Average Error: 23.3 → 23.3
Time: 15.1s
Precision: 64
\[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\]
↓
\[\frac{\left(x \cdot y + t \cdot z\right) + z \cdot \left(-a\right)}{y + z \cdot \left(b - y\right)}\]
\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}
↓
\frac{\left(x \cdot y + t \cdot z\right) + z \cdot \left(-a\right)}{y + z \cdot \left(b - y\right)}
double f(double x, double y, double z, double t, double a, double b) {
        double r513463 = x;
        double r513464 = y;
        double r513465 = r513463 * r513464;
        double r513466 = z;
        double r513467 = t;
        double r513468 = a;
        double r513469 = r513467 - r513468;
        double r513470 = r513466 * r513469;
        double r513471 = r513465 + r513470;
        double r513472 = b;
        double r513473 = r513472 - r513464;
        double r513474 = r513466 * r513473;
        double r513475 = r513464 + r513474;
        double r513476 = r513471 / r513475;
        return r513476;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r513477 = x;
        double r513478 = y;
        double r513479 = r513477 * r513478;
        double r513480 = t;
        double r513481 = z;
        double r513482 = r513480 * r513481;
        double r513483 = r513479 + r513482;
        double r513484 = a;
        double r513485 = -r513484;
        double r513486 = r513481 * r513485;
        double r513487 = r513483 + r513486;
        double r513488 = b;
        double r513489 = r513488 - r513478;
        double r513490 = r513481 * r513489;
        double r513491 = r513478 + r513490;
        double r513492 = r513487 / r513491;
        return r513492;
}

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

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

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)))))