Average Error: 0.2 → 0.0
Time: 1.6s
Precision: 64
\[\left(d1 \cdot 10 + d1 \cdot d2\right) + d1 \cdot 20\]
↓
\[d1 \cdot \left(d2 + 30\right)\]
\left(d1 \cdot 10 + d1 \cdot d2\right) + d1 \cdot 20
↓
d1 \cdot \left(d2 + 30\right)
double f(double d1, double d2) {
        double r238462 = d1;
        double r238463 = 10.0;
        double r238464 = r238462 * r238463;
        double r238465 = d2;
        double r238466 = r238462 * r238465;
        double r238467 = r238464 + r238466;
        double r238468 = 20.0;
        double r238469 = r238462 * r238468;
        double r238470 = r238467 + r238469;
        return r238470;
}
↓
double f(double d1, double d2) {
        double r238471 = d1;
        double r238472 = d2;
        double r238473 = 30.0;
        double r238474 = r238472 + r238473;
        double r238475 = r238471 * r238474;
        return r238475;
}

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. Taylor expanded around 0 0.0

    \[\leadsto d1 \cdot \color{blue}{\left(d2 + 30\right)}\]

  4. Final simplification0.0

    \[\leadsto d1 \cdot \left(d2 + 30\right)\]

Reproduce

herbie shell --seed 2020056 
(FPCore (d1 d2)
  :name "FastMath test2"
  :precision binary64

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

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