Average Error: 0.1 → 0.1
Time: 11.2s
Precision: 64
\[\left(d1 \cdot 3 + d1 \cdot d2\right) + d1 \cdot d3\]
↓
\[\left(\left(d3 + d2\right) + 3\right) \cdot d1\]
\left(d1 \cdot 3 + d1 \cdot d2\right) + d1 \cdot d3
↓
\left(\left(d3 + d2\right) + 3\right) \cdot d1
double f(double d1, double d2, double d3) {
        double r4307024 = d1;
        double r4307025 = 3.0;
        double r4307026 = r4307024 * r4307025;
        double r4307027 = d2;
        double r4307028 = r4307024 * r4307027;
        double r4307029 = r4307026 + r4307028;
        double r4307030 = d3;
        double r4307031 = r4307024 * r4307030;
        double r4307032 = r4307029 + r4307031;
        return r4307032;
}
↓
double f(double d1, double d2, double d3) {
        double r4307033 = d3;
        double r4307034 = d2;
        double r4307035 = r4307033 + r4307034;
        double r4307036 = 3.0;
        double r4307037 = r4307035 + r4307036;
        double r4307038 = d1;
        double r4307039 = r4307037 * r4307038;
        return r4307039;
}

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. Taylor expanded around 0 0.1

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

  3. Simplified0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019155 
(FPCore (d1 d2 d3)
  :name "FastMath test3"

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

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