FastMath dist

Average Error: 0.0 → 0.0

Time: 3.8s

Precision: 64

Math

\[d1 \cdot d2 + d1 \cdot d3\]

↓

\[\mathsf{fma}\left(d1, d2, d1 \cdot d3\right)\]

C

double f(double d1, double d2, double d3) {
        double r11393165 = d1;
        double r11393166 = d2;
        double r11393167 = r11393165 * r11393166;
        double r11393168 = d3;
        double r11393169 = r11393165 * r11393168;
        double r11393170 = r11393167 + r11393169;
        return r11393170;
}

↓

double f(double d1, double d2, double d3) {
        double r11393171 = d1;
        double r11393172 = d2;
        double r11393173 = d3;
        double r11393174 = r11393171 * r11393173;
        double r11393175 = fma(r11393171, r11393172, r11393174);
        return r11393175;
}

Error

Bits error versus d1

Bits error versus d2

Bits error versus d3

Target

Original	0.0
Target	0.0
Herbie	0.0

\[d1 \cdot \left(d2 + d3\right)\]

Derivation

1. Initial program 0.0

   \[d1 \cdot d2 + d1 \cdot d3\]
2. Using strategy rm

3. Applied fma-def 0.0

   \[\leadsto \color{blue}{\mathsf{fma}\left(d1, d2, d1 \cdot d3\right)}\]

4. Final simplification 0.0

   \[\leadsto \mathsf{fma}\left(d1, d2, d1 \cdot d3\right)\]

Reproduce

herbie shell --seed 2019144 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath dist"

  :herbie-target
  (* d1 (+ d2 d3))

  (+ (* d1 d2) (* d1 d3)))