Average Error: 1.9 → 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 r632301 = x;
        double r632302 = y;
        double r632303 = z;
        double r632304 = r632302 - r632303;
        double r632305 = t;
        double r632306 = r632305 - r632303;
        double r632307 = 1.0;
        double r632308 = r632306 + r632307;
        double r632309 = a;
        double r632310 = r632308 / r632309;
        double r632311 = r632304 / r632310;
        double r632312 = r632301 - r632311;
        return r632312;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r632313 = x;
        double r632314 = y;
        double r632315 = z;
        double r632316 = r632314 - r632315;
        double r632317 = t;
        double r632318 = r632317 - r632315;
        double r632319 = 1.0;
        double r632320 = r632318 + r632319;
        double r632321 = r632316 / r632320;
        double r632322 = a;
        double r632323 = r632321 * r632322;
        double r632324 = r632313 - r632323;
        return r632324;
}

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

Original1.9
Target0.2
Herbie0.2
\[x - \frac{y - z}{\left(t - z\right) + 1} \cdot a\]

Derivation

  1. Initial program 1.9

    \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
  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 2020060 +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))))