Average Error: 0.0 → 0.0
Time: 6.0s
Precision: 64
\[\left(\frac{1.0}{8.0} \cdot x - \frac{y \cdot z}{2.0}\right) + t\]
↓
\[\mathsf{fma}\left(\frac{x}{8.0}, 1.0, t - \frac{z}{2.0} \cdot y\right)\]
\left(\frac{1.0}{8.0} \cdot x - \frac{y \cdot z}{2.0}\right) + t
↓
\mathsf{fma}\left(\frac{x}{8.0}, 1.0, t - \frac{z}{2.0} \cdot y\right)
double f(double x, double y, double z, double t) {
        double r13815041 = 1.0;
        double r13815042 = 8.0;
        double r13815043 = r13815041 / r13815042;
        double r13815044 = x;
        double r13815045 = r13815043 * r13815044;
        double r13815046 = y;
        double r13815047 = z;
        double r13815048 = r13815046 * r13815047;
        double r13815049 = 2.0;
        double r13815050 = r13815048 / r13815049;
        double r13815051 = r13815045 - r13815050;
        double r13815052 = t;
        double r13815053 = r13815051 + r13815052;
        return r13815053;
}
↓
double f(double x, double y, double z, double t) {
        double r13815054 = x;
        double r13815055 = 8.0;
        double r13815056 = r13815054 / r13815055;
        double r13815057 = 1.0;
        double r13815058 = t;
        double r13815059 = z;
        double r13815060 = 2.0;
        double r13815061 = r13815059 / r13815060;
        double r13815062 = y;
        double r13815063 = r13815061 * r13815062;
        double r13815064 = r13815058 - r13815063;
        double r13815065 = fma(r13815056, r13815057, r13815064);
        return r13815065;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original0.0
Target0.0
Herbie0.0
\[\left(\frac{x}{8.0} + t\right) - \frac{z}{2.0} \cdot y\]

Derivation

  1. Initial program 0.0

    \[\left(\frac{1.0}{8.0} \cdot x - \frac{y \cdot z}{2.0}\right) + t\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{8.0}, 1.0, t - \frac{z}{2.0} \cdot y\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(\frac{x}{8.0}, 1.0, t - \frac{z}{2.0} \cdot y\right)\]

Reproduce

herbie shell --seed 2019156 +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))