Average Error: 7.9 → 8.2
Time: 3.4s
Precision: 64
\[\frac{x \cdot y - z \cdot t}{a}\]
↓
\[\frac{1}{\frac{a}{x \cdot y - z \cdot t}}\]
\frac{x \cdot y - z \cdot t}{a}
↓
\frac{1}{\frac{a}{x \cdot y - z \cdot t}}
double f(double x, double y, double z, double t, double a) {
        double r827083 = x;
        double r827084 = y;
        double r827085 = r827083 * r827084;
        double r827086 = z;
        double r827087 = t;
        double r827088 = r827086 * r827087;
        double r827089 = r827085 - r827088;
        double r827090 = a;
        double r827091 = r827089 / r827090;
        return r827091;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r827092 = 1.0;
        double r827093 = a;
        double r827094 = x;
        double r827095 = y;
        double r827096 = r827094 * r827095;
        double r827097 = z;
        double r827098 = t;
        double r827099 = r827097 * r827098;
        double r827100 = r827096 - r827099;
        double r827101 = r827093 / r827100;
        double r827102 = r827092 / r827101;
        return r827102;
}

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

Original7.9
Target6.0
Herbie8.2
\[\begin{array}{l} \mathbf{if}\;z \lt -2.46868496869954822 \cdot 10^{170}:\\ \;\;\;\;\frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \mathbf{elif}\;z \lt 6.30983112197837121 \cdot 10^{-71}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \end{array}\]

Derivation

  1. Initial program 7.9

    \[\frac{x \cdot y - z \cdot t}{a}\]
  2. Using strategy rm

  3. Applied clear-num8.2

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

  4. Final simplification8.2

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

Reproduce

herbie shell --seed 2020083 
(FPCore (x y z t a)
  :name "Data.Colour.Matrix:inverse from colour-2.3.3, B"
  :precision binary64

  :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))