Average Error: 1.9 → 0.3
Time: 5.5s
Precision: 64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
↓
\[x - \frac{1}{\frac{\left(t - z\right) + 1}{y - z}} \cdot a\]
x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}
↓
x - \frac{1}{\frac{\left(t - z\right) + 1}{y - z}} \cdot a
double f(double x, double y, double z, double t, double a) {
        double r683378 = x;
        double r683379 = y;
        double r683380 = z;
        double r683381 = r683379 - r683380;
        double r683382 = t;
        double r683383 = r683382 - r683380;
        double r683384 = 1.0;
        double r683385 = r683383 + r683384;
        double r683386 = a;
        double r683387 = r683385 / r683386;
        double r683388 = r683381 / r683387;
        double r683389 = r683378 - r683388;
        return r683389;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r683390 = x;
        double r683391 = 1.0;
        double r683392 = t;
        double r683393 = z;
        double r683394 = r683392 - r683393;
        double r683395 = 1.0;
        double r683396 = r683394 + r683395;
        double r683397 = y;
        double r683398 = r683397 - r683393;
        double r683399 = r683396 / r683398;
        double r683400 = r683391 / r683399;
        double r683401 = a;
        double r683402 = r683400 * r683401;
        double r683403 = r683390 - r683402;
        return r683403;
}

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

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. Using strategy rm

  5. Applied clear-num0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2020057 +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))))