Average Error: 7.5 → 7.5
Time: 18.9s
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 r42731245 = x;
        double r42731246 = y;
        double r42731247 = r42731245 * r42731246;
        double r42731248 = z;
        double r42731249 = t;
        double r42731250 = r42731248 * r42731249;
        double r42731251 = r42731247 - r42731250;
        double r42731252 = a;
        double r42731253 = r42731251 / r42731252;
        return r42731253;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r42731254 = x;
        double r42731255 = y;
        double r42731256 = r42731254 * r42731255;
        double r42731257 = z;
        double r42731258 = t;
        double r42731259 = r42731257 * r42731258;
        double r42731260 = r42731256 - r42731259;
        double r42731261 = a;
        double r42731262 = r42731260 / r42731261;
        return r42731262;
}

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 
(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))