Average Error: 7.4 → 7.4
Time: 4.1s
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 r774275 = x;
        double r774276 = y;
        double r774277 = r774275 * r774276;
        double r774278 = z;
        double r774279 = 9.0;
        double r774280 = r774278 * r774279;
        double r774281 = t;
        double r774282 = r774280 * r774281;
        double r774283 = r774277 - r774282;
        double r774284 = a;
        double r774285 = 2.0;
        double r774286 = r774284 * r774285;
        double r774287 = r774283 / r774286;
        return r774287;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r774288 = x;
        double r774289 = y;
        double r774290 = r774288 * r774289;
        double r774291 = z;
        double r774292 = 9.0;
        double r774293 = t;
        double r774294 = r774292 * r774293;
        double r774295 = r774291 * r774294;
        double r774296 = r774290 - r774295;
        double r774297 = a;
        double r774298 = 2.0;
        double r774299 = r774297 * r774298;
        double r774300 = r774296 / r774299;
        return r774300;
}

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 
(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)))