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

Average Error: 0.0 → 0.0

Time: 20.3s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t) {
        double r31201558 = 1.0;
        double r31201559 = 8.0;
        double r31201560 = r31201558 / r31201559;
        double r31201561 = x;
        double r31201562 = r31201560 * r31201561;
        double r31201563 = y;
        double r31201564 = z;
        double r31201565 = r31201563 * r31201564;
        double r31201566 = 2.0;
        double r31201567 = r31201565 / r31201566;
        double r31201568 = r31201562 - r31201567;
        double r31201569 = t;
        double r31201570 = r31201568 + r31201569;
        return r31201570;
}

↓

double f(double x, double y, double z, double t) {
        double r31201571 = x;
        double r31201572 = 8.0;
        double r31201573 = r31201571 / r31201572;
        double r31201574 = 1.0;
        double r31201575 = t;
        double r31201576 = fma(r31201573, r31201574, r31201575);
        double r31201577 = z;
        double r31201578 = y;
        double r31201579 = r31201577 * r31201578;
        double r31201580 = 2.0;
        double r31201581 = r31201579 / r31201580;
        double r31201582 = r31201576 - r31201581;
        return r31201582;
}

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

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

3. Final simplification 0.0

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

Reproduce

herbie shell --seed 2019179 +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))