Average Error: 7.8 → 7.8
Time: 10.9s
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 r640078 = x;
        double r640079 = y;
        double r640080 = r640078 * r640079;
        double r640081 = z;
        double r640082 = t;
        double r640083 = r640081 * r640082;
        double r640084 = r640080 - r640083;
        double r640085 = a;
        double r640086 = r640084 / r640085;
        return r640086;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r640087 = x;
        double r640088 = y;
        double r640089 = r640087 * r640088;
        double r640090 = z;
        double r640091 = t;
        double r640092 = r640090 * r640091;
        double r640093 = r640089 - r640092;
        double r640094 = a;
        double r640095 = r640093 / r640094;
        return r640095;
}

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 pow17.8

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

  4. Final simplification7.8

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

Reproduce

herbie shell --seed 2019235 
(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))