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

Average Error: 0.0 → 0.0

Time: 6.6s

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 r543176 = 1.0;
        double r543177 = 8.0;
        double r543178 = r543176 / r543177;
        double r543179 = x;
        double r543180 = r543178 * r543179;
        double r543181 = y;
        double r543182 = z;
        double r543183 = r543181 * r543182;
        double r543184 = 2.0;
        double r543185 = r543183 / r543184;
        double r543186 = r543180 - r543185;
        double r543187 = t;
        double r543188 = r543186 + r543187;
        return r543188;
}

↓

double f(double x, double y, double z, double t) {
        double r543189 = y;
        double r543190 = 2.0;
        double r543191 = r543189 / r543190;
        double r543192 = -r543191;
        double r543193 = z;
        double r543194 = x;
        double r543195 = 1.0;
        double r543196 = 8.0;
        double r543197 = r543195 / r543196;
        double r543198 = t;
        double r543199 = fma(r543194, r543197, r543198);
        double r543200 = fma(r543192, r543193, r543199);
        return r543200;
}

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 2019209 +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))