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

Average Error: 0.0 → 0.0

Time: 2.9s

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 r1195057 = 1.0;
        double r1195058 = 8.0;
        double r1195059 = r1195057 / r1195058;
        double r1195060 = x;
        double r1195061 = r1195059 * r1195060;
        double r1195062 = y;
        double r1195063 = z;
        double r1195064 = r1195062 * r1195063;
        double r1195065 = 2.0;
        double r1195066 = r1195064 / r1195065;
        double r1195067 = r1195061 - r1195066;
        double r1195068 = t;
        double r1195069 = r1195067 + r1195068;
        return r1195069;
}

↓

double f(double x, double y, double z, double t) {
        double r1195070 = y;
        double r1195071 = 2.0;
        double r1195072 = r1195070 / r1195071;
        double r1195073 = -r1195072;
        double r1195074 = z;
        double r1195075 = x;
        double r1195076 = 1.0;
        double r1195077 = 8.0;
        double r1195078 = r1195076 / r1195077;
        double r1195079 = t;
        double r1195080 = fma(r1195075, r1195078, r1195079);
        double r1195081 = fma(r1195073, r1195074, r1195080);
        return r1195081;
}

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 2019306 +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))