Average Error: 0.2 → 0.0
Time: 2.0s
Precision: 64
\[\left(d1 \cdot 10 + d1 \cdot d2\right) + d1 \cdot 20\]
↓
\[d1 \cdot \left(10 + \left(d2 + 20\right)\right)\]
\left(d1 \cdot 10 + d1 \cdot d2\right) + d1 \cdot 20
↓
d1 \cdot \left(10 + \left(d2 + 20\right)\right)
double f(double d1, double d2) {
        double r275627 = d1;
        double r275628 = 10.0;
        double r275629 = r275627 * r275628;
        double r275630 = d2;
        double r275631 = r275627 * r275630;
        double r275632 = r275629 + r275631;
        double r275633 = 20.0;
        double r275634 = r275627 * r275633;
        double r275635 = r275632 + r275634;
        return r275635;
}
↓
double f(double d1, double d2) {
        double r275636 = d1;
        double r275637 = 10.0;
        double r275638 = d2;
        double r275639 = 20.0;
        double r275640 = r275638 + r275639;
        double r275641 = r275637 + r275640;
        double r275642 = r275636 * r275641;
        return r275642;
}

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. Using strategy rm

  4. Applied associate-+l+0.0

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

  5. Final simplification0.0

    \[\leadsto d1 \cdot \left(10 + \left(d2 + 20\right)\right)\]

Reproduce

herbie shell --seed 2020083 
(FPCore (d1 d2)
  :name "FastMath test2"
  :precision binary64

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

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