Average Error: 2.0 → 0.2
Time: 3.5s
Precision: 64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
↓
\[x - \left(\frac{y}{\left(t - z\right) + 1} - \frac{z}{\left(t - z\right) + 1}\right) \cdot a\]
x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}
↓
x - \left(\frac{y}{\left(t - z\right) + 1} - \frac{z}{\left(t - z\right) + 1}\right) \cdot a
double f(double x, double y, double z, double t, double a) {
        double r650335 = x;
        double r650336 = y;
        double r650337 = z;
        double r650338 = r650336 - r650337;
        double r650339 = t;
        double r650340 = r650339 - r650337;
        double r650341 = 1.0;
        double r650342 = r650340 + r650341;
        double r650343 = a;
        double r650344 = r650342 / r650343;
        double r650345 = r650338 / r650344;
        double r650346 = r650335 - r650345;
        return r650346;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r650347 = x;
        double r650348 = y;
        double r650349 = t;
        double r650350 = z;
        double r650351 = r650349 - r650350;
        double r650352 = 1.0;
        double r650353 = r650351 + r650352;
        double r650354 = r650348 / r650353;
        double r650355 = r650350 / r650353;
        double r650356 = r650354 - r650355;
        double r650357 = a;
        double r650358 = r650356 * r650357;
        double r650359 = r650347 - r650358;
        return r650359;
}

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. Using strategy rm

  5. Applied div-sub0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2020056 
(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))))