Average Error: 0.3 → 0
Time: 547.0ms
Precision: 64
\[d \cdot 10 + d \cdot 20\]
↓
\[30 \cdot d\]
d \cdot 10 + d \cdot 20
↓
30 \cdot d
double f(double d) {
        double r123707 = d;
        double r123708 = 10.0;
        double r123709 = r123707 * r123708;
        double r123710 = 20.0;
        double r123711 = r123707 * r123710;
        double r123712 = r123709 + r123711;
        return r123712;
}
↓
double f(double d) {
        double r123713 = 30.0;
        double r123714 = d;
        double r123715 = r123713 * r123714;
        return r123715;
}

Error

Bits error versus d

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.3
Target0
Herbie0
\[d \cdot 30\]

Derivation

  1. Initial program 0.3

    \[d \cdot 10 + d \cdot 20\]

  2. Simplified0.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(d, 10, d \cdot 20\right)}\]

  3. Taylor expanded around 0 0

    \[\leadsto \color{blue}{30 \cdot d}\]

  4. Final simplification0

    \[\leadsto 30 \cdot d\]

Reproduce

herbie shell --seed 2020035 +o rules:numerics
(FPCore (d)
  :name "FastMath test1"
  :precision binary64

  :herbie-target
  (* d 30)

  (+ (* d 10) (* d 20)))