Average Error: 7.4 → 7.4
Time: 4.9s
Precision: 64
\[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\]
↓
\[\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\]
\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}
↓
\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}
double f(double x, double y, double z, double t, double a) {
        double r742540 = x;
        double r742541 = y;
        double r742542 = r742540 * r742541;
        double r742543 = z;
        double r742544 = 9.0;
        double r742545 = r742543 * r742544;
        double r742546 = t;
        double r742547 = r742545 * r742546;
        double r742548 = r742542 - r742547;
        double r742549 = a;
        double r742550 = 2.0;
        double r742551 = r742549 * r742550;
        double r742552 = r742548 / r742551;
        return r742552;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r742553 = x;
        double r742554 = y;
        double r742555 = r742553 * r742554;
        double r742556 = z;
        double r742557 = 9.0;
        double r742558 = t;
        double r742559 = r742557 * r742558;
        double r742560 = r742556 * r742559;
        double r742561 = r742555 - r742560;
        double r742562 = a;
        double r742563 = 2.0;
        double r742564 = r742562 * r742563;
        double r742565 = r742561 / r742564;
        return r742565;
}

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

Original7.4
Target5.4
Herbie7.4
\[\begin{array}{l} \mathbf{if}\;a \lt -2.090464557976709 \cdot 10^{86}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{a} - 4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;a \lt 2.14403070783397609 \cdot 10^{99}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(x \cdot 0.5\right) - \frac{t}{a} \cdot \left(z \cdot 4.5\right)\\ \end{array}\]

Derivation

  1. Initial program 7.4

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

  3. Applied associate-*l*7.4

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

  4. Final simplification7.4

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

Reproduce

herbie shell --seed 2020035 +o rules:numerics
(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)))