Average Error: 7.8 → 7.8
Time: 15.4s
Precision: 64
\[\frac{x \cdot y - z \cdot t}{a}\]
↓
\[\frac{x \cdot y + \left(-t \cdot z\right)}{a}\]
\frac{x \cdot y - z \cdot t}{a}
↓
\frac{x \cdot y + \left(-t \cdot z\right)}{a}
double f(double x, double y, double z, double t, double a) {
        double r500347 = x;
        double r500348 = y;
        double r500349 = r500347 * r500348;
        double r500350 = z;
        double r500351 = t;
        double r500352 = r500350 * r500351;
        double r500353 = r500349 - r500352;
        double r500354 = a;
        double r500355 = r500353 / r500354;
        return r500355;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r500356 = x;
        double r500357 = y;
        double r500358 = r500356 * r500357;
        double r500359 = t;
        double r500360 = z;
        double r500361 = r500359 * r500360;
        double r500362 = -r500361;
        double r500363 = r500358 + r500362;
        double r500364 = a;
        double r500365 = r500363 / r500364;
        return r500365;
}

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
Target5.8
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 sub-neg7.8

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

  4. Simplified7.8

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

  5. Final simplification7.8

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

Reproduce

herbie shell --seed 2019303 +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 -2.46868496869954822e170) (- (* (/ 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))