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

Average Error: 0.0 → 0.0

Time: 11.4s

Precision: 64

Math

\[\left(\frac{1.0}{8.0} \cdot x - \frac{y \cdot z}{2.0}\right) + t\]

↓

\[\mathsf{fma}\left(\frac{x}{8.0}, 1.0, t - \frac{z \cdot y}{2.0}\right)\]

C

double f(double x, double y, double z, double t) {
        double r29724806 = 1.0;
        double r29724807 = 8.0;
        double r29724808 = r29724806 / r29724807;
        double r29724809 = x;
        double r29724810 = r29724808 * r29724809;
        double r29724811 = y;
        double r29724812 = z;
        double r29724813 = r29724811 * r29724812;
        double r29724814 = 2.0;
        double r29724815 = r29724813 / r29724814;
        double r29724816 = r29724810 - r29724815;
        double r29724817 = t;
        double r29724818 = r29724816 + r29724817;
        return r29724818;
}

↓

double f(double x, double y, double z, double t) {
        double r29724819 = x;
        double r29724820 = 8.0;
        double r29724821 = r29724819 / r29724820;
        double r29724822 = 1.0;
        double r29724823 = t;
        double r29724824 = z;
        double r29724825 = y;
        double r29724826 = r29724824 * r29724825;
        double r29724827 = 2.0;
        double r29724828 = r29724826 / r29724827;
        double r29724829 = r29724823 - r29724828;
        double r29724830 = fma(r29724821, r29724822, r29724829);
        return r29724830;
}

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

\[\left(\frac{x}{8.0} + t\right) - \frac{z}{2.0} \cdot y\]

Derivation

1. Initial program 0.0

   \[\left(\frac{1.0}{8.0} \cdot x - \frac{y \cdot z}{2.0}\right) + t\]

2. Simplified 0.0

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{8.0}, 1.0, t - \frac{z \cdot y}{2.0}\right)}\]

3. Final simplification 0.0

   \[\leadsto \mathsf{fma}\left(\frac{x}{8.0}, 1.0, t - \frac{z \cdot y}{2.0}\right)\]

Reproduce

herbie shell --seed 2019164 +o rules:numerics
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, B"

  :herbie-target
  (- (+ (/ x 8.0) t) (* (/ z 2.0) y))

  (+ (- (* (/ 1.0 8.0) x) (/ (* y z) 2.0)) t))