Main:bigenough2 from A

Average Error: 0.0 → 0.0

Time: 562.0ms

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

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

↓

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

C

double f(double x, double y, double z) {
        double r103803 = x;
        double r103804 = y;
        double r103805 = z;
        double r103806 = r103805 + r103803;
        double r103807 = r103804 * r103806;
        double r103808 = r103803 + r103807;
        return r103808;
}

↓

double f(double x, double y, double z) {
        double r103809 = z;
        double r103810 = x;
        double r103811 = r103809 + r103810;
        double r103812 = y;
        double r103813 = fma(r103811, r103812, r103810);
        return r103813;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

1. Initial program 0.0

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

2. Simplified 0.0

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

3. Final simplification 0.0

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

Reproduce

herbie shell --seed 2020042 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))