Average Error: 7.9 → 7.9
Time: 3.5s
Precision: 64
\[\frac{x \cdot y - z \cdot t}{a}\]
↓
\[\frac{x \cdot y - z \cdot t}{a}\]
\frac{x \cdot y - z \cdot t}{a}
↓
\frac{x \cdot y - z \cdot t}{a}
double f(double x, double y, double z, double t, double a) {
        double r774754 = x;
        double r774755 = y;
        double r774756 = r774754 * r774755;
        double r774757 = z;
        double r774758 = t;
        double r774759 = r774757 * r774758;
        double r774760 = r774756 - r774759;
        double r774761 = a;
        double r774762 = r774760 / r774761;
        return r774762;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r774763 = x;
        double r774764 = y;
        double r774765 = r774763 * r774764;
        double r774766 = z;
        double r774767 = t;
        double r774768 = r774766 * r774767;
        double r774769 = r774765 - r774768;
        double r774770 = a;
        double r774771 = r774769 / r774770;
        return r774771;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original7.9
Target6.3
Herbie7.9
\[\begin{array}{l} \mathbf{if}\;z \lt -2.46868496869954822 \cdot 10^{170}:\\ \;\;\;\;\frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \mathbf{elif}\;z \lt 6.30983112197837121 \cdot 10^{-71}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \end{array}\]

Derivation

  1. Initial program 7.9

    \[\frac{x \cdot y - z \cdot t}{a}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity7.9

    \[\leadsto \frac{x \cdot y - z \cdot t}{\color{blue}{1 \cdot a}}\]

  4. Applied *-un-lft-identity7.9

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

  5. Applied times-frac7.9

    \[\leadsto \color{blue}{\frac{1}{1} \cdot \frac{x \cdot y - z \cdot t}{a}}\]

  6. Simplified7.9

    \[\leadsto \color{blue}{1} \cdot \frac{x \cdot y - z \cdot t}{a}\]

  7. Final simplification7.9

    \[\leadsto \frac{x \cdot y - z \cdot t}{a}\]

Reproduce

herbie shell --seed 2020100 
(FPCore (x y z t a)
  :name "Data.Colour.Matrix:inverse from colour-2.3.3, B"
  :precision binary64

  :herbie-target
  (if (< z -2.468684968699548e+170) (- (* (/ y a) x) (* (/ t a) z)) (if (< z 6.309831121978371e-71) (/ (- (* x y) (* z t)) a) (- (* (/ y a) x) (* (/ t a) z))))

  (/ (- (* x y) (* z t)) a))