Average Error: 1.8 → 0.3
Time: 9.9s
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 r730584 = x;
        double r730585 = y;
        double r730586 = z;
        double r730587 = r730585 - r730586;
        double r730588 = t;
        double r730589 = r730588 - r730586;
        double r730590 = 1.0;
        double r730591 = r730589 + r730590;
        double r730592 = a;
        double r730593 = r730591 / r730592;
        double r730594 = r730587 / r730593;
        double r730595 = r730584 - r730594;
        return r730595;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r730596 = x;
        double r730597 = 1.0;
        double r730598 = t;
        double r730599 = z;
        double r730600 = r730598 - r730599;
        double r730601 = 1.0;
        double r730602 = r730600 + r730601;
        double r730603 = y;
        double r730604 = r730603 - r730599;
        double r730605 = r730602 / r730604;
        double r730606 = r730597 / r730605;
        double r730607 = a;
        double r730608 = r730606 * r730607;
        double r730609 = r730596 - r730608;
        return r730609;
}

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

Original1.8
Target0.2
Herbie0.3
\[x - \frac{y - z}{\left(t - z\right) + 1} \cdot a\]

Derivation

  1. Initial program 1.8

    \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
  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 2020045 
(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))))