Average Error: 0.0 → 0.0
Time: 13.9s
Precision: 64
\[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32\]
↓
\[32 \cdot d1 + \mathsf{fma}\left(d1, d2, \left(\left(5 + d3\right) \cdot d1\right)\right)\]
\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32
↓
32 \cdot d1 + \mathsf{fma}\left(d1, d2, \left(\left(5 + d3\right) \cdot d1\right)\right)
double f(double d1, double d2, double d3) {
        double r11300970 = d1;
        double r11300971 = d2;
        double r11300972 = r11300970 * r11300971;
        double r11300973 = d3;
        double r11300974 = 5.0;
        double r11300975 = r11300973 + r11300974;
        double r11300976 = r11300975 * r11300970;
        double r11300977 = r11300972 + r11300976;
        double r11300978 = 32.0;
        double r11300979 = r11300970 * r11300978;
        double r11300980 = r11300977 + r11300979;
        return r11300980;
}
↓
double f(double d1, double d2, double d3) {
        double r11300981 = 32.0;
        double r11300982 = d1;
        double r11300983 = r11300981 * r11300982;
        double r11300984 = d2;
        double r11300985 = 5.0;
        double r11300986 = d3;
        double r11300987 = r11300985 + r11300986;
        double r11300988 = r11300987 * r11300982;
        double r11300989 = fma(r11300982, r11300984, r11300988);
        double r11300990 = r11300983 + r11300989;
        return r11300990;
}

Error

Bits error versus d1

Bits error versus d2

Bits error versus d3

Target

Original0.0
Target0.0
Herbie0.0
\[d1 \cdot \left(\left(37 + d3\right) + d2\right)\]

Derivation

  1. Initial program 0.0

    \[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32\]
  2. Using strategy rm

  3. Applied fma-def0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(d1, d2, \left(\left(d3 + 5\right) \cdot d1\right)\right)} + d1 \cdot 32\]

  4. Final simplification0.0

    \[\leadsto 32 \cdot d1 + \mathsf{fma}\left(d1, d2, \left(\left(5 + d3\right) \cdot d1\right)\right)\]

Reproduce

herbie shell --seed 2019132 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath dist3"

  :herbie-target
  (* d1 (+ (+ 37 d3) d2))

  (+ (+ (* d1 d2) (* (+ d3 5) d1)) (* d1 32)))