Average Error: 0.2 → 0.0
Time: 4.1s
Precision: 64
\[\left(d1 \cdot 10 + d1 \cdot d2\right) + d1 \cdot 20\]
↓
\[d1 \cdot \left(20 + \left(10 + d2\right)\right)\]
\left(d1 \cdot 10 + d1 \cdot d2\right) + d1 \cdot 20
↓
d1 \cdot \left(20 + \left(10 + d2\right)\right)
double f(double d1, double d2) {
        double r199776 = d1;
        double r199777 = 10.0;
        double r199778 = r199776 * r199777;
        double r199779 = d2;
        double r199780 = r199776 * r199779;
        double r199781 = r199778 + r199780;
        double r199782 = 20.0;
        double r199783 = r199776 * r199782;
        double r199784 = r199781 + r199783;
        return r199784;
}
↓
double f(double d1, double d2) {
        double r199785 = d1;
        double r199786 = 20.0;
        double r199787 = 10.0;
        double r199788 = d2;
        double r199789 = r199787 + r199788;
        double r199790 = r199786 + r199789;
        double r199791 = r199785 * r199790;
        return r199791;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020042 +o rules:numerics
(FPCore (d1 d2)
  :name "FastMath test2"
  :precision binary64

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

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