Average Error: 0.2 → 0.0
Time: 12.3s
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 r161780 = d1;
        double r161781 = 10.0;
        double r161782 = r161780 * r161781;
        double r161783 = d2;
        double r161784 = r161780 * r161783;
        double r161785 = r161782 + r161784;
        double r161786 = 20.0;
        double r161787 = r161780 * r161786;
        double r161788 = r161785 + r161787;
        return r161788;
}
↓
double f(double d1, double d2) {
        double r161789 = d1;
        double r161790 = d2;
        double r161791 = 30.0;
        double r161792 = r161790 + r161791;
        double r161793 = r161789 * r161792;
        return r161793;
}

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

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

  3. Taylor expanded around 0 0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(FPCore (d1 d2)
  :name "FastMath test2"
  :precision binary64

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

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