Average Error: 0.1 → 0.1
Time: 14.7s
Precision: 64
\[\left(d1 \cdot 3 + d1 \cdot d2\right) + d1 \cdot d3\]
↓
\[d1 \cdot \left(d3 + \left(3 + d2\right)\right)\]
\left(d1 \cdot 3 + d1 \cdot d2\right) + d1 \cdot d3
↓
d1 \cdot \left(d3 + \left(3 + d2\right)\right)
double f(double d1, double d2, double d3) {
        double r238413 = d1;
        double r238414 = 3.0;
        double r238415 = r238413 * r238414;
        double r238416 = d2;
        double r238417 = r238413 * r238416;
        double r238418 = r238415 + r238417;
        double r238419 = d3;
        double r238420 = r238413 * r238419;
        double r238421 = r238418 + r238420;
        return r238421;
}
↓
double f(double d1, double d2, double d3) {
        double r238422 = d1;
        double r238423 = d3;
        double r238424 = 3.0;
        double r238425 = d2;
        double r238426 = r238424 + r238425;
        double r238427 = r238423 + r238426;
        double r238428 = r238422 * r238427;
        return r238428;
}

Error

Bits error versus d1

Bits error versus d2

Bits error versus d3

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0.1
Herbie0.1
\[d1 \cdot \left(\left(3 + d2\right) + d3\right)\]

Derivation

  1. Initial program 0.1

    \[\left(d1 \cdot 3 + d1 \cdot d2\right) + d1 \cdot d3\]

  2. Simplified0.1

    \[\leadsto \color{blue}{d1 \cdot \left(d3 + \left(3 + d2\right)\right)}\]

  3. Final simplification0.1

    \[\leadsto d1 \cdot \left(d3 + \left(3 + d2\right)\right)\]

Reproduce

herbie shell --seed 2019198 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath test3"

  :herbie-target
  (* d1 (+ (+ 3.0 d2) d3))

  (+ (+ (* d1 3.0) (* d1 d2)) (* d1 d3)))