Average Error: 2.1 → 0.3
Time: 4.8s
Precision: 64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
↓
\[x - \frac{\frac{y - z}{\left(t - z\right) + 1}}{\frac{1}{a}}\]
x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}
↓
x - \frac{\frac{y - z}{\left(t - z\right) + 1}}{\frac{1}{a}}
double f(double x, double y, double z, double t, double a) {
        double r538704 = x;
        double r538705 = y;
        double r538706 = z;
        double r538707 = r538705 - r538706;
        double r538708 = t;
        double r538709 = r538708 - r538706;
        double r538710 = 1.0;
        double r538711 = r538709 + r538710;
        double r538712 = a;
        double r538713 = r538711 / r538712;
        double r538714 = r538707 / r538713;
        double r538715 = r538704 - r538714;
        return r538715;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r538716 = x;
        double r538717 = y;
        double r538718 = z;
        double r538719 = r538717 - r538718;
        double r538720 = t;
        double r538721 = r538720 - r538718;
        double r538722 = 1.0;
        double r538723 = r538721 + r538722;
        double r538724 = r538719 / r538723;
        double r538725 = 1.0;
        double r538726 = a;
        double r538727 = r538725 / r538726;
        double r538728 = r538724 / r538727;
        double r538729 = r538716 - r538728;
        return r538729;
}

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

Derivation

  1. Initial program 2.1

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

  3. Applied div-inv2.2

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

  4. Applied associate-/r*0.3

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

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 2019353 +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))))