Diagrams.Solve.Polynomial:quartForm from diagrams-solve-0.1, B

Average Error: 0.0 → 0.0

Time: 11.9s

Precision: 64

Math

\[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t\]

↓

\[\mathsf{fma}\left(-\frac{y}{2}, z, \mathsf{fma}\left(x, \frac{1}{8}, t\right)\right)\]

C

double f(double x, double y, double z, double t) {
        double r496094 = 1.0;
        double r496095 = 8.0;
        double r496096 = r496094 / r496095;
        double r496097 = x;
        double r496098 = r496096 * r496097;
        double r496099 = y;
        double r496100 = z;
        double r496101 = r496099 * r496100;
        double r496102 = 2.0;
        double r496103 = r496101 / r496102;
        double r496104 = r496098 - r496103;
        double r496105 = t;
        double r496106 = r496104 + r496105;
        return r496106;
}

↓

double f(double x, double y, double z, double t) {
        double r496107 = y;
        double r496108 = 2.0;
        double r496109 = r496107 / r496108;
        double r496110 = -r496109;
        double r496111 = z;
        double r496112 = x;
        double r496113 = 1.0;
        double r496114 = 8.0;
        double r496115 = r496113 / r496114;
        double r496116 = t;
        double r496117 = fma(r496112, r496115, r496116);
        double r496118 = fma(r496110, r496111, r496117);
        return r496118;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	0.0
Target	0.0
Herbie	0.0

\[\left(\frac{x}{8} + t\right) - \frac{z}{2} \cdot y\]

Derivation

1. Initial program 0.0

   \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t\]

2. Simplified 0.0

   \[\leadsto \color{blue}{\mathsf{fma}\left(-\frac{y}{2}, z, \mathsf{fma}\left(x, \frac{1}{8}, t\right)\right)}\]

3. Final simplification 0.0

   \[\leadsto \mathsf{fma}\left(-\frac{y}{2}, z, \mathsf{fma}\left(x, \frac{1}{8}, t\right)\right)\]

Reproduce

herbie shell --seed 2019305 +o rules:numerics
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, B"
  :precision binary64

  :herbie-target
  (- (+ (/ x 8) t) (* (/ z 2) y))

  (+ (- (* (/ 1 8) x) (/ (* y z) 2)) t))