Average Error: 2.0 → 0.2
Time: 11.8s
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 r10694311 = x;
        double r10694312 = y;
        double r10694313 = z;
        double r10694314 = r10694312 - r10694313;
        double r10694315 = t;
        double r10694316 = r10694315 - r10694313;
        double r10694317 = 1.0;
        double r10694318 = r10694316 + r10694317;
        double r10694319 = a;
        double r10694320 = r10694318 / r10694319;
        double r10694321 = r10694314 / r10694320;
        double r10694322 = r10694311 - r10694321;
        return r10694322;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r10694323 = x;
        double r10694324 = a;
        double r10694325 = y;
        double r10694326 = z;
        double r10694327 = r10694325 - r10694326;
        double r10694328 = t;
        double r10694329 = r10694328 - r10694326;
        double r10694330 = 1.0;
        double r10694331 = r10694329 + r10694330;
        double r10694332 = r10694327 / r10694331;
        double r10694333 = r10694324 * r10694332;
        double r10694334 = r10694323 - r10694333;
        return r10694334;
}

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 2019156 
(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))))