Average Error: 0.1 → 0.1
Time: 7.4s
Precision: 64
\[\left(d1 \cdot 3 + d1 \cdot d2\right) + d1 \cdot d3\]
↓
\[d1 \cdot \left(d3 + \left(3 + d2\right)\right)\]
\left(d1 \cdot 3 + d1 \cdot d2\right) + d1 \cdot d3
↓
d1 \cdot \left(d3 + \left(3 + d2\right)\right)
double f(double d1, double d2, double d3) {
        double r344881 = d1;
        double r344882 = 3.0;
        double r344883 = r344881 * r344882;
        double r344884 = d2;
        double r344885 = r344881 * r344884;
        double r344886 = r344883 + r344885;
        double r344887 = d3;
        double r344888 = r344881 * r344887;
        double r344889 = r344886 + r344888;
        return r344889;
}
↓
double f(double d1, double d2, double d3) {
        double r344890 = d1;
        double r344891 = d3;
        double r344892 = 3.0;
        double r344893 = d2;
        double r344894 = r344892 + r344893;
        double r344895 = r344891 + r344894;
        double r344896 = r344890 * r344895;
        return r344896;
}

Error

Bits error versus d1

Bits error versus d2

Bits error versus d3

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0.1
Herbie0.1
\[d1 \cdot \left(\left(3 + d2\right) + d3\right)\]

Derivation

  1. Initial program 0.1

    \[\left(d1 \cdot 3 + d1 \cdot d2\right) + d1 \cdot d3\]

  2. Simplified0.1

    \[\leadsto \color{blue}{d1 \cdot \left(d3 + \left(3 + d2\right)\right)}\]

  3. Final simplification0.1

    \[\leadsto d1 \cdot \left(d3 + \left(3 + d2\right)\right)\]

Reproduce

herbie shell --seed 2020045 
(FPCore (d1 d2 d3)
  :name "FastMath test3"
  :precision binary64

  :herbie-target
  (* d1 (+ (+ 3 d2) d3))

  (+ (+ (* d1 3) (* d1 d2)) (* d1 d3)))