Average Error: 2.0 → 0.2
Time: 3.3s
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 r485176 = x;
        double r485177 = y;
        double r485178 = z;
        double r485179 = r485177 - r485178;
        double r485180 = t;
        double r485181 = r485180 - r485178;
        double r485182 = 1.0;
        double r485183 = r485181 + r485182;
        double r485184 = a;
        double r485185 = r485183 / r485184;
        double r485186 = r485179 / r485185;
        double r485187 = r485176 - r485186;
        return r485187;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r485188 = x;
        double r485189 = y;
        double r485190 = z;
        double r485191 = r485189 - r485190;
        double r485192 = t;
        double r485193 = r485192 - r485190;
        double r485194 = 1.0;
        double r485195 = r485193 + r485194;
        double r485196 = r485191 / r485195;
        double r485197 = a;
        double r485198 = r485196 * r485197;
        double r485199 = r485188 - r485198;
        return r485199;
}

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

Derivation

  1. Initial program 2.0

    \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
  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 2020001 +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))))