Average Error: 0.3 → 0
Time: 446.0ms
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 r189570 = d;
        double r189571 = 10.0;
        double r189572 = r189570 * r189571;
        double r189573 = 20.0;
        double r189574 = r189570 * r189573;
        double r189575 = r189572 + r189574;
        return r189575;
}
↓
double f(double d) {
        double r189576 = 30.0;
        double r189577 = d;
        double r189578 = r189576 * r189577;
        return r189578;
}

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 2020057 +o rules:numerics
(FPCore (d)
  :name "FastMath test1"
  :precision binary64

  :herbie-target
  (* d 30)

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