Average Error: 0.0 → 0.0
Time: 6.5s
Precision: 64
\[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32\]
↓
\[d1 \cdot \left(\left(\left(d3 + 5\right) + 32\right) + d2\right)\]
\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32
↓
d1 \cdot \left(\left(\left(d3 + 5\right) + 32\right) + d2\right)
double f(double d1, double d2, double d3) {
        double r189477 = d1;
        double r189478 = d2;
        double r189479 = r189477 * r189478;
        double r189480 = d3;
        double r189481 = 5.0;
        double r189482 = r189480 + r189481;
        double r189483 = r189482 * r189477;
        double r189484 = r189479 + r189483;
        double r189485 = 32.0;
        double r189486 = r189477 * r189485;
        double r189487 = r189484 + r189486;
        return r189487;
}
↓
double f(double d1, double d2, double d3) {
        double r189488 = d1;
        double r189489 = d3;
        double r189490 = 5.0;
        double r189491 = r189489 + r189490;
        double r189492 = 32.0;
        double r189493 = r189491 + r189492;
        double r189494 = d2;
        double r189495 = r189493 + r189494;
        double r189496 = r189488 * r189495;
        return r189496;
}

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

Original0.0
Target0.0
Herbie0.0
\[d1 \cdot \left(\left(37 + d3\right) + d2\right)\]

Derivation

  1. Initial program 0.0

    \[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32\]

  2. Simplified0.0

    \[\leadsto \color{blue}{d1 \cdot \left(\left(\left(d3 + 5\right) + 32\right) + d2\right)}\]

  3. Final simplification0.0

    \[\leadsto d1 \cdot \left(\left(\left(d3 + 5\right) + 32\right) + d2\right)\]

Reproduce

herbie shell --seed 2019325 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath dist3"
  :precision binary64

  :herbie-target
  (* d1 (+ (+ 37 d3) d2))

  (+ (+ (* d1 d2) (* (+ d3 5) d1)) (* d1 32)))