Average Error: 7.5 → 7.5
Time: 17.8s
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 r35868065 = x;
        double r35868066 = y;
        double r35868067 = r35868065 * r35868066;
        double r35868068 = z;
        double r35868069 = t;
        double r35868070 = r35868068 * r35868069;
        double r35868071 = r35868067 - r35868070;
        double r35868072 = a;
        double r35868073 = r35868071 / r35868072;
        return r35868073;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r35868074 = x;
        double r35868075 = y;
        double r35868076 = r35868074 * r35868075;
        double r35868077 = z;
        double r35868078 = t;
        double r35868079 = r35868077 * r35868078;
        double r35868080 = r35868076 - r35868079;
        double r35868081 = a;
        double r35868082 = r35868080 / r35868081;
        return r35868082;
}

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))