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

Average Error: 0.0 → 0.0

Time: 2.1s

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 r455794 = 1.0;
        double r455795 = 8.0;
        double r455796 = r455794 / r455795;
        double r455797 = x;
        double r455798 = r455796 * r455797;
        double r455799 = y;
        double r455800 = z;
        double r455801 = r455799 * r455800;
        double r455802 = 2.0;
        double r455803 = r455801 / r455802;
        double r455804 = r455798 - r455803;
        double r455805 = t;
        double r455806 = r455804 + r455805;
        return r455806;
}

↓

double f(double x, double y, double z, double t) {
        double r455807 = y;
        double r455808 = 2.0;
        double r455809 = r455807 / r455808;
        double r455810 = -r455809;
        double r455811 = z;
        double r455812 = x;
        double r455813 = 1.0;
        double r455814 = 8.0;
        double r455815 = r455813 / r455814;
        double r455816 = t;
        double r455817 = fma(r455812, r455815, r455816);
        double r455818 = fma(r455810, r455811, r455817);
        return r455818;
}

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 2019303 +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))