Average Error: 8.0 → 8.0
Time: 6.5s
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 r1471392 = x;
        double r1471393 = y;
        double r1471394 = r1471392 * r1471393;
        double r1471395 = z;
        double r1471396 = 9.0;
        double r1471397 = r1471395 * r1471396;
        double r1471398 = t;
        double r1471399 = r1471397 * r1471398;
        double r1471400 = r1471394 - r1471399;
        double r1471401 = a;
        double r1471402 = 2.0;
        double r1471403 = r1471401 * r1471402;
        double r1471404 = r1471400 / r1471403;
        return r1471404;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r1471405 = x;
        double r1471406 = y;
        double r1471407 = r1471405 * r1471406;
        double r1471408 = 9.0;
        double r1471409 = t;
        double r1471410 = z;
        double r1471411 = r1471409 * r1471410;
        double r1471412 = r1471408 * r1471411;
        double r1471413 = -r1471412;
        double r1471414 = r1471407 + r1471413;
        double r1471415 = a;
        double r1471416 = 2.0;
        double r1471417 = r1471415 * r1471416;
        double r1471418 = r1471414 / r1471417;
        return r1471418;
}

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)))