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

Average Error: 0.0 → 0.0

Time: 798.0ms

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 r642325 = 1.0;
        double r642326 = 8.0;
        double r642327 = r642325 / r642326;
        double r642328 = x;
        double r642329 = r642327 * r642328;
        double r642330 = y;
        double r642331 = z;
        double r642332 = r642330 * r642331;
        double r642333 = 2.0;
        double r642334 = r642332 / r642333;
        double r642335 = r642329 - r642334;
        double r642336 = t;
        double r642337 = r642335 + r642336;
        return r642337;
}

↓

double f(double x, double y, double z, double t) {
        double r642338 = x;
        double r642339 = 8.0;
        double r642340 = r642338 / r642339;
        double r642341 = 1.0;
        double r642342 = y;
        double r642343 = 2.0;
        double r642344 = r642342 / r642343;
        double r642345 = -r642344;
        double r642346 = z;
        double r642347 = t;
        double r642348 = fma(r642345, r642346, r642347);
        double r642349 = fma(r642340, r642341, r642348);
        return r642349;
}

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 2020020 +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))