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

Average Error: 0.0 → 0.0

Time: 817.0ms

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 r715180 = 1.0;
        double r715181 = 8.0;
        double r715182 = r715180 / r715181;
        double r715183 = x;
        double r715184 = r715182 * r715183;
        double r715185 = y;
        double r715186 = z;
        double r715187 = r715185 * r715186;
        double r715188 = 2.0;
        double r715189 = r715187 / r715188;
        double r715190 = r715184 - r715189;
        double r715191 = t;
        double r715192 = r715190 + r715191;
        return r715192;
}

↓

double f(double x, double y, double z, double t) {
        double r715193 = x;
        double r715194 = 8.0;
        double r715195 = r715193 / r715194;
        double r715196 = 1.0;
        double r715197 = y;
        double r715198 = 2.0;
        double r715199 = r715197 / r715198;
        double r715200 = -r715199;
        double r715201 = z;
        double r715202 = t;
        double r715203 = fma(r715200, r715201, r715202);
        double r715204 = fma(r715195, r715196, r715203);
        return r715204;
}

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 2020021 +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))