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 r774948 = x;
        double r774949 = y;
        double r774950 = r774948 * r774949;
        double r774951 = z;
        double r774952 = t;
        double r774953 = r774951 * r774952;
        double r774954 = r774950 - r774953;
        double r774955 = a;
        double r774956 = r774954 / r774955;
        return r774956;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r774957 = x;
        double r774958 = y;
        double r774959 = r774957 * r774958;
        double r774960 = z;
        double r774961 = t;
        double r774962 = r774960 * r774961;
        double r774963 = r774959 - r774962;
        double r774964 = a;
        double r774965 = r774963 / r774964;
        return r774965;
}

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))