Average Error: 0.2 → 0.0
Time: 11.0s
Precision: 64
\[\left(d1 \cdot 10 + d1 \cdot d2\right) + d1 \cdot 20\]
↓
\[\left(d2 + 30\right) \cdot d1\]
\left(d1 \cdot 10 + d1 \cdot d2\right) + d1 \cdot 20
↓
\left(d2 + 30\right) \cdot d1
double f(double d1, double d2) {
        double r180322 = d1;
        double r180323 = 10.0;
        double r180324 = r180322 * r180323;
        double r180325 = d2;
        double r180326 = r180322 * r180325;
        double r180327 = r180324 + r180326;
        double r180328 = 20.0;
        double r180329 = r180322 * r180328;
        double r180330 = r180327 + r180329;
        return r180330;
}
↓
double f(double d1, double d2) {
        double r180331 = d2;
        double r180332 = 30.0;
        double r180333 = r180331 + r180332;
        double r180334 = d1;
        double r180335 = r180333 * r180334;
        return r180335;
}

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

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

  3. Taylor expanded around 0 0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019323 
(FPCore (d1 d2)
  :name "FastMath test2"
  :precision binary64

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

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