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

Average Error: 0.0 → 0.0

Time: 926.0ms

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t) {
        double r640700 = 1.0;
        double r640701 = 8.0;
        double r640702 = r640700 / r640701;
        double r640703 = x;
        double r640704 = r640702 * r640703;
        double r640705 = y;
        double r640706 = z;
        double r640707 = r640705 * r640706;
        double r640708 = 2.0;
        double r640709 = r640707 / r640708;
        double r640710 = r640704 - r640709;
        double r640711 = t;
        double r640712 = r640710 + r640711;
        return r640712;
}

↓

double f(double x, double y, double z, double t) {
        double r640713 = x;
        double r640714 = 8.0;
        double r640715 = r640713 / r640714;
        double r640716 = 1.0;
        double r640717 = y;
        double r640718 = 2.0;
        double r640719 = r640717 / r640718;
        double r640720 = -r640719;
        double r640721 = z;
        double r640722 = t;
        double r640723 = fma(r640720, r640721, r640722);
        double r640724 = fma(r640715, r640716, r640723);
        return r640724;
}

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

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

3. Final simplification 0.0

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

Reproduce

herbie shell --seed 2020001 +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))