Average Error: 0.2 → 0.0
Time: 11.1s
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 r228706 = d1;
        double r228707 = 10.0;
        double r228708 = r228706 * r228707;
        double r228709 = d2;
        double r228710 = r228706 * r228709;
        double r228711 = r228708 + r228710;
        double r228712 = 20.0;
        double r228713 = r228706 * r228712;
        double r228714 = r228711 + r228713;
        return r228714;
}
↓
double f(double d1, double d2) {
        double r228715 = d1;
        double r228716 = d2;
        double r228717 = 30.0;
        double r228718 = r228716 + r228717;
        double r228719 = r228715 * r228718;
        return r228719;
}

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

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

  4. Final simplification0.0

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

Reproduce

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

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

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