Average Error: 7.7 → 7.7
Time: 18.2s
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 r601448 = x;
        double r601449 = y;
        double r601450 = r601448 * r601449;
        double r601451 = z;
        double r601452 = t;
        double r601453 = r601451 * r601452;
        double r601454 = r601450 - r601453;
        double r601455 = a;
        double r601456 = r601454 / r601455;
        return r601456;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r601457 = x;
        double r601458 = y;
        double r601459 = r601457 * r601458;
        double r601460 = z;
        double r601461 = t;
        double r601462 = r601460 * r601461;
        double r601463 = r601459 - r601462;
        double r601464 = a;
        double r601465 = r601463 / r601464;
        return r601465;
}

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

Original7.7
Target6.2
Herbie7.7
\[\begin{array}{l} \mathbf{if}\;z \lt -2.46868496869954822 \cdot 10^{170}:\\ \;\;\;\;\frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \mathbf{elif}\;z \lt 6.30983112197837121 \cdot 10^{-71}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \end{array}\]

Derivation

  1. Initial program 7.7

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

  3. Applied *-un-lft-identity7.7

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

  4. Final simplification7.7

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

Reproduce

herbie shell --seed 2019198 
(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))