Average Error: 23.3 → 23.3
Time: 16.9s
Precision: 64
\[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\]
↓
\[\left(\left(x \cdot y + t \cdot z\right) + z \cdot \left(-a\right)\right) \cdot \frac{1}{y + z \cdot \left(b - y\right)}\]
\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}
↓
\left(\left(x \cdot y + t \cdot z\right) + z \cdot \left(-a\right)\right) \cdot \frac{1}{y + z \cdot \left(b - y\right)}
double f(double x, double y, double z, double t, double a, double b) {
        double r1235860 = x;
        double r1235861 = y;
        double r1235862 = r1235860 * r1235861;
        double r1235863 = z;
        double r1235864 = t;
        double r1235865 = a;
        double r1235866 = r1235864 - r1235865;
        double r1235867 = r1235863 * r1235866;
        double r1235868 = r1235862 + r1235867;
        double r1235869 = b;
        double r1235870 = r1235869 - r1235861;
        double r1235871 = r1235863 * r1235870;
        double r1235872 = r1235861 + r1235871;
        double r1235873 = r1235868 / r1235872;
        return r1235873;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r1235874 = x;
        double r1235875 = y;
        double r1235876 = r1235874 * r1235875;
        double r1235877 = t;
        double r1235878 = z;
        double r1235879 = r1235877 * r1235878;
        double r1235880 = r1235876 + r1235879;
        double r1235881 = a;
        double r1235882 = -r1235881;
        double r1235883 = r1235878 * r1235882;
        double r1235884 = r1235880 + r1235883;
        double r1235885 = 1.0;
        double r1235886 = b;
        double r1235887 = r1235886 - r1235875;
        double r1235888 = r1235878 * r1235887;
        double r1235889 = r1235875 + r1235888;
        double r1235890 = r1235885 / r1235889;
        double r1235891 = r1235884 * r1235890;
        return r1235891;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original23.3
Target18.1
Herbie23.3
\[\frac{z \cdot t + y \cdot x}{y + z \cdot \left(b - y\right)} - \frac{a}{\left(b - y\right) + \frac{y}{z}}\]

Derivation

  1. Initial program 23.3

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

  3. Applied div-inv23.3

    \[\leadsto \color{blue}{\left(x \cdot y + z \cdot \left(t - a\right)\right) \cdot \frac{1}{y + z \cdot \left(b - y\right)}}\]
  4. Using strategy rm

  5. Applied sub-neg23.3

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

  6. Applied distribute-lft-in23.3

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

  7. Applied associate-+r+23.3

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

  8. Simplified23.3

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

  9. Final simplification23.3

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

Reproduce

herbie shell --seed 2019303 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

  :herbie-target
  (- (/ (+ (* z t) (* y x)) (+ y (* z (- b y)))) (/ a (+ (- b y) (/ y z))))

  (/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y)))))