Average Error: 8.0 → 8.0
Time: 8.8s
Precision: 64
\[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\]
↓
\[\frac{x \cdot y + \left(-9 \cdot \left(t \cdot z\right)\right)}{a \cdot 2}\]
\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}
↓
\frac{x \cdot y + \left(-9 \cdot \left(t \cdot z\right)\right)}{a \cdot 2}
double f(double x, double y, double z, double t, double a) {
        double r774407 = x;
        double r774408 = y;
        double r774409 = r774407 * r774408;
        double r774410 = z;
        double r774411 = 9.0;
        double r774412 = r774410 * r774411;
        double r774413 = t;
        double r774414 = r774412 * r774413;
        double r774415 = r774409 - r774414;
        double r774416 = a;
        double r774417 = 2.0;
        double r774418 = r774416 * r774417;
        double r774419 = r774415 / r774418;
        return r774419;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r774420 = x;
        double r774421 = y;
        double r774422 = r774420 * r774421;
        double r774423 = 9.0;
        double r774424 = t;
        double r774425 = z;
        double r774426 = r774424 * r774425;
        double r774427 = r774423 * r774426;
        double r774428 = -r774427;
        double r774429 = r774422 + r774428;
        double r774430 = a;
        double r774431 = 2.0;
        double r774432 = r774430 * r774431;
        double r774433 = r774429 / r774432;
        return r774433;
}

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 sub-neg8.0

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

  4. Simplified8.0

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

  5. Final simplification8.0

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

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)))