Average Error: 7.8 → 7.8
Time: 11.7s
Precision: 64
\[\frac{x \cdot y - z \cdot t}{a}\]
↓
\[\frac{{\left(x \cdot y - z \cdot t\right)}^{1}}{a}\]
\frac{x \cdot y - z \cdot t}{a}
↓
\frac{{\left(x \cdot y - z \cdot t\right)}^{1}}{a}
double f(double x, double y, double z, double t, double a) {
        double r550295 = x;
        double r550296 = y;
        double r550297 = r550295 * r550296;
        double r550298 = z;
        double r550299 = t;
        double r550300 = r550298 * r550299;
        double r550301 = r550297 - r550300;
        double r550302 = a;
        double r550303 = r550301 / r550302;
        return r550303;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r550304 = x;
        double r550305 = y;
        double r550306 = r550304 * r550305;
        double r550307 = z;
        double r550308 = t;
        double r550309 = r550307 * r550308;
        double r550310 = r550306 - r550309;
        double r550311 = 1.0;
        double r550312 = pow(r550310, r550311);
        double r550313 = a;
        double r550314 = r550312 / r550313;
        return r550314;
}

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 pow17.8

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

  4. Final simplification7.8

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

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))