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

Average Error: 0.0 → 0.0

Time: 767.0ms

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 r794551 = 1.0;
        double r794552 = 8.0;
        double r794553 = r794551 / r794552;
        double r794554 = x;
        double r794555 = r794553 * r794554;
        double r794556 = y;
        double r794557 = z;
        double r794558 = r794556 * r794557;
        double r794559 = 2.0;
        double r794560 = r794558 / r794559;
        double r794561 = r794555 - r794560;
        double r794562 = t;
        double r794563 = r794561 + r794562;
        return r794563;
}

↓

double f(double x, double y, double z, double t) {
        double r794564 = x;
        double r794565 = 8.0;
        double r794566 = r794564 / r794565;
        double r794567 = 1.0;
        double r794568 = y;
        double r794569 = 2.0;
        double r794570 = r794568 / r794569;
        double r794571 = -r794570;
        double r794572 = z;
        double r794573 = t;
        double r794574 = fma(r794571, r794572, r794573);
        double r794575 = fma(r794566, r794567, r794574);
        return r794575;
}

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 2020018 +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))