Average Error: 7.8 → 7.8
Time: 15.5s
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 r533603 = x;
        double r533604 = y;
        double r533605 = r533603 * r533604;
        double r533606 = z;
        double r533607 = t;
        double r533608 = r533606 * r533607;
        double r533609 = r533605 - r533608;
        double r533610 = a;
        double r533611 = r533609 / r533610;
        return r533611;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r533612 = x;
        double r533613 = y;
        double r533614 = r533612 * r533613;
        double r533615 = z;
        double r533616 = t;
        double r533617 = r533615 * r533616;
        double r533618 = -r533617;
        double r533619 = r533614 + r533618;
        double r533620 = a;
        double r533621 = r533619 / r533620;
        return r533621;
}

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))