Average Error: 7.6 → 7.7
Time: 22.3s
Precision: 64
\[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\]
↓
\[\frac{1}{a \cdot 2} \cdot \left(x \cdot y - 9 \cdot \left(t \cdot z\right)\right)\]
\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}
↓
\frac{1}{a \cdot 2} \cdot \left(x \cdot y - 9 \cdot \left(t \cdot z\right)\right)
double f(double x, double y, double z, double t, double a) {
        double r26565408 = x;
        double r26565409 = y;
        double r26565410 = r26565408 * r26565409;
        double r26565411 = z;
        double r26565412 = 9.0;
        double r26565413 = r26565411 * r26565412;
        double r26565414 = t;
        double r26565415 = r26565413 * r26565414;
        double r26565416 = r26565410 - r26565415;
        double r26565417 = a;
        double r26565418 = 2.0;
        double r26565419 = r26565417 * r26565418;
        double r26565420 = r26565416 / r26565419;
        return r26565420;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r26565421 = 1.0;
        double r26565422 = a;
        double r26565423 = 2.0;
        double r26565424 = r26565422 * r26565423;
        double r26565425 = r26565421 / r26565424;
        double r26565426 = x;
        double r26565427 = y;
        double r26565428 = r26565426 * r26565427;
        double r26565429 = 9.0;
        double r26565430 = t;
        double r26565431 = z;
        double r26565432 = r26565430 * r26565431;
        double r26565433 = r26565429 * r26565432;
        double r26565434 = r26565428 - r26565433;
        double r26565435 = r26565425 * r26565434;
        return r26565435;
}

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

Original7.6
Target5.6
Herbie7.7
\[\begin{array}{l} \mathbf{if}\;a \lt -2.090464557976709043451944897028999329376 \cdot 10^{86}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{a} - 4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;a \lt 2.144030707833976090627817222818061808815 \cdot 10^{99}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(x \cdot 0.5\right) - \frac{t}{a} \cdot \left(z \cdot 4.5\right)\\ \end{array}\]

Derivation

  1. Initial program 7.6

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

  2. Taylor expanded around 0 7.6

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

  4. Applied div-inv7.7

    \[\leadsto \color{blue}{\left(x \cdot y - 9 \cdot \left(t \cdot z\right)\right) \cdot \frac{1}{a \cdot 2}}\]

  5. Final simplification7.7

    \[\leadsto \frac{1}{a \cdot 2} \cdot \left(x \cdot y - 9 \cdot \left(t \cdot z\right)\right)\]

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (x y z t a)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, I"

  :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 (* 9.0 t))) (* a 2.0)) (- (* (/ y a) (* x 0.5)) (* (/ t a) (* z 4.5)))))

  (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0)))