Average Error: 7.8 → 7.7
Time: 4.7s
Precision: 64
\[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\]
↓
\[\frac{x \cdot y - 9 \cdot \left(t \cdot z\right)}{a \cdot 2}\]
\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}
↓
\frac{x \cdot y - 9 \cdot \left(t \cdot z\right)}{a \cdot 2}
double f(double x, double y, double z, double t, double a) {
        double r710242 = x;
        double r710243 = y;
        double r710244 = r710242 * r710243;
        double r710245 = z;
        double r710246 = 9.0;
        double r710247 = r710245 * r710246;
        double r710248 = t;
        double r710249 = r710247 * r710248;
        double r710250 = r710244 - r710249;
        double r710251 = a;
        double r710252 = 2.0;
        double r710253 = r710251 * r710252;
        double r710254 = r710250 / r710253;
        return r710254;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r710255 = x;
        double r710256 = y;
        double r710257 = r710255 * r710256;
        double r710258 = 9.0;
        double r710259 = t;
        double r710260 = z;
        double r710261 = r710259 * r710260;
        double r710262 = r710258 * r710261;
        double r710263 = r710257 - r710262;
        double r710264 = a;
        double r710265 = 2.0;
        double r710266 = r710264 * r710265;
        double r710267 = r710263 / r710266;
        return r710267;
}

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
Target5.6
Herbie7.7
\[\begin{array}{l} \mathbf{if}\;a \lt -2.090464557976709 \cdot 10^{86}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{a} - 4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;a \lt 2.14403070783397609 \cdot 10^{99}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(x \cdot 0.5\right) - \frac{t}{a} \cdot \left(z \cdot 4.5\right)\\ \end{array}\]

Derivation

  1. Initial program 7.8

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

  2. Taylor expanded around inf 7.7

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

  3. Final simplification7.7

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

Reproduce

herbie shell --seed 2020036 +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)))