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

Average Error: 0.0 → 0.0

Time: 1.2s

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 r622127 = 1.0;
        double r622128 = 8.0;
        double r622129 = r622127 / r622128;
        double r622130 = x;
        double r622131 = r622129 * r622130;
        double r622132 = y;
        double r622133 = z;
        double r622134 = r622132 * r622133;
        double r622135 = 2.0;
        double r622136 = r622134 / r622135;
        double r622137 = r622131 - r622136;
        double r622138 = t;
        double r622139 = r622137 + r622138;
        return r622139;
}

↓

double f(double x, double y, double z, double t) {
        double r622140 = y;
        double r622141 = 2.0;
        double r622142 = r622140 / r622141;
        double r622143 = -r622142;
        double r622144 = z;
        double r622145 = x;
        double r622146 = 1.0;
        double r622147 = 8.0;
        double r622148 = r622146 / r622147;
        double r622149 = t;
        double r622150 = fma(r622145, r622148, r622149);
        double r622151 = fma(r622143, r622144, r622150);
        return r622151;
}

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 2019351 +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))