Average Error: 0.2 → 0.0
Time: 15.4s
Precision: 64
\[\left(d1 \cdot 10 + d1 \cdot d2\right) + d1 \cdot 20\]
↓
\[d1 \cdot \left(d2 + 30\right)\]
\left(d1 \cdot 10 + d1 \cdot d2\right) + d1 \cdot 20
↓
d1 \cdot \left(d2 + 30\right)
double f(double d1, double d2) {
        double r224901 = d1;
        double r224902 = 10.0;
        double r224903 = r224901 * r224902;
        double r224904 = d2;
        double r224905 = r224901 * r224904;
        double r224906 = r224903 + r224905;
        double r224907 = 20.0;
        double r224908 = r224901 * r224907;
        double r224909 = r224906 + r224908;
        return r224909;
}
↓
double f(double d1, double d2) {
        double r224910 = d1;
        double r224911 = d2;
        double r224912 = 30.0;
        double r224913 = r224911 + r224912;
        double r224914 = r224910 * r224913;
        return r224914;
}

Error

Bits error versus d1

Bits error versus d2

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.0
Herbie0.0
\[d1 \cdot \left(30 + d2\right)\]

Derivation

  1. Initial program 0.2

    \[\left(d1 \cdot 10 + d1 \cdot d2\right) + d1 \cdot 20\]

  2. Simplified0.0

    \[\leadsto \color{blue}{d1 \cdot \left(\left(10 + d2\right) + 20\right)}\]

  3. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{30 \cdot d1 + d1 \cdot d2}\]

  4. Simplified0.0

    \[\leadsto \color{blue}{d1 \cdot \left(d2 + 30\right)}\]

  5. Final simplification0.0

    \[\leadsto d1 \cdot \left(d2 + 30\right)\]

Reproduce

herbie shell --seed 2019326 
(FPCore (d1 d2)
  :name "FastMath test2"
  :precision binary64

  :herbie-target
  (* d1 (+ 30 d2))

  (+ (+ (* d1 10) (* d1 d2)) (* d1 20)))