Average Error: 7.8 → 7.8
Time: 12.0s
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 r540511 = x;
        double r540512 = y;
        double r540513 = r540511 * r540512;
        double r540514 = z;
        double r540515 = t;
        double r540516 = r540514 * r540515;
        double r540517 = r540513 - r540516;
        double r540518 = a;
        double r540519 = r540517 / r540518;
        return r540519;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r540520 = x;
        double r540521 = y;
        double r540522 = r540520 * r540521;
        double r540523 = z;
        double r540524 = t;
        double r540525 = r540523 * r540524;
        double r540526 = r540522 - r540525;
        double r540527 = a;
        double r540528 = r540526 / r540527;
        return r540528;
}

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
Target6.0
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 *-un-lft-identity7.8

    \[\leadsto \frac{\color{blue}{1 \cdot \left(x \cdot y - z \cdot t\right)}}{a}\]

  4. Final simplification7.8

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

Reproduce

herbie shell --seed 2019235 +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 -2.46868496869954822e170) (- (* (/ 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))