Average Error: 0.3 → 0
Time: 459.0ms
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 r153853 = d;
        double r153854 = 10.0;
        double r153855 = r153853 * r153854;
        double r153856 = 20.0;
        double r153857 = r153853 * r153856;
        double r153858 = r153855 + r153857;
        return r153858;
}
↓
double f(double d) {
        double r153859 = 30.0;
        double r153860 = d;
        double r153861 = r153859 * r153860;
        return r153861;
}

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 2020089 +o rules:numerics
(FPCore (d)
  :name "FastMath test1"
  :precision binary64

  :herbie-target
  (* d 30)

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