Average Error: 0.1 → 0.1
Time: 10.6s
Precision: 64
\[\left(d1 \cdot 3 + d1 \cdot d2\right) + d1 \cdot d3\]
↓
\[\left(\left(d2 + 3\right) + d3\right) \cdot d1\]
\left(d1 \cdot 3 + d1 \cdot d2\right) + d1 \cdot d3
↓
\left(\left(d2 + 3\right) + d3\right) \cdot d1
double f(double d1, double d2, double d3) {
        double r4705537 = d1;
        double r4705538 = 3.0;
        double r4705539 = r4705537 * r4705538;
        double r4705540 = d2;
        double r4705541 = r4705537 * r4705540;
        double r4705542 = r4705539 + r4705541;
        double r4705543 = d3;
        double r4705544 = r4705537 * r4705543;
        double r4705545 = r4705542 + r4705544;
        return r4705545;
}
↓
double f(double d1, double d2, double d3) {
        double r4705546 = d2;
        double r4705547 = 3.0;
        double r4705548 = r4705546 + r4705547;
        double r4705549 = d3;
        double r4705550 = r4705548 + r4705549;
        double r4705551 = d1;
        double r4705552 = r4705550 * r4705551;
        return r4705552;
}

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

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

  3. Taylor expanded around -inf 0.1

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

  4. Simplified0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019139 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath test3"

  :herbie-target
  (* d1 (+ (+ 3 d2) d3))

  (+ (+ (* d1 3) (* d1 d2)) (* d1 d3)))