Average Error: 7.8 → 7.9
Time: 3.6s
Precision: 64
\[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\]
↓
\[\frac{1}{a} \cdot \frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{2}\]
\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}
↓
\frac{1}{a} \cdot \frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{2}
double f(double x, double y, double z, double t, double a) {
        double r739441 = x;
        double r739442 = y;
        double r739443 = r739441 * r739442;
        double r739444 = z;
        double r739445 = 9.0;
        double r739446 = r739444 * r739445;
        double r739447 = t;
        double r739448 = r739446 * r739447;
        double r739449 = r739443 - r739448;
        double r739450 = a;
        double r739451 = 2.0;
        double r739452 = r739450 * r739451;
        double r739453 = r739449 / r739452;
        return r739453;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r739454 = 1.0;
        double r739455 = a;
        double r739456 = r739454 / r739455;
        double r739457 = x;
        double r739458 = y;
        double r739459 = r739457 * r739458;
        double r739460 = z;
        double r739461 = 9.0;
        double r739462 = r739460 * r739461;
        double r739463 = t;
        double r739464 = r739462 * r739463;
        double r739465 = r739459 - r739464;
        double r739466 = 2.0;
        double r739467 = r739465 / r739466;
        double r739468 = r739456 * r739467;
        return r739468;
}

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

Derivation

  1. Initial program 7.8

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

  3. Applied *-un-lft-identity7.8

    \[\leadsto \frac{\color{blue}{1 \cdot \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)}}{a \cdot 2}\]

  4. Applied times-frac7.9

    \[\leadsto \color{blue}{\frac{1}{a} \cdot \frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{2}}\]

  5. Final simplification7.9

    \[\leadsto \frac{1}{a} \cdot \frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{2}\]

Reproduce

herbie shell --seed 2020002 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, I"
  :precision binary64

  :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 t))) (* a 2)) (- (* (/ y a) (* x 0.5)) (* (/ t a) (* z 4.5)))))

  (/ (- (* x y) (* (* z 9) t)) (* a 2)))