Average Error: 0.1 → 0.1
Time: 4.0s
Precision: 64
\[\left(d1 \cdot 3 + d1 \cdot d2\right) + d1 \cdot d3\]
↓
\[d1 \cdot \left(\left(3 + d2\right) + d3\right)\]
\left(d1 \cdot 3 + d1 \cdot d2\right) + d1 \cdot d3
↓
d1 \cdot \left(\left(3 + d2\right) + d3\right)
double f(double d1, double d2, double d3) {
        double r226853 = d1;
        double r226854 = 3.0;
        double r226855 = r226853 * r226854;
        double r226856 = d2;
        double r226857 = r226853 * r226856;
        double r226858 = r226855 + r226857;
        double r226859 = d3;
        double r226860 = r226853 * r226859;
        double r226861 = r226858 + r226860;
        return r226861;
}
↓
double f(double d1, double d2, double d3) {
        double r226862 = d1;
        double r226863 = 3.0;
        double r226864 = d2;
        double r226865 = r226863 + r226864;
        double r226866 = d3;
        double r226867 = r226865 + r226866;
        double r226868 = r226862 * r226867;
        return r226868;
}

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

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2020033 
(FPCore (d1 d2 d3)
  :name "FastMath test3"
  :precision binary64

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

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