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

Average Error: 0.0 → 0.0

Time: 2.4s

Precision: 64

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 r50938 = 1.0;
        double r50939 = 8.0;
        double r50940 = r50938 / r50939;
        double r50941 = x;
        double r50942 = r50940 * r50941;
        double r50943 = y;
        double r50944 = z;
        double r50945 = r50943 * r50944;
        double r50946 = 2.0;
        double r50947 = r50945 / r50946;
        double r50948 = r50942 - r50947;
        double r50949 = t;
        double r50950 = r50948 + r50949;
        return r50950;
}

↓

double f(double x, double y, double z, double t) {
        double r50951 = y;
        double r50952 = 2.0;
        double r50953 = r50951 / r50952;
        double r50954 = -r50953;
        double r50955 = z;
        double r50956 = x;
        double r50957 = 1.0;
        double r50958 = 8.0;
        double r50959 = r50957 / r50958;
        double r50960 = t;
        double r50961 = fma(r50956, r50959, r50960);
        double r50962 = fma(r50954, r50955, r50961);
        return r50962;
}

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 2019315 +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))