Average Error: 7.5 → 7.5
Time: 18.2s
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 r36713973 = x;
        double r36713974 = y;
        double r36713975 = r36713973 * r36713974;
        double r36713976 = z;
        double r36713977 = t;
        double r36713978 = r36713976 * r36713977;
        double r36713979 = r36713975 - r36713978;
        double r36713980 = a;
        double r36713981 = r36713979 / r36713980;
        return r36713981;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r36713982 = x;
        double r36713983 = y;
        double r36713984 = r36713982 * r36713983;
        double r36713985 = z;
        double r36713986 = t;
        double r36713987 = r36713985 * r36713986;
        double r36713988 = r36713984 - r36713987;
        double r36713989 = a;
        double r36713990 = r36713988 / r36713989;
        return r36713990;
}

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

Original7.5
Target6.0
Herbie7.5
\[\begin{array}{l} \mathbf{if}\;z \lt -2.468684968699548224247694913169778644284 \cdot 10^{170}:\\ \;\;\;\;\frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \mathbf{elif}\;z \lt 6.309831121978371209578784129518242708809 \cdot 10^{-71}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \end{array}\]

Derivation

  1. Initial program 7.5

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

  2. Final simplification7.5

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

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (x y z t a)
  :name "Data.Colour.Matrix:inverse from colour-2.3.3, B"

  :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))