Average Error: 2.0 → 0.2
Time: 4.7s
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 r525367 = x;
        double r525368 = y;
        double r525369 = z;
        double r525370 = r525368 - r525369;
        double r525371 = t;
        double r525372 = r525371 - r525369;
        double r525373 = 1.0;
        double r525374 = r525372 + r525373;
        double r525375 = a;
        double r525376 = r525374 / r525375;
        double r525377 = r525370 / r525376;
        double r525378 = r525367 - r525377;
        return r525378;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r525379 = x;
        double r525380 = y;
        double r525381 = t;
        double r525382 = z;
        double r525383 = r525381 - r525382;
        double r525384 = 1.0;
        double r525385 = r525383 + r525384;
        double r525386 = r525380 / r525385;
        double r525387 = r525382 / r525385;
        double r525388 = r525386 - r525387;
        double r525389 = a;
        double r525390 = r525388 * r525389;
        double r525391 = r525379 - r525390;
        return r525391;
}

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 2020100 +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))))