Average Error: 23.1 → 23.1
Time: 6.5s
Precision: 64
\[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\]
↓
\[\frac{1}{y + z \cdot \left(b - y\right)} \cdot \left(x \cdot y + z \cdot \left(t - a\right)\right)\]
\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}
↓
\frac{1}{y + z \cdot \left(b - y\right)} \cdot \left(x \cdot y + z \cdot \left(t - a\right)\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r840721 = x;
        double r840722 = y;
        double r840723 = r840721 * r840722;
        double r840724 = z;
        double r840725 = t;
        double r840726 = a;
        double r840727 = r840725 - r840726;
        double r840728 = r840724 * r840727;
        double r840729 = r840723 + r840728;
        double r840730 = b;
        double r840731 = r840730 - r840722;
        double r840732 = r840724 * r840731;
        double r840733 = r840722 + r840732;
        double r840734 = r840729 / r840733;
        return r840734;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r840735 = 1.0;
        double r840736 = y;
        double r840737 = z;
        double r840738 = b;
        double r840739 = r840738 - r840736;
        double r840740 = r840737 * r840739;
        double r840741 = r840736 + r840740;
        double r840742 = r840735 / r840741;
        double r840743 = x;
        double r840744 = r840743 * r840736;
        double r840745 = t;
        double r840746 = a;
        double r840747 = r840745 - r840746;
        double r840748 = r840737 * r840747;
        double r840749 = r840744 + r840748;
        double r840750 = r840742 * r840749;
        return r840750;
}

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

Original23.1
Target18.0
Herbie23.1
\[\frac{z \cdot t + y \cdot x}{y + z \cdot \left(b - y\right)} - \frac{a}{\left(b - y\right) + \frac{y}{z}}\]

Derivation

  1. Initial program 23.1

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

  3. Applied clear-num23.2

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

  5. Applied div-inv23.3

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

  6. Applied add-cube-cbrt23.3

    \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{\left(y + z \cdot \left(b - y\right)\right) \cdot \frac{1}{x \cdot y + z \cdot \left(t - a\right)}}\]

  7. Applied times-frac23.2

    \[\leadsto \color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{y + z \cdot \left(b - y\right)} \cdot \frac{\sqrt[3]{1}}{\frac{1}{x \cdot y + z \cdot \left(t - a\right)}}}\]

  8. Simplified23.2

    \[\leadsto \color{blue}{\frac{1}{y + z \cdot \left(b - y\right)}} \cdot \frac{\sqrt[3]{1}}{\frac{1}{x \cdot y + z \cdot \left(t - a\right)}}\]

  9. Simplified23.1

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

  10. Final simplification23.1

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

Reproduce

herbie shell --seed 2020027 
(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)))))