Average Error: 8.0 → 8.0
Time: 7.6s
Precision: 64
\[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\]
↓
\[\frac{\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a}}{2}\]
\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}
↓
\frac{\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a}}{2}
double f(double x, double y, double z, double t, double a) {
        double r874595 = x;
        double r874596 = y;
        double r874597 = r874595 * r874596;
        double r874598 = z;
        double r874599 = 9.0;
        double r874600 = r874598 * r874599;
        double r874601 = t;
        double r874602 = r874600 * r874601;
        double r874603 = r874597 - r874602;
        double r874604 = a;
        double r874605 = 2.0;
        double r874606 = r874604 * r874605;
        double r874607 = r874603 / r874606;
        return r874607;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r874608 = x;
        double r874609 = y;
        double r874610 = r874608 * r874609;
        double r874611 = z;
        double r874612 = 9.0;
        double r874613 = r874611 * r874612;
        double r874614 = t;
        double r874615 = r874613 * r874614;
        double r874616 = r874610 - r874615;
        double r874617 = a;
        double r874618 = r874616 / r874617;
        double r874619 = 2.0;
        double r874620 = r874618 / r874619;
        return r874620;
}

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

Original8.0
Target5.9
Herbie8.0
\[\begin{array}{l} \mathbf{if}\;a \lt -2.090464557976709 \cdot 10^{86}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{a} - 4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;a \lt 2.14403070783397609 \cdot 10^{99}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(x \cdot 0.5\right) - \frac{t}{a} \cdot \left(z \cdot 4.5\right)\\ \end{array}\]

Derivation

  1. Initial program 8.0

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

  3. Applied *-un-lft-identity8.0

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

  4. Applied times-frac8.1

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

  6. Applied associate-*r/8.1

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

  7. Simplified8.0

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

  8. Final simplification8.0

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

Reproduce

herbie shell --seed 2020047 
(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)))