Average Error: 23.8 → 23.9
Time: 9.8s
Precision: 64
\[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\]
↓
\[\frac{x \cdot y + \left(z \cdot t + z \cdot \left(-a\right)\right)}{y + \left(b \cdot z + \left(-y\right) \cdot z\right)}\]
\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}
↓
\frac{x \cdot y + \left(z \cdot t + z \cdot \left(-a\right)\right)}{y + \left(b \cdot z + \left(-y\right) \cdot z\right)}
double f(double x, double y, double z, double t, double a, double b) {
        double r935903 = x;
        double r935904 = y;
        double r935905 = r935903 * r935904;
        double r935906 = z;
        double r935907 = t;
        double r935908 = a;
        double r935909 = r935907 - r935908;
        double r935910 = r935906 * r935909;
        double r935911 = r935905 + r935910;
        double r935912 = b;
        double r935913 = r935912 - r935904;
        double r935914 = r935906 * r935913;
        double r935915 = r935904 + r935914;
        double r935916 = r935911 / r935915;
        return r935916;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r935917 = x;
        double r935918 = y;
        double r935919 = r935917 * r935918;
        double r935920 = z;
        double r935921 = t;
        double r935922 = r935920 * r935921;
        double r935923 = a;
        double r935924 = -r935923;
        double r935925 = r935920 * r935924;
        double r935926 = r935922 + r935925;
        double r935927 = r935919 + r935926;
        double r935928 = b;
        double r935929 = r935928 * r935920;
        double r935930 = -r935918;
        double r935931 = r935930 * r935920;
        double r935932 = r935929 + r935931;
        double r935933 = r935918 + r935932;
        double r935934 = r935927 / r935933;
        return r935934;
}

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

Original23.8
Target18.5
Herbie23.9
\[\frac{z \cdot t + y \cdot x}{y + z \cdot \left(b - y\right)} - \frac{a}{\left(b - y\right) + \frac{y}{z}}\]

Derivation

  1. Initial program 23.8

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

  3. Applied sub-neg23.8

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

  4. Applied distribute-lft-in23.8

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

  6. Applied sub-neg23.8

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

  7. Applied distribute-lft-in23.9

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

  8. Simplified23.9

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

  9. Simplified23.9

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

  10. Final simplification23.9

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

Reproduce

herbie shell --seed 2020047 
(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)))))