Average Error: 0.1 → 0.1
Time: 17.5s
Precision: 64
\[\left(d1 \cdot 3 + d1 \cdot d2\right) + d1 \cdot d3\]
↓
\[\left(d3 + \left(d2 + 3\right)\right) \cdot d1\]
double f(double d1, double d2, double d3) {
        double r56598962 = d1;
        double r56598963 = 3.0;
        double r56598964 = r56598962 * r56598963;
        double r56598965 = d2;
        double r56598966 = r56598962 * r56598965;
        double r56598967 = r56598964 + r56598966;
        double r56598968 = d3;
        double r56598969 = r56598962 * r56598968;
        double r56598970 = r56598967 + r56598969;
        return r56598970;
}
↓
double f(double d1, double d2, double d3) {
        double r56598971 = d3;
        double r56598972 = d2;
        double r56598973 = 3.0;
        double r56598974 = r56598972 + r56598973;
        double r56598975 = r56598971 + r56598974;
        double r56598976 = d1;
        double r56598977 = r56598975 * r56598976;
        return r56598977;
}


\left(d1 \cdot 3 + d1 \cdot d2\right) + d1 \cdot d3
↓
\left(d3 + \left(d2 + 3\right)\right) \cdot d1

Error

Bits error versus d1

Bits error versus d2

Bits error versus d3

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

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019101 
(FPCore (d1 d2 d3)
  :name "FastMath test3"

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

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