Average Error: 1.9 → 0.3
Time: 5.5s
Precision: 64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
↓
\[x - \frac{y - z}{\left(t - z\right) + 1} \cdot a\]
x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}
↓
x - \frac{y - z}{\left(t - z\right) + 1} \cdot a
double f(double x, double y, double z, double t, double a) {
        double r528701 = x;
        double r528702 = y;
        double r528703 = z;
        double r528704 = r528702 - r528703;
        double r528705 = t;
        double r528706 = r528705 - r528703;
        double r528707 = 1.0;
        double r528708 = r528706 + r528707;
        double r528709 = a;
        double r528710 = r528708 / r528709;
        double r528711 = r528704 / r528710;
        double r528712 = r528701 - r528711;
        return r528712;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r528713 = x;
        double r528714 = y;
        double r528715 = z;
        double r528716 = r528714 - r528715;
        double r528717 = t;
        double r528718 = r528717 - r528715;
        double r528719 = 1.0;
        double r528720 = r528718 + r528719;
        double r528721 = r528716 / r528720;
        double r528722 = a;
        double r528723 = r528721 * r528722;
        double r528724 = r528713 - r528723;
        return r528724;
}

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
Target0.3
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/0.3

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

  4. Final simplification0.3

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

Reproduce

herbie shell --seed 2020083 +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))))