        double r24612836 = z;
        double r24612837 = r24612835 - r24612836;
        double r24612838 = t;
        double r24612839 = r24612838 - r24612836;
        double r24612840 = 1.0;
        double r24612841 = r24612839 + r24612840;
        double r24612842 = r24612837 / r24612841;
        double r24612843 = r24612834 * r24612842;
        double r24612844 = r24612833 - r24612843;
        return r24612844;
}

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

Original2.0
Target0.2
Herbie0.2
\[x - \frac{y - z}{\left(t - z\right) + 1.0} \cdot a\]

Derivation

  1. Initial program 2.0

    \[x - \frac{y - z}{\frac{\left(t - z\right) + 1.0}{a}}\]
  2. Using strategy rm

  3. Applied associate-/r/0.2

    \[\leadsto x - \color{blue}{\frac{y - z}{\left(t - z\right) + 1.0} \cdot a}\]

  4. Final simplification0.2

    \[\leadsto x - a \cdot \frac{y - z}{\left(t - z\right) + 1.0}\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"

  :herbie-target
  (- x (* (/ (- y z) (+ (- t z) 1.0)) a))

  (- x (/ (- y z) (/ (+ (- t z) 1.0) a))))