Average Error: 0.1 → 0.1
Time: 4.1s
Precision: 64
\[\left(d1 \cdot 3 + d1 \cdot d2\right) + d1 \cdot d3\]
↓
\[d1 \cdot \left(\left(3 + d2\right) + d3\right)\]
\left(d1 \cdot 3 + d1 \cdot d2\right) + d1 \cdot d3
↓
d1 \cdot \left(\left(3 + d2\right) + d3\right)
double f(double d1, double d2, double d3) {
        double r373070 = d1;
        double r373071 = 3.0;
        double r373072 = r373070 * r373071;
        double r373073 = d2;
        double r373074 = r373070 * r373073;
        double r373075 = r373072 + r373074;
        double r373076 = d3;
        double r373077 = r373070 * r373076;
        double r373078 = r373075 + r373077;
        return r373078;
}
↓
double f(double d1, double d2, double d3) {
        double r373079 = d1;
        double r373080 = 3.0;
        double r373081 = d2;
        double r373082 = r373080 + r373081;
        double r373083 = d3;
        double r373084 = r373082 + r373083;
        double r373085 = r373079 * r373084;
        return r373085;
}

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

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2020065 
(FPCore (d1 d2 d3)
  :name "FastMath test3"
  :precision binary64

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

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