Average Error: 7.7 → 7.8
Time: 26.1s
Precision: 64
\[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\]
↓
\[\frac{x \cdot y - \sqrt{9} \cdot \left(\left(\sqrt{9} \cdot t\right) \cdot z\right)}{a \cdot 2}\]
\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}
↓
\frac{x \cdot y - \sqrt{9} \cdot \left(\left(\sqrt{9} \cdot t\right) \cdot z\right)}{a \cdot 2}
double f(double x, double y, double z, double t, double a) {
        double r256135410 = x;
        double r256135411 = y;
        double r256135412 = r256135410 * r256135411;
        double r256135413 = z;
        double r256135414 = 9.0;
        double r256135415 = r256135413 * r256135414;
        double r256135416 = t;
        double r256135417 = r256135415 * r256135416;
        double r256135418 = r256135412 - r256135417;
        double r256135419 = a;
        double r256135420 = 2.0;
        double r256135421 = r256135419 * r256135420;
        double r256135422 = r256135418 / r256135421;
        return r256135422;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r256135423 = x;
        double r256135424 = y;
        double r256135425 = r256135423 * r256135424;
        double r256135426 = 9.0;
        double r256135427 = sqrt(r256135426);
        double r256135428 = t;
        double r256135429 = r256135427 * r256135428;
        double r256135430 = z;
        double r256135431 = r256135429 * r256135430;
        double r256135432 = r256135427 * r256135431;
        double r256135433 = r256135425 - r256135432;
        double r256135434 = a;
        double r256135435 = 2.0;
        double r256135436 = r256135434 * r256135435;
        double r256135437 = r256135433 / r256135436;
        return r256135437;
}

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
Target5.7
Herbie7.8
\[\begin{array}{l} \mathbf{if}\;a \lt -2.090464557976709043451944897028999329376 \cdot 10^{86}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{a} - 4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;a \lt 2.144030707833976090627817222818061808815 \cdot 10^{99}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(x \cdot 0.5\right) - \frac{t}{a} \cdot \left(z \cdot 4.5\right)\\ \end{array}\]

Derivation

  1. Initial program 7.7

    \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\]

  2. Taylor expanded around inf 7.7

    \[\leadsto \frac{\color{blue}{x \cdot y - 9 \cdot \left(t \cdot z\right)}}{a \cdot 2}\]
  3. Using strategy rm

  4. Applied add-sqr-sqrt7.7

    \[\leadsto \frac{x \cdot y - \color{blue}{\left(\sqrt{9} \cdot \sqrt{9}\right)} \cdot \left(t \cdot z\right)}{a \cdot 2}\]

  5. Applied associate-*l*7.8

    \[\leadsto \frac{x \cdot y - \color{blue}{\sqrt{9} \cdot \left(\sqrt{9} \cdot \left(t \cdot z\right)\right)}}{a \cdot 2}\]
  6. Using strategy rm

  7. Applied associate-*r*7.8

    \[\leadsto \frac{x \cdot y - \sqrt{9} \cdot \color{blue}{\left(\left(\sqrt{9} \cdot t\right) \cdot z\right)}}{a \cdot 2}\]

  8. Final simplification7.8

    \[\leadsto \frac{x \cdot y - \sqrt{9} \cdot \left(\left(\sqrt{9} \cdot t\right) \cdot z\right)}{a \cdot 2}\]

Reproduce

herbie shell --seed 2019173 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, I"

  :herbie-target
  (if (< a -2.090464557976709e+86) (- (* 0.5 (/ (* y x) a)) (* 4.5 (/ t (/ a z)))) (if (< a 2.144030707833976e+99) (/ (- (* x y) (* z (* 9.0 t))) (* a 2.0)) (- (* (/ y a) (* x 0.5)) (* (/ t a) (* z 4.5)))))

  (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0)))