Average Error: 0.1 → 0.1
Time: 35.0s
Precision: 64
\[\left(d1 \cdot 3 + d1 \cdot d2\right) + d1 \cdot d3\]
↓
\[\left(d2 + \left(d3 + 3\right)\right) \cdot d1\]
\left(d1 \cdot 3 + d1 \cdot d2\right) + d1 \cdot d3
↓
\left(d2 + \left(d3 + 3\right)\right) \cdot d1
double f(double d1, double d2, double d3) {
        double r34278781 = d1;
        double r34278782 = 3.0;
        double r34278783 = r34278781 * r34278782;
        double r34278784 = d2;
        double r34278785 = r34278781 * r34278784;
        double r34278786 = r34278783 + r34278785;
        double r34278787 = d3;
        double r34278788 = r34278781 * r34278787;
        double r34278789 = r34278786 + r34278788;
        return r34278789;
}
↓
double f(double d1, double d2, double d3) {
        double r34278790 = d2;
        double r34278791 = d3;
        double r34278792 = 3.0;
        double r34278793 = r34278791 + r34278792;
        double r34278794 = r34278790 + r34278793;
        double r34278795 = d1;
        double r34278796 = r34278794 * r34278795;
        return r34278796;
}

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

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019112 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath test3"

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

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