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

Average Error: 0.0 → 0.0

Time: 1.3s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

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

↓

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

C

double f(double x, double y, double z, double t) {
        double r602055 = 1.0;
        double r602056 = 8.0;
        double r602057 = r602055 / r602056;
        double r602058 = x;
        double r602059 = r602057 * r602058;
        double r602060 = y;
        double r602061 = z;
        double r602062 = r602060 * r602061;
        double r602063 = 2.0;
        double r602064 = r602062 / r602063;
        double r602065 = r602059 - r602064;
        double r602066 = t;
        double r602067 = r602065 + r602066;
        return r602067;
}

↓

double f(double x, double y, double z, double t) {
        double r602068 = y;
        double r602069 = 2.0;
        double r602070 = r602068 / r602069;
        double r602071 = -r602070;
        double r602072 = z;
        double r602073 = x;
        double r602074 = 1.0;
        double r602075 = 8.0;
        double r602076 = r602074 / r602075;
        double r602077 = t;
        double r602078 = fma(r602073, r602076, r602077);
        double r602079 = fma(r602071, r602072, r602078);
        return r602079;
}

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

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

3. Final simplification 0.0

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

Reproduce

herbie shell --seed 2019350 +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))