Average Error: 0.1 → 0.1
Time: 12.4s
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 r112705 = d1;
        double r112706 = 3.0;
        double r112707 = r112705 * r112706;
        double r112708 = d2;
        double r112709 = r112705 * r112708;
        double r112710 = r112707 + r112709;
        double r112711 = d3;
        double r112712 = r112705 * r112711;
        double r112713 = r112710 + r112712;
        return r112713;
}
↓
double f(double d1, double d2, double d3) {
        double r112714 = d2;
        double r112715 = d3;
        double r112716 = 3.0;
        double r112717 = r112715 + r112716;
        double r112718 = r112714 + r112717;
        double r112719 = d1;
        double r112720 = r112718 * r112719;
        return r112720;
}

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 2019195 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath test3"

  :herbie-target
  (* d1 (+ (+ 3.0 d2) d3))

  (+ (+ (* d1 3.0) (* d1 d2)) (* d1 d3)))