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

Average Error: 0.0 → 0.0

Time: 13.0s

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 r37377318 = 1.0;
        double r37377319 = 8.0;
        double r37377320 = r37377318 / r37377319;
        double r37377321 = x;
        double r37377322 = r37377320 * r37377321;
        double r37377323 = y;
        double r37377324 = z;
        double r37377325 = r37377323 * r37377324;
        double r37377326 = 2.0;
        double r37377327 = r37377325 / r37377326;
        double r37377328 = r37377322 - r37377327;
        double r37377329 = t;
        double r37377330 = r37377328 + r37377329;
        return r37377330;
}

↓

double f(double x, double y, double z, double t) {
        double r37377331 = x;
        double r37377332 = 8.0;
        double r37377333 = r37377331 / r37377332;
        double r37377334 = 1.0;
        double r37377335 = t;
        double r37377336 = z;
        double r37377337 = y;
        double r37377338 = r37377336 * r37377337;
        double r37377339 = 2.0;
        double r37377340 = r37377338 / r37377339;
        double r37377341 = r37377335 - r37377340;
        double r37377342 = fma(r37377333, r37377334, r37377341);
        return r37377342;
}

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 2019163 +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))