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

Average Error: 0.0 → 0.0

Time: 820.0ms

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 r718150 = 1.0;
        double r718151 = 8.0;
        double r718152 = r718150 / r718151;
        double r718153 = x;
        double r718154 = r718152 * r718153;
        double r718155 = y;
        double r718156 = z;
        double r718157 = r718155 * r718156;
        double r718158 = 2.0;
        double r718159 = r718157 / r718158;
        double r718160 = r718154 - r718159;
        double r718161 = t;
        double r718162 = r718160 + r718161;
        return r718162;
}

↓

double f(double x, double y, double z, double t) {
        double r718163 = x;
        double r718164 = 8.0;
        double r718165 = r718163 / r718164;
        double r718166 = 1.0;
        double r718167 = y;
        double r718168 = 2.0;
        double r718169 = r718167 / r718168;
        double r718170 = -r718169;
        double r718171 = z;
        double r718172 = t;
        double r718173 = fma(r718170, r718171, r718172);
        double r718174 = fma(r718165, r718166, r718173);
        return r718174;
}

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 2020047 +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))