\[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t\]

↓

\[\mathsf{fma}\left(\frac{x}{8}, 1, t\right) - \frac{z \cdot y}{2}\]

\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t

↓

\mathsf{fma}\left(\frac{x}{8}, 1, t\right) - \frac{z \cdot y}{2}

double f(double x, double y, double z, double t) {
        double r599217 = 1.0;
        double r599218 = 8.0;
        double r599219 = r599217 / r599218;
        double r599220 = x;
        double r599221 = r599219 * r599220;
        double r599222 = y;
        double r599223 = z;
        double r599224 = r599222 * r599223;
        double r599225 = 2.0;
        double r599226 = r599224 / r599225;
        double r599227 = r599221 - r599226;
        double r599228 = t;
        double r599229 = r599227 + r599228;
        return r599229;
}

↓

double f(double x, double y, double z, double t) {
        double r599230 = x;
        double r599231 = 8.0;
        double r599232 = r599230 / r599231;
        double r599233 = 1.0;
        double r599234 = t;
        double r599235 = fma(r599232, r599233, r599234);
        double r599236 = z;
        double r599237 = y;
        double r599238 = r599236 * r599237;
        double r599239 = 2.0;
        double r599240 = r599238 / r599239;
        double r599241 = r599235 - r599240;
        return r599241;
}

Original	0.0
Target	0.0
Herbie	0.0

Derivation

Initial program 0.0
\[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t\]
Simplified0.0
\[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{8}, 1, t\right) - \frac{y \cdot z}{2}}\]
Final simplification0.0
\[\leadsto \mathsf{fma}\left(\frac{x}{8}, 1, t\right) - \frac{z \cdot y}{2}\]

Reproduce

herbie shell --seed 2019194 +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))

Error

Target

Derivation

Reproduce