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

Average Error: 0.0 → 0.0

Time: 2.3s

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 r583961 = 1.0;
        double r583962 = 8.0;
        double r583963 = r583961 / r583962;
        double r583964 = x;
        double r583965 = r583963 * r583964;
        double r583966 = y;
        double r583967 = z;
        double r583968 = r583966 * r583967;
        double r583969 = 2.0;
        double r583970 = r583968 / r583969;
        double r583971 = r583965 - r583970;
        double r583972 = t;
        double r583973 = r583971 + r583972;
        return r583973;
}

↓

double f(double x, double y, double z, double t) {
        double r583974 = y;
        double r583975 = 2.0;
        double r583976 = r583974 / r583975;
        double r583977 = -r583976;
        double r583978 = z;
        double r583979 = x;
        double r583980 = 1.0;
        double r583981 = 8.0;
        double r583982 = r583980 / r583981;
        double r583983 = t;
        double r583984 = fma(r583979, r583982, r583983);
        double r583985 = fma(r583977, r583978, r583984);
        return r583985;
}

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 2019323 +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))