Average Error: 7.8 → 7.8
Time: 16.2s
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 r538724 = x;
        double r538725 = y;
        double r538726 = r538724 * r538725;
        double r538727 = z;
        double r538728 = t;
        double r538729 = r538727 * r538728;
        double r538730 = r538726 - r538729;
        double r538731 = a;
        double r538732 = r538730 / r538731;
        return r538732;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r538733 = x;
        double r538734 = y;
        double r538735 = r538733 * r538734;
        double r538736 = z;
        double r538737 = t;
        double r538738 = r538736 * r538737;
        double r538739 = r538735 - r538738;
        double r538740 = a;
        double r538741 = r538739 / r538740;
        return r538741;
}

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 *-un-lft-identity7.8

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

  4. Applied *-un-lft-identity7.8

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

  5. Applied times-frac7.8

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

  6. Simplified7.8

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

  7. Final simplification7.8

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

Reproduce

herbie shell --seed 2019303 +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))