Average Error: 23.8 → 23.9
Time: 9.0s
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 r1400374 = x;
        double r1400375 = y;
        double r1400376 = r1400374 * r1400375;
        double r1400377 = z;
        double r1400378 = t;
        double r1400379 = a;
        double r1400380 = r1400378 - r1400379;
        double r1400381 = r1400377 * r1400380;
        double r1400382 = r1400376 + r1400381;
        double r1400383 = b;
        double r1400384 = r1400383 - r1400375;
        double r1400385 = r1400377 * r1400384;
        double r1400386 = r1400375 + r1400385;
        double r1400387 = r1400382 / r1400386;
        return r1400387;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r1400388 = x;
        double r1400389 = y;
        double r1400390 = r1400388 * r1400389;
        double r1400391 = z;
        double r1400392 = t;
        double r1400393 = r1400391 * r1400392;
        double r1400394 = a;
        double r1400395 = -r1400394;
        double r1400396 = r1400391 * r1400395;
        double r1400397 = r1400393 + r1400396;
        double r1400398 = r1400390 + r1400397;
        double r1400399 = b;
        double r1400400 = r1400399 * r1400391;
        double r1400401 = -r1400389;
        double r1400402 = r1400401 * r1400391;
        double r1400403 = r1400400 + r1400402;
        double r1400404 = r1400389 + r1400403;
        double r1400405 = r1400398 / r1400404;
        return r1400405;
}

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)))))