Average Error: 7.4 → 7.4
Time: 3.2s
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 r736973 = x;
        double r736974 = y;
        double r736975 = r736973 * r736974;
        double r736976 = z;
        double r736977 = t;
        double r736978 = r736976 * r736977;
        double r736979 = r736975 - r736978;
        double r736980 = a;
        double r736981 = r736979 / r736980;
        return r736981;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r736982 = x;
        double r736983 = y;
        double r736984 = r736982 * r736983;
        double r736985 = z;
        double r736986 = t;
        double r736987 = r736985 * r736986;
        double r736988 = r736984 - r736987;
        double r736989 = a;
        double r736990 = r736988 / r736989;
        return r736990;
}

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

Original7.4
Target5.8
Herbie7.4
\[\begin{array}{l} \mathbf{if}\;z \lt -2.46868496869954822 \cdot 10^{170}:\\ \;\;\;\;\frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \mathbf{elif}\;z \lt 6.30983112197837121 \cdot 10^{-71}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \end{array}\]

Derivation

  1. Initial program 7.4

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

  3. Applied clear-num7.7

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

  4. Taylor expanded around inf 7.4

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

  5. Simplified7.4

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

  6. Final simplification7.4

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

Reproduce

herbie shell --seed 2020062 +o rules:numerics
(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))