Average Error: 7.8 → 7.8
Time: 4.0s
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 r697400 = x;
        double r697401 = y;
        double r697402 = r697400 * r697401;
        double r697403 = z;
        double r697404 = 9.0;
        double r697405 = r697403 * r697404;
        double r697406 = t;
        double r697407 = r697405 * r697406;
        double r697408 = r697402 - r697407;
        double r697409 = a;
        double r697410 = 2.0;
        double r697411 = r697409 * r697410;
        double r697412 = r697408 / r697411;
        return r697412;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r697413 = x;
        double r697414 = y;
        double r697415 = r697413 * r697414;
        double r697416 = 9.0;
        double r697417 = t;
        double r697418 = z;
        double r697419 = r697417 * r697418;
        double r697420 = r697416 * r697419;
        double r697421 = r697415 - r697420;
        double r697422 = a;
        double r697423 = 2.0;
        double r697424 = r697422 * r697423;
        double r697425 = r697421 / r697424;
        return r697425;
}

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
Target5.7
Herbie7.8
\[\begin{array}{l} \mathbf{if}\;a \lt -2.090464557976709 \cdot 10^{86}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{a} - 4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;a \lt 2.14403070783397609 \cdot 10^{99}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(x \cdot 0.5\right) - \frac{t}{a} \cdot \left(z \cdot 4.5\right)\\ \end{array}\]

Derivation

  1. Initial program 7.8

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

  3. Applied associate-*l*7.8

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

  4. Taylor expanded around inf 7.8

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

  5. Final simplification7.8

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

Reproduce

herbie shell --seed 2020064 +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)))