Average Error: 7.5 → 7.5
Time: 15.2s
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 r33933554 = x;
        double r33933555 = y;
        double r33933556 = r33933554 * r33933555;
        double r33933557 = z;
        double r33933558 = t;
        double r33933559 = r33933557 * r33933558;
        double r33933560 = r33933556 - r33933559;
        double r33933561 = a;
        double r33933562 = r33933560 / r33933561;
        return r33933562;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r33933563 = x;
        double r33933564 = y;
        double r33933565 = r33933563 * r33933564;
        double r33933566 = z;
        double r33933567 = t;
        double r33933568 = r33933566 * r33933567;
        double r33933569 = r33933565 - r33933568;
        double r33933570 = a;
        double r33933571 = r33933569 / r33933570;
        return r33933571;
}

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 +o rules:numerics
(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))