Average Error: 23.3 → 23.3
Time: 16.1s
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 r519053 = x;
        double r519054 = y;
        double r519055 = r519053 * r519054;
        double r519056 = z;
        double r519057 = t;
        double r519058 = a;
        double r519059 = r519057 - r519058;
        double r519060 = r519056 * r519059;
        double r519061 = r519055 + r519060;
        double r519062 = b;
        double r519063 = r519062 - r519054;
        double r519064 = r519056 * r519063;
        double r519065 = r519054 + r519064;
        double r519066 = r519061 / r519065;
        return r519066;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r519067 = x;
        double r519068 = y;
        double r519069 = r519067 * r519068;
        double r519070 = t;
        double r519071 = z;
        double r519072 = r519070 * r519071;
        double r519073 = r519069 + r519072;
        double r519074 = a;
        double r519075 = -r519074;
        double r519076 = r519071 * r519075;
        double r519077 = r519073 + r519076;
        double r519078 = 1.0;
        double r519079 = b;
        double r519080 = r519079 - r519068;
        double r519081 = r519071 * r519080;
        double r519082 = r519068 + r519081;
        double r519083 = r519078 / r519082;
        double r519084 = r519077 * r519083;
        return r519084;
}

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)))))