Average Error: 0.0 → 0.0
Time: 11.1s
Precision: 64
\[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32\]
↓
\[\left(\left(d3 + 37\right) + d2\right) \cdot d1\]
\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32
↓
\left(\left(d3 + 37\right) + d2\right) \cdot d1
double f(double d1, double d2, double d3) {
        double r8506225 = d1;
        double r8506226 = d2;
        double r8506227 = r8506225 * r8506226;
        double r8506228 = d3;
        double r8506229 = 5.0;
        double r8506230 = r8506228 + r8506229;
        double r8506231 = r8506230 * r8506225;
        double r8506232 = r8506227 + r8506231;
        double r8506233 = 32.0;
        double r8506234 = r8506225 * r8506233;
        double r8506235 = r8506232 + r8506234;
        return r8506235;
}
↓
double f(double d1, double d2, double d3) {
        double r8506236 = d3;
        double r8506237 = 37.0;
        double r8506238 = r8506236 + r8506237;
        double r8506239 = d2;
        double r8506240 = r8506238 + r8506239;
        double r8506241 = d1;
        double r8506242 = r8506240 * r8506241;
        return r8506242;
}

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

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

  3. Taylor expanded around inf 0.0

    \[\leadsto \color{blue}{d2 \cdot d1 + \left(d3 \cdot d1 + 37 \cdot d1\right)}\]

  4. Simplified0.0

    \[\leadsto \color{blue}{\left(d2 + \left(d3 + 37\right)\right) \cdot d1}\]

  5. Final simplification0.0

    \[\leadsto \left(\left(d3 + 37\right) + d2\right) \cdot d1\]

Reproduce

herbie shell --seed 2019134 
(FPCore (d1 d2 d3)
  :name "FastMath dist3"

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

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