Average Error: 7.8 → 7.8
Time: 10.6s
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 r933558 = x;
        double r933559 = y;
        double r933560 = r933558 * r933559;
        double r933561 = z;
        double r933562 = t;
        double r933563 = r933561 * r933562;
        double r933564 = r933560 - r933563;
        double r933565 = a;
        double r933566 = r933564 / r933565;
        return r933566;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r933567 = x;
        double r933568 = y;
        double r933569 = r933567 * r933568;
        double r933570 = z;
        double r933571 = t;
        double r933572 = r933570 * r933571;
        double r933573 = r933569 - r933572;
        double r933574 = a;
        double r933575 = r933573 / r933574;
        return r933575;
}

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
Target6.1
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 clear-num8.0

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

  4. Taylor expanded around inf 7.8

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

  5. Simplified7.8

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

  6. Final simplification7.8

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

Reproduce

herbie shell --seed 2019350 +o rules:numerics
(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))