Average Error: 0.2 → 0.0
Time: 13.3s
Precision: 64
\[\left(d1 \cdot 10 + d1 \cdot d2\right) + d1 \cdot 20\]
↓
\[\left(d2 + \left(20 + 10\right)\right) \cdot d1\]
\left(d1 \cdot 10 + d1 \cdot d2\right) + d1 \cdot 20
↓
\left(d2 + \left(20 + 10\right)\right) \cdot d1
double f(double d1, double d2) {
        double r8176458 = d1;
        double r8176459 = 10.0;
        double r8176460 = r8176458 * r8176459;
        double r8176461 = d2;
        double r8176462 = r8176458 * r8176461;
        double r8176463 = r8176460 + r8176462;
        double r8176464 = 20.0;
        double r8176465 = r8176458 * r8176464;
        double r8176466 = r8176463 + r8176465;
        return r8176466;
}
↓
double f(double d1, double d2) {
        double r8176467 = d2;
        double r8176468 = 20.0;
        double r8176469 = 10.0;
        double r8176470 = r8176468 + r8176469;
        double r8176471 = r8176467 + r8176470;
        double r8176472 = d1;
        double r8176473 = r8176471 * r8176472;
        return r8176473;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (d1 d2)
  :name "FastMath test2"

  :herbie-target
  (* d1 (+ 30.0 d2))

  (+ (+ (* d1 10.0) (* d1 d2)) (* d1 20.0)))