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

Average Error: 0.0 → 0.0

Time: 5.2s

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 r708524 = 1.0;
        double r708525 = 8.0;
        double r708526 = r708524 / r708525;
        double r708527 = x;
        double r708528 = r708526 * r708527;
        double r708529 = y;
        double r708530 = z;
        double r708531 = r708529 * r708530;
        double r708532 = 2.0;
        double r708533 = r708531 / r708532;
        double r708534 = r708528 - r708533;
        double r708535 = t;
        double r708536 = r708534 + r708535;
        return r708536;
}

↓

double f(double x, double y, double z, double t) {
        double r708537 = x;
        double r708538 = 8.0;
        double r708539 = r708537 / r708538;
        double r708540 = 1.0;
        double r708541 = y;
        double r708542 = 2.0;
        double r708543 = r708541 / r708542;
        double r708544 = -r708543;
        double r708545 = z;
        double r708546 = t;
        double r708547 = fma(r708544, r708545, r708546);
        double r708548 = fma(r708539, r708540, r708547);
        return r708548;
}

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 2020089 +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))