Average Error: 2.1 → 0.3
Time: 23.5s
Precision: 64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
↓
\[x - \frac{\frac{y - z}{\left(t - z\right) + 1}}{\frac{1}{a}}\]
x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}
↓
x - \frac{\frac{y - z}{\left(t - z\right) + 1}}{\frac{1}{a}}
double f(double x, double y, double z, double t, double a) {
        double r414310 = x;
        double r414311 = y;
        double r414312 = z;
        double r414313 = r414311 - r414312;
        double r414314 = t;
        double r414315 = r414314 - r414312;
        double r414316 = 1.0;
        double r414317 = r414315 + r414316;
        double r414318 = a;
        double r414319 = r414317 / r414318;
        double r414320 = r414313 / r414319;
        double r414321 = r414310 - r414320;
        return r414321;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r414322 = x;
        double r414323 = y;
        double r414324 = z;
        double r414325 = r414323 - r414324;
        double r414326 = t;
        double r414327 = r414326 - r414324;
        double r414328 = 1.0;
        double r414329 = r414327 + r414328;
        double r414330 = r414325 / r414329;
        double r414331 = 1.0;
        double r414332 = a;
        double r414333 = r414331 / r414332;
        double r414334 = r414330 / r414333;
        double r414335 = r414322 - r414334;
        return r414335;
}

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
Herbie0.3
\[x - \frac{y - z}{\left(t - z\right) + 1} \cdot a\]

Derivation

  1. Initial program 2.1

    \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
  2. Using strategy rm

  3. Applied div-inv2.1

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

  4. Applied associate-/r*0.3

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

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 2019208 +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))))