Average Error: 0.0 → 0
Time: 1.3s
Precision: 64
\[x - y \cdot z\]
↓
\[\mathsf{fma}\left(-z, y, x\right)\]
x - y \cdot z
↓
\mathsf{fma}\left(-z, y, x\right)
double f(double x, double y, double z) {
        double r657144 = x;
        double r657145 = y;
        double r657146 = z;
        double r657147 = r657145 * r657146;
        double r657148 = r657144 - r657147;
        return r657148;
}
↓
double f(double x, double y, double z) {
        double r657149 = z;
        double r657150 = -r657149;
        double r657151 = y;
        double r657152 = x;
        double r657153 = fma(r657150, r657151, r657152);
        return r657153;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original0.0
Target0.0
Herbie0
\[\frac{x + y \cdot z}{\frac{x + y \cdot z}{x - y \cdot z}}\]

Derivation

  1. Initial program 0.0

    \[x - y \cdot z\]

  2. Simplified0

    \[\leadsto \color{blue}{\mathsf{fma}\left(-z, y, x\right)}\]

  3. Final simplification0

    \[\leadsto \mathsf{fma}\left(-z, y, x\right)\]

Reproduce

herbie shell --seed 2019196 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, C"

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

  (- x (* y z)))