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

Average Error: 0.0 → 0.0

Time: 1.0s

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 r634534 = 1.0;
        double r634535 = 8.0;
        double r634536 = r634534 / r634535;
        double r634537 = x;
        double r634538 = r634536 * r634537;
        double r634539 = y;
        double r634540 = z;
        double r634541 = r634539 * r634540;
        double r634542 = 2.0;
        double r634543 = r634541 / r634542;
        double r634544 = r634538 - r634543;
        double r634545 = t;
        double r634546 = r634544 + r634545;
        return r634546;
}

↓

double f(double x, double y, double z, double t) {
        double r634547 = x;
        double r634548 = 8.0;
        double r634549 = r634547 / r634548;
        double r634550 = 1.0;
        double r634551 = y;
        double r634552 = 2.0;
        double r634553 = r634551 / r634552;
        double r634554 = -r634553;
        double r634555 = z;
        double r634556 = t;
        double r634557 = fma(r634554, r634555, r634556);
        double r634558 = fma(r634549, r634550, r634557);
        return r634558;
}

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 2019353 +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))