Average Error: 7.8 → 7.8
Time: 14.6s
Precision: 64
\[\frac{x \cdot y - z \cdot t}{a}\]
↓
\[\frac{x \cdot y + \left(-z \cdot t\right)}{a}\]
\frac{x \cdot y - z \cdot t}{a}
↓
\frac{x \cdot y + \left(-z \cdot t\right)}{a}
double f(double x, double y, double z, double t, double a) {
        double r521614 = x;
        double r521615 = y;
        double r521616 = r521614 * r521615;
        double r521617 = z;
        double r521618 = t;
        double r521619 = r521617 * r521618;
        double r521620 = r521616 - r521619;
        double r521621 = a;
        double r521622 = r521620 / r521621;
        return r521622;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r521623 = x;
        double r521624 = y;
        double r521625 = r521623 * r521624;
        double r521626 = z;
        double r521627 = t;
        double r521628 = r521626 * r521627;
        double r521629 = -r521628;
        double r521630 = r521625 + r521629;
        double r521631 = a;
        double r521632 = r521630 / r521631;
        return r521632;
}

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

Original7.8
Target5.8
Herbie7.8
\[\begin{array}{l} \mathbf{if}\;z \lt -2.468684968699548224247694913169778644284 \cdot 10^{170}:\\ \;\;\;\;\frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \mathbf{elif}\;z \lt 6.309831121978371209578784129518242708809 \cdot 10^{-71}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \end{array}\]

Derivation

  1. Initial program 7.8

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

  3. Applied sub-neg7.8

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

  4. Final simplification7.8

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

Reproduce

herbie shell --seed 2019303 
(FPCore (x y z t a)
  :name "Data.Colour.Matrix:inverse from colour-2.3.3, B"
  :precision binary64

  :herbie-target
  (if (< z -2.46868496869954822e170) (- (* (/ y a) x) (* (/ t a) z)) (if (< z 6.30983112197837121e-71) (/ (- (* x y) (* z t)) a) (- (* (/ y a) x) (* (/ t a) z))))

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