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

Average Error: 0.0 → 0.0

Time: 2.2s

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 r649189 = 1.0;
        double r649190 = 8.0;
        double r649191 = r649189 / r649190;
        double r649192 = x;
        double r649193 = r649191 * r649192;
        double r649194 = y;
        double r649195 = z;
        double r649196 = r649194 * r649195;
        double r649197 = 2.0;
        double r649198 = r649196 / r649197;
        double r649199 = r649193 - r649198;
        double r649200 = t;
        double r649201 = r649199 + r649200;
        return r649201;
}

↓

double f(double x, double y, double z, double t) {
        double r649202 = x;
        double r649203 = 8.0;
        double r649204 = r649202 / r649203;
        double r649205 = 1.0;
        double r649206 = y;
        double r649207 = 2.0;
        double r649208 = r649206 / r649207;
        double r649209 = -r649208;
        double r649210 = z;
        double r649211 = t;
        double r649212 = fma(r649209, r649210, r649211);
        double r649213 = fma(r649204, r649205, r649212);
        return r649213;
}

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 2020100 +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))