Average Error: 0.1 → 0.1
Time: 14.2s
Precision: 64
\[\left(d1 \cdot 3 + d1 \cdot d2\right) + d1 \cdot d3\]
↓
\[\left(\left(3 + d3\right) + d2\right) \cdot d1\]
\left(d1 \cdot 3 + d1 \cdot d2\right) + d1 \cdot d3
↓
\left(\left(3 + d3\right) + d2\right) \cdot d1
double f(double d1, double d2, double d3) {
        double r8933152 = d1;
        double r8933153 = 3.0;
        double r8933154 = r8933152 * r8933153;
        double r8933155 = d2;
        double r8933156 = r8933152 * r8933155;
        double r8933157 = r8933154 + r8933156;
        double r8933158 = d3;
        double r8933159 = r8933152 * r8933158;
        double r8933160 = r8933157 + r8933159;
        return r8933160;
}
↓
double f(double d1, double d2, double d3) {
        double r8933161 = 3.0;
        double r8933162 = d3;
        double r8933163 = r8933161 + r8933162;
        double r8933164 = d2;
        double r8933165 = r8933163 + r8933164;
        double r8933166 = d1;
        double r8933167 = r8933165 * r8933166;
        return r8933167;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2019152 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath test3"

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

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