Average Error: 2.1 → 0.2
Time: 14.0s
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 r357651 = x;
        double r357652 = y;
        double r357653 = z;
        double r357654 = r357652 - r357653;
        double r357655 = t;
        double r357656 = r357655 - r357653;
        double r357657 = 1.0;
        double r357658 = r357656 + r357657;
        double r357659 = a;
        double r357660 = r357658 / r357659;
        double r357661 = r357654 / r357660;
        double r357662 = r357651 - r357661;
        return r357662;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r357663 = x;
        double r357664 = y;
        double r357665 = z;
        double r357666 = r357664 - r357665;
        double r357667 = t;
        double r357668 = r357667 - r357665;
        double r357669 = 1.0;
        double r357670 = r357668 + r357669;
        double r357671 = r357666 / r357670;
        double r357672 = a;
        double r357673 = r357671 * r357672;
        double r357674 = r357663 - r357673;
        return r357674;
}

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

Original2.1
Target0.2
Herbie0.2
\[x - \frac{y - z}{\left(t - z\right) + 1} \cdot a\]

Derivation

  1. Initial program 2.1

    \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
  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. Final simplification0.2

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

Reproduce

herbie shell --seed 2019326 
(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))))