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

Average Error: 0.0 → 0.0

Time: 5.3s

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 r630669 = 1.0;
        double r630670 = 8.0;
        double r630671 = r630669 / r630670;
        double r630672 = x;
        double r630673 = r630671 * r630672;
        double r630674 = y;
        double r630675 = z;
        double r630676 = r630674 * r630675;
        double r630677 = 2.0;
        double r630678 = r630676 / r630677;
        double r630679 = r630673 - r630678;
        double r630680 = t;
        double r630681 = r630679 + r630680;
        return r630681;
}

↓

double f(double x, double y, double z, double t) {
        double r630682 = x;
        double r630683 = 8.0;
        double r630684 = r630682 / r630683;
        double r630685 = 1.0;
        double r630686 = y;
        double r630687 = 2.0;
        double r630688 = r630686 / r630687;
        double r630689 = -r630688;
        double r630690 = z;
        double r630691 = t;
        double r630692 = fma(r630689, r630690, r630691);
        double r630693 = fma(r630684, r630685, r630692);
        return r630693;
}

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 2020035 +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))