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

Average Error: 0.0 → 0.0

Time: 1.0s

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 r654195 = 1.0;
        double r654196 = 8.0;
        double r654197 = r654195 / r654196;
        double r654198 = x;
        double r654199 = r654197 * r654198;
        double r654200 = y;
        double r654201 = z;
        double r654202 = r654200 * r654201;
        double r654203 = 2.0;
        double r654204 = r654202 / r654203;
        double r654205 = r654199 - r654204;
        double r654206 = t;
        double r654207 = r654205 + r654206;
        return r654207;
}

↓

double f(double x, double y, double z, double t) {
        double r654208 = x;
        double r654209 = 8.0;
        double r654210 = r654208 / r654209;
        double r654211 = 1.0;
        double r654212 = y;
        double r654213 = 2.0;
        double r654214 = r654212 / r654213;
        double r654215 = -r654214;
        double r654216 = z;
        double r654217 = t;
        double r654218 = fma(r654215, r654216, r654217);
        double r654219 = fma(r654210, r654211, r654218);
        return r654219;
}

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 2020083 +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))