Average Error: 0.0 → 0.0
Time: 19.7s
Precision: 64
\[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32\]
↓
\[32 \cdot d1 + \left(\left(d3 + d2\right) + 5\right) \cdot d1\]
\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32
↓
32 \cdot d1 + \left(\left(d3 + d2\right) + 5\right) \cdot d1
double f(double d1, double d2, double d3) {
        double r9403407 = d1;
        double r9403408 = d2;
        double r9403409 = r9403407 * r9403408;
        double r9403410 = d3;
        double r9403411 = 5.0;
        double r9403412 = r9403410 + r9403411;
        double r9403413 = r9403412 * r9403407;
        double r9403414 = r9403409 + r9403413;
        double r9403415 = 32.0;
        double r9403416 = r9403407 * r9403415;
        double r9403417 = r9403414 + r9403416;
        return r9403417;
}
↓
double f(double d1, double d2, double d3) {
        double r9403418 = 32.0;
        double r9403419 = d1;
        double r9403420 = r9403418 * r9403419;
        double r9403421 = d3;
        double r9403422 = d2;
        double r9403423 = r9403421 + r9403422;
        double r9403424 = 5.0;
        double r9403425 = r9403423 + r9403424;
        double r9403426 = r9403425 * r9403419;
        double r9403427 = r9403420 + r9403426;
        return r9403427;
}

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. Taylor expanded around 0 0.0

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

  3. Simplified0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019200 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath dist3"

  :herbie-target
  (* d1 (+ (+ 37.0 d3) d2))

  (+ (+ (* d1 d2) (* (+ d3 5.0) d1)) (* d1 32.0)))