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

Average Error: 0.0 → 0.0

Time: 985.0ms

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 r663792 = 1.0;
        double r663793 = 8.0;
        double r663794 = r663792 / r663793;
        double r663795 = x;
        double r663796 = r663794 * r663795;
        double r663797 = y;
        double r663798 = z;
        double r663799 = r663797 * r663798;
        double r663800 = 2.0;
        double r663801 = r663799 / r663800;
        double r663802 = r663796 - r663801;
        double r663803 = t;
        double r663804 = r663802 + r663803;
        return r663804;
}

↓

double f(double x, double y, double z, double t) {
        double r663805 = x;
        double r663806 = 8.0;
        double r663807 = r663805 / r663806;
        double r663808 = 1.0;
        double r663809 = y;
        double r663810 = 2.0;
        double r663811 = r663809 / r663810;
        double r663812 = -r663811;
        double r663813 = z;
        double r663814 = t;
        double r663815 = fma(r663812, r663813, r663814);
        double r663816 = fma(r663807, r663808, r663815);
        return r663816;
}

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))