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

Average Error: 0.0 → 0.0

Time: 8.3s

Precision: 64

Math

\[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t\]

↓

\[\mathsf{fma}\left(\frac{x}{8}, 1, t - \frac{z \cdot y}{2}\right)\]

C

double f(double x, double y, double z, double t) {
        double r34392544 = 1.0;
        double r34392545 = 8.0;
        double r34392546 = r34392544 / r34392545;
        double r34392547 = x;
        double r34392548 = r34392546 * r34392547;
        double r34392549 = y;
        double r34392550 = z;
        double r34392551 = r34392549 * r34392550;
        double r34392552 = 2.0;
        double r34392553 = r34392551 / r34392552;
        double r34392554 = r34392548 - r34392553;
        double r34392555 = t;
        double r34392556 = r34392554 + r34392555;
        return r34392556;
}

↓

double f(double x, double y, double z, double t) {
        double r34392557 = x;
        double r34392558 = 8.0;
        double r34392559 = r34392557 / r34392558;
        double r34392560 = 1.0;
        double r34392561 = t;
        double r34392562 = z;
        double r34392563 = y;
        double r34392564 = r34392562 * r34392563;
        double r34392565 = 2.0;
        double r34392566 = r34392564 / r34392565;
        double r34392567 = r34392561 - r34392566;
        double r34392568 = fma(r34392559, r34392560, r34392567);
        return r34392568;
}

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

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{8}, 1, t - \frac{z \cdot y}{2}\right)}\]

3. Final simplification 0.0

   \[\leadsto \mathsf{fma}\left(\frac{x}{8}, 1, t - \frac{z \cdot y}{2}\right)\]

Reproduce

herbie shell --seed 2019170 +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))