Average Error: 0.1 → 0.1
Time: 3.8s
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 r266024 = d1;
        double r266025 = 3.0;
        double r266026 = r266024 * r266025;
        double r266027 = d2;
        double r266028 = r266024 * r266027;
        double r266029 = r266026 + r266028;
        double r266030 = d3;
        double r266031 = r266024 * r266030;
        double r266032 = r266029 + r266031;
        return r266032;
}
↓
double f(double d1, double d2, double d3) {
        double r266033 = d1;
        double r266034 = 3.0;
        double r266035 = d2;
        double r266036 = r266034 + r266035;
        double r266037 = d3;
        double r266038 = r266036 + r266037;
        double r266039 = r266033 * r266038;
        return r266039;
}

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 2020001 
(FPCore (d1 d2 d3)
  :name "FastMath test3"
  :precision binary64

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

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