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

Average Error: 0.0 → 0.0

Time: 1.1s

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 r676499 = 1.0;
        double r676500 = 8.0;
        double r676501 = r676499 / r676500;
        double r676502 = x;
        double r676503 = r676501 * r676502;
        double r676504 = y;
        double r676505 = z;
        double r676506 = r676504 * r676505;
        double r676507 = 2.0;
        double r676508 = r676506 / r676507;
        double r676509 = r676503 - r676508;
        double r676510 = t;
        double r676511 = r676509 + r676510;
        return r676511;
}

↓

double f(double x, double y, double z, double t) {
        double r676512 = x;
        double r676513 = 8.0;
        double r676514 = r676512 / r676513;
        double r676515 = 1.0;
        double r676516 = y;
        double r676517 = 2.0;
        double r676518 = r676516 / r676517;
        double r676519 = -r676518;
        double r676520 = z;
        double r676521 = t;
        double r676522 = fma(r676519, r676520, r676521);
        double r676523 = fma(r676514, r676515, r676522);
        return r676523;
}

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))