Average Error: 0.1 → 0.1
Time: 1.2m
Precision: 64
\[\left(d1 \cdot 3 + d1 \cdot d2\right) + d1 \cdot d3\]
↓
\[\left(d3 + \left(d2 + 3\right)\right) \cdot d1\]
\left(d1 \cdot 3 + d1 \cdot d2\right) + d1 \cdot d3
↓
\left(d3 + \left(d2 + 3\right)\right) \cdot d1
double f(double d1, double d2, double d3) {
        double r57844539 = d1;
        double r57844540 = 3.0;
        double r57844541 = r57844539 * r57844540;
        double r57844542 = d2;
        double r57844543 = r57844539 * r57844542;
        double r57844544 = r57844541 + r57844543;
        double r57844545 = d3;
        double r57844546 = r57844539 * r57844545;
        double r57844547 = r57844544 + r57844546;
        return r57844547;
}
↓
double f(double d1, double d2, double d3) {
        double r57844548 = d3;
        double r57844549 = d2;
        double r57844550 = 3.0;
        double r57844551 = r57844549 + r57844550;
        double r57844552 = r57844548 + r57844551;
        double r57844553 = d1;
        double r57844554 = r57844552 * r57844553;
        return r57844554;
}

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

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

Reproduce

herbie shell --seed 2019120 
(FPCore (d1 d2 d3)
  :name "FastMath test3"

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

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