Average Error: 0.2 → 0.0
Time: 2.0s
Precision: 64
\[\left(d1 \cdot 10 + d1 \cdot d2\right) + d1 \cdot 20\]
↓
\[d1 \cdot \left(d2 + 30\right)\]
\left(d1 \cdot 10 + d1 \cdot d2\right) + d1 \cdot 20
↓
d1 \cdot \left(d2 + 30\right)
double f(double d1, double d2) {
        double r205062 = d1;
        double r205063 = 10.0;
        double r205064 = r205062 * r205063;
        double r205065 = d2;
        double r205066 = r205062 * r205065;
        double r205067 = r205064 + r205066;
        double r205068 = 20.0;
        double r205069 = r205062 * r205068;
        double r205070 = r205067 + r205069;
        return r205070;
}
↓
double f(double d1, double d2) {
        double r205071 = d1;
        double r205072 = d2;
        double r205073 = 30.0;
        double r205074 = r205072 + r205073;
        double r205075 = r205071 * r205074;
        return r205075;
}

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 2020027 
(FPCore (d1 d2)
  :name "FastMath test2"
  :precision binary64

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

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