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

Average Error: 0.0 → 0.0

Time: 8.7s

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 r458959 = 1.0;
        double r458960 = 8.0;
        double r458961 = r458959 / r458960;
        double r458962 = x;
        double r458963 = r458961 * r458962;
        double r458964 = y;
        double r458965 = z;
        double r458966 = r458964 * r458965;
        double r458967 = 2.0;
        double r458968 = r458966 / r458967;
        double r458969 = r458963 - r458968;
        double r458970 = t;
        double r458971 = r458969 + r458970;
        return r458971;
}

↓

double f(double x, double y, double z, double t) {
        double r458972 = y;
        double r458973 = 2.0;
        double r458974 = r458972 / r458973;
        double r458975 = -r458974;
        double r458976 = z;
        double r458977 = x;
        double r458978 = 1.0;
        double r458979 = 8.0;
        double r458980 = r458978 / r458979;
        double r458981 = t;
        double r458982 = fma(r458977, r458980, r458981);
        double r458983 = fma(r458975, r458976, r458982);
        return r458983;
}

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 2019199 +o rules:numerics
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, B"

  :herbie-target
  (- (+ (/ x 8.0) t) (* (/ z 2.0) y))

  (+ (- (* (/ 1.0 8.0) x) (/ (* y z) 2.0)) t))