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

Average Error: 0.0 → 0.0

Time: 2.0s

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 r633201 = 1.0;
        double r633202 = 8.0;
        double r633203 = r633201 / r633202;
        double r633204 = x;
        double r633205 = r633203 * r633204;
        double r633206 = y;
        double r633207 = z;
        double r633208 = r633206 * r633207;
        double r633209 = 2.0;
        double r633210 = r633208 / r633209;
        double r633211 = r633205 - r633210;
        double r633212 = t;
        double r633213 = r633211 + r633212;
        return r633213;
}

↓

double f(double x, double y, double z, double t) {
        double r633214 = x;
        double r633215 = 8.0;
        double r633216 = r633214 / r633215;
        double r633217 = 1.0;
        double r633218 = y;
        double r633219 = 2.0;
        double r633220 = r633218 / r633219;
        double r633221 = -r633220;
        double r633222 = z;
        double r633223 = t;
        double r633224 = fma(r633221, r633222, r633223);
        double r633225 = fma(r633216, r633217, r633224);
        return r633225;
}

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 2020027 +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))