Average Error: 0.1 → 0.1
Time: 4.9s
Precision: 64
\[\left(d1 \cdot 3 + d1 \cdot d2\right) + d1 \cdot d3\]
↓
\[d1 \cdot \left(3 + \left(d2 + d3\right)\right)\]
\left(d1 \cdot 3 + d1 \cdot d2\right) + d1 \cdot d3
↓
d1 \cdot \left(3 + \left(d2 + d3\right)\right)
double f(double d1, double d2, double d3) {
        double r191839 = d1;
        double r191840 = 3.0;
        double r191841 = r191839 * r191840;
        double r191842 = d2;
        double r191843 = r191839 * r191842;
        double r191844 = r191841 + r191843;
        double r191845 = d3;
        double r191846 = r191839 * r191845;
        double r191847 = r191844 + r191846;
        return r191847;
}
↓
double f(double d1, double d2, double d3) {
        double r191848 = d1;
        double r191849 = 3.0;
        double r191850 = d2;
        double r191851 = d3;
        double r191852 = r191850 + r191851;
        double r191853 = r191849 + r191852;
        double r191854 = r191848 * r191853;
        return r191854;
}

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. Using strategy rm

  4. Applied associate-+l+0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020049 
(FPCore (d1 d2 d3)
  :name "FastMath test3"
  :precision binary64

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

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