Average Error: 0.0 → 0.0
Time: 9.5s
Precision: 64
\[x \cdot y + \left(x - 1\right) \cdot z\]
↓
\[\mathsf{fma}\left(x, y, \left(x - 1\right) \cdot z\right)\]
x \cdot y + \left(x - 1\right) \cdot z
↓
\mathsf{fma}\left(x, y, \left(x - 1\right) \cdot z\right)
double f(double x, double y, double z) {
        double r8363504 = x;
        double r8363505 = y;
        double r8363506 = r8363504 * r8363505;
        double r8363507 = 1.0;
        double r8363508 = r8363504 - r8363507;
        double r8363509 = z;
        double r8363510 = r8363508 * r8363509;
        double r8363511 = r8363506 + r8363510;
        return r8363511;
}
↓
double f(double x, double y, double z) {
        double r8363512 = x;
        double r8363513 = y;
        double r8363514 = 1.0;
        double r8363515 = r8363512 - r8363514;
        double r8363516 = z;
        double r8363517 = r8363515 * r8363516;
        double r8363518 = fma(r8363512, r8363513, r8363517);
        return r8363518;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

    \[x \cdot y + \left(x - 1\right) \cdot z\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \left(x - 1\right) \cdot z\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x, y, \left(x - 1\right) \cdot z\right)\]

Reproduce

herbie shell --seed 2019170 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  (+ (* x y) (* (- x 1.0) z)))